Regularization for uniform spatial resolution properties in penalized-likelihood image reconstruction

Performance study of a 360° CZT camera for monitoring 177Lu-PSMA treatment

BACKGROUND

The aim of this study was to investigate the quantification performance of a 360° CZT camera for 177Lu-based treatment monitoring.

METHODS

Three phantoms with known 177Lu activity concentrations were acquired: (1) a uniform cylindrical phantom for calibration, (2) a NEMA IEC body phantom for analysis of different-sized spheres to optimise quantification parameters and (3) a phantom containing two large vials simulating organs at risk for tests. Four sets of reconstruction parameters were tested: (1) Scatter, (2) Scatter and Point Spread Function Recovery (PSFR), (3) PSFR only and (4) Penalised likelihood option and Scatter, varying the number of updates (iterations × subsets) with CT-based attenuation correction only. For each, activity concentration (ARC) and contrast recovery coefficients (CRC) were estimated as well as root mean square. Visualisation and quantification parameters were applied to reconstructed patient image data.

RESULTS

Optimised quantification parameters were determined to be: CT-based attenuation correction, scatter correction, 12 iterations, 8 subsets and no filter. ARC, CRC and RMS results were dependant on the methodology used for calculations. Two different reconstruction parameters were recommended for visualisation and for quantification. 3D whole-body SPECT images were acquired and reconstructed for 177Lu-PSMA patients in 2-3 times faster than the time taken for a conventional gamma camera.

CONCLUSION

Quantification of whole-body 3D images of patients treated with 177Lu-PSMA is feasible and an optimised set of parameters has been determined. This camera greatly reduces procedure time for whole-body SPECT.

Inter-phase 4D Cardiac MRI Registration with a Motion Prior Derived from CTA

OBJECTIVE

Registration between phases in 4D cardiac MRI is essential for reconstructing high-quality images and appreciating the dynamics. Complex motion and limited image quality make it challenging to design regularization functionals. We propose to introduce a motion representation model (MRM) into a registration network to impose customized, site-specific, and spatially variant prior for cardiac motion.

METHODS

We propose a novel approach to regularize deep registration with a DVF representation model using CTA. In the form of a convolutional auto-encoder, the MRM was trained to capture the spatially variant pattern of feasible DVF Jacobian. The CTA-derived MRM was then incorporated into an unsupervised network to facilitate MRI registration. In the experiment, 10 CTAs were used to derive the MRM. The method was tested on 10 0.35T scans in long-axis view with manual segmentation and 15 3T scans in short-axis view with tagging-based landmarks.

RESULTS

Introducing the MRM improved registration accuracy and achieved 2.23, 7.21, and 4.42mm 80% Hausdorff distance on left ventricle, right ventricle, and pulmonary artery, respectively, and 2.23mm landmark registration error. The results were comparable to carefully tuned SimpleElastix, but reduced the registration time from 40 to 0.02s. The MRM presented good robustness to different DVF sample generation methods.

CONCLUSION

The model enjoys high accuracy as meticulously tuned optimization model and the efficiency of deep networks.

SIGNIFICANCE

The method enables model to go beyond the quality limitation of MRI. The robustness to training DVF generation scheme makes the method attractive to adapting to the available data and software resources in various clinics.

Artificial Intelligence-Based Image Enhancement in PET Imaging: Noise Reduction and Resolution Enhancement

High noise and low spatial resolution are two key confounding factors that limit the qualitative and quantitative accuracy of PET images. Artificial intelligence models for image denoising and deblurring are becoming increasingly popular for the postreconstruction enhancement of PET images. We present a detailed review of recent efforts for artificial intelligence-based PET image enhancement with a focus on network architectures, data types, loss functions, and evaluation metrics. We also highlight emerging areas in this field that are quickly gaining popularity, identify barriers to large-scale adoption of artificial intelligence models for PET image enhancement, and discuss future directions.

Theory, method, and test tools for determination of 3D MTF characteristics in cone-beam CT

PURPOSE

The modulation transfer function (MTF) is widely used as an objective metric of spatial resolution of medical imaging systems. Despite advances in capability for three-dimensional (3D) isotropic spatial resolution in computed tomography (CT) and cone-beam CT (CBCT), MTF evaluation for such systems is typically reported only in the axial plane, and practical methodology for assessment of fully 3D spatial resolution characteristics is lacking. This work reviews fundamental theoretical relationships of two-dimensional (2D) and 3D spread functions and reports practical methods and test tools for analysis of 3D MTF in CBCT.

METHODS

Fundamental aspects of 2D and 3D MTF measurement are reviewed within a common notational framework, and three MTF test tools with analysis code are reported and made available online (https://istar.jhu.edu/downloads/): (a) a multi-wire tool for measurement of the axial plane MTF [denoted as M T F ( f r ; φ = 0 ∘ ) , where φ is the measurement angle out of the axial plane] as a function of position in the axial plane; (b) a wedge tool for measurement of the MTF in any direction in the 3D Fourier domain [e.g.,  φ  = 45°, denoted as M T F ( f r ; φ = 45 ∘ ) ]; and (c) a sphere tool for measurement of the MTF in any or all directions in the 3D Fourier domain. Experiments were performed on a mobile C-arm with CBCT capability, showing that M T F ( f r ; φ = 45 ∘ ) yields an informative one-dimensional (1D) representation of the overall 3D spatial resolution characteristics, capturing important characteristics of the 3D MTF that might be missed in conventional analysis. The effects of anisotropic filters and detector readout mode were investigated, and the extent to which a system can be said to provide "isotropic" resolution was evaluated by quantitative comparison of MTF at various φ .

RESULTS

All three test tools provided consistent measurement of M T F ( f r ; φ = 0 ∘ ) , and the wedge and sphere tools demonstrated how measurement of the MTF in directions outside the axial plane ( φ > 0 ∘ ) can reveal spatial resolution characteristics to which conventional axial MTF measurement is blind. The wedge tool was shown to reduce statistical measurement error compared to the sphere tool due to improved sampling, and the sphere tool was shown to provide a basis for measurement of the MTF in any or all directions (outside the null cone) from a single scan. The C-arm system exhibited non-isotropic spatial resolution with conventional non-isotropic 1D apodization filters (i.e., frequency cutoff filters) - which is common in CBCT - and implementation of isotropic 2D apodization yielded quantifiably isotropic MTF. Asymmetric pixel binning modes were similarly shown to impart non-isotropic effects on the 3D MTF, and the overall 3D MTF characteristics were evident in each case with a single, 1D measurement of the 1D M T F ( f r ; φ = 45 ∘ ).

CONCLUSION

Three test tools and corresponding MTF analysis methods were presented within a consistent framework for analysis of 3D spatial resolution characteristics in a manner amenable to routine, practical measurements. Experiments on a CBCT C-arm validated many intuitive aspects of 3D spatial resolution and quantified the extent to which a CBCT system may be considered to have isotropic resolution. Measurement of M T F ( f r ; φ = 45 ∘ ) provided a practical 1D measure of the underlying 3D MTF characteristics and is extensible to other CT or CBCT systems offering high, isotropic spatial resolution.

ADAPTIVE-NET: deep computed tomography reconstruction network with analytical domain transformation knowledge

Background

Recently, the paradigm of computed tomography (CT) reconstruction has shifted as the deep learning technique evolves. In this study, we proposed a new convolutional neural network (called ADAPTIVE-NET) to perform CT image reconstruction directly from a sinogram by integrating the analytical domain transformation knowledge.

Methods

In the proposed ADAPTIVE-NET, a specific network layer with constant weights was customized to transform the sinogram onto the CT image domain via analytical back-projection. With this new framework, feature extractions were performed simultaneously on both the sinogram domain and the CT image domain. The Mayo low dose CT (LDCT) data was used to validate the new network. In particular, the new network was compared with the previously proposed residual encoder-decoder (RED)-CNN network. For each network, the mean square error (MSE) loss with and without VGG-based perceptual loss was compared. Furthermore, to evaluate the image quality with certain metrics, the noise correlation was quantified via the noise power spectrum (NPS) on the reconstructed LDCT for each method.

Results

CT images that have clinically relevant dimensions of 512×512 can be easily reconstructed from a sinogram on a single graphics processing unit (GPU) with moderate memory size (e.g., 11 GB) by ADAPTIVE-NET. With the same MSE loss function, the new network is able to generate better results than the RED-CNN. Moreover, the new network is able to reconstruct natural looking CT images with enhanced image quality if jointly using the VGG loss.

Conclusions

The newly proposed end-to-end supervised ADAPTIVE-NET is able to reconstruct high-quality LDCT images directly from a sinogram.

Fast submillimeter diffusion MRI using gSlider-SMS and SNR-enhancing joint reconstruction

PURPOSE

We evaluate a new approach for achieving diffusion MRI data with high spatial resolution, large volume coverage, and fast acquisition speed.

THEORY AND METHODS

A recent method called gSlider-SMS enables whole-brain submillimeter diffusion MRI with high signal-to-noise ratio (SNR) efficiency. However, despite the efficient acquisition, the resulting images can still suffer from low SNR due to the small size of the imaging voxels. This work proposes to mitigate the SNR problem by combining gSlider-SMS with a regularized SNR-enhancing reconstruction approach.

RESULTS

Illustrative results show that, from gSlider-SMS data acquired over a span of only 25 minutes on a 3T scanner, the proposed method is able to produce 71 MRI images (64 diffusion encoding orientations with b = 1500 s/ mm 2 , and 7 images without diffusion weighting) of the entire in vivo human brain with nominal 0.66 mm spatial resolution. Using data acquired from 75 minutes of acquisition as a gold standard reference, we demonstrate that the proposed SNR-enhancement procedure leads to substantial improvements in estimated diffusion parameters compared to conventional gSlider reconstruction. Results also demonstrate that the proposed method has advantages relative to denoising methods based on low-rank matrix modeling. A theoretical analysis of the trade-off between spatial resolution and SNR suggests that the proposed approach has high efficiency.

CONCLUSIONS

The combination of gSlider-SMS with advanced regularized reconstruction enables high-resolution quantitative diffusion MRI from a relatively fast acquisition.

Benefits of Using a Spatially-Variant Penalty Strength With Anatomical Priors in PET Reconstruction

In this study, we explore the use of a spatially-variant penalty strength in penalized image reconstruction using anatomical priors to reduce the dependence of lesion contrast on surrounding activity and lesion location. This work builds on a previous method to make the local perturbation response (LPR) approximately spatially invariant. While the dependence of lesion contrast on the local properties introduced by the anatomical penalty is intentional, the method aims to reduce the influence from surroundings lying along the lines of response (LORs) but not in the penalty neighborhood structure. The method is evaluated using simulated data, assuming that the anatomical information is absent or well-aligned with the corresponding activity images. Since the parallel level sets (PLS) penalty is convex and has shown promising results in the literature, it is chosen as the representative anatomical penalty and incorporated into the previously proposed preconditioned algorithm (L-BFGS-B-PC) for achieving good image quality and fast convergence rate. A 2D disc phantom with a feature at the center and a 3D XCAT thorax phantom with lesions inserted in different slices are used to study how surrounding activity and lesion location affect the visual appearance and quantitative consistency. A bias and noise analysis is also performed with the 2D disc phantom. The consistency of the algorithm convergence rate with respect to different data noise and background levels is also investigated using the XCAT phantom. Finally, an example of reconstruction for a patient dataset with inserted pseudo lesions is used as a demonstration in a clinical context. We show that applying the spatially-variant penalization with PLS can reduce the dependence of the lesion contrast on the surrounding activity and lesion location. It does not affect the bias and noise trade-off curves for matched local resolution. Moreover, when using the proposed penalization, significant improvement in algorithm convergence rate and convergence consistency is observed.

Patient-specific reconstruction of volumetric computed tomography images from a single projection view via deep learning

Tomographic imaging via penetrating waves generates cross-sectional views of the internal anatomy of a living subject. For artefact-free volumetric imaging, projection views from a large number of angular positions are required. Here, we show that a deep-learning model trained to map projection radiographs of a patient to the corresponding 3D anatomy can subsequently generate volumetric tomographic X-ray images of the patient from a single projection view. We demonstrate the feasibility of the approach with upper-abdomen, lung, and head-and-neck computed tomography scans from three patients. Volumetric reconstruction via deep learning could be useful in image-guided interventional procedures such as radiation therapy and needle biopsy, and might help simplify the hardware of tomographic imaging systems.

Known-component 3D image reconstruction for improved intraoperative imaging in spine surgery: A clinical pilot study

PURPOSE

Intraoperative imaging plays an increased role in support of surgical guidance and quality assurance for interventional approaches. However, image quality sufficient to detect complications and provide quantitative assessment of the surgical product is often confounded by image noise and artifacts. In this work, we translated a three-dimensional model-based image reconstruction (referred to as "Known-Component Reconstruction," KC-Recon) for the first time to clinical studies with the aim of resolving both limitations.

METHODS

KC-Recon builds upon a penalized weighted least-squares (PWLS) method by incorporating models of surgical instrumentation ("known components") within a joint image registration-reconstruction process to improve image quality. Under IRB approval, a clinical pilot study was conducted with 17 spine surgery patients imaged under informed consent using the O-arm cone-beam CT system (Medtronic, Littleton MA) before and after spinal instrumentation. Volumetric images were generated for each patient using KC-Recon in comparison to conventional filtered backprojection (FBP). Imaging performance prior to instrumentation ("preinstrumentation") was evaluated in terms of soft-tissue contrast-to-noise ratio (CNR) and spatial resolution. The quality of images obtained after the instrumentation ("postinstrumentation") was assessed by quantifying the magnitude of metal artifacts (blooming and streaks) arising from pedicle screws. The potential low-dose advantages of the algorithm were tested by simulating low-dose data (down to one-tenth of the dose of standard protocols) from images acquired at normal dose.

RESULTS

Preinstrumentation images (at normal clinical dose and matched resolution) exhibited an average 24.0% increase in soft-tissue CNR with KC-Recon compared to FBP (N = 16, P = 0.02), improving visualization of paraspinal muscles, major vessels, and other soft-tissues about the spine and abdomen. For a total of 72 screws in postinstrumentation images, KC-Recon yielded a significant reduction in metal artifacts: 66.3% reduction in overestimation of screw shaft width due to blooming (P < 0.0001) and reduction in streaks at the screw tip (65.8% increase in attenuation accuracy, P < 0.0001), enabling clearer depiction of the screw within the pedicle and vertebral body for an assessment of breach. Depending on the imaging task, dose reduction up to an order of magnitude appeared feasible while maintaining soft-tissue visibility and metal artifact reduction.

CONCLUSIONS

KC-Recon offers a promising means to improve visualization in the presence of surgical instrumentation and reduce patient dose in image-guided procedures. The improved soft-tissue visibility could facilitate the use of cone-beam CT to soft-tissue surgeries, and the ability to precisely quantify and visualize instrument placement could provide a valuable check against complications in the operating room (cf., postoperative CT).

Task-driven source-detector trajectories in cone-beam computed tomography: II. Application to neuroradiology

We apply the methodology detailed in "Task-driven source-detector trajectories in cone-beam computed tomography: I. Theory and methods" by Stayman et al. for task-driven optimization of source-detector orbits in cone-beam computed tomography (CBCT) to scenarios emulating imaging tasks in interventional neuroradiology. The task-driven imaging framework is used to optimize the CBCT source-detector trajectory by maximizing the detectability index, d ' . The approach was applied to simulated cases of endovascular embolization of an aneurysm and arteriovenous malformation and was translated to real data first using a CBCT test bench followed by implementation on an interventional robotic C-arm. Task-driven trajectories were found to generally favor higher fidelity (i.e., less noisy) views, with an average increase in d ' ranging from 7% to 28%. Visually, this resulted in improved conspicuity of particular stimuli by reducing the noise and altering the noise correlation to a form distinct from the spatial frequencies associated with the imaging task. The improvements in detectability and the demonstration of the task-driven workflow using a real interventional imaging system show the potential of the task-driven imaging framework to improve imaging performance on motorized, multiaxis C-arms in neuroradiology.

Task-driven source-detector trajectories in cone-beam computed tomography: I. Theory and methods

We develop a mathematical framework for the design of orbital trajectories that are optimal to a particular imaging task (or tasks) in advanced cone-beam computed tomography systems that have the capability of general source-detector positioning. The framework allows various parameterizations of the orbit as well as constraints based on imaging system capabilities. To accommodate nonstandard system geometries, a model-based iterative reconstruction method is applied. Such algorithms generally complicate the assessment and prediction of reconstructed image properties; however, we leverage efficient implementations of analytical predictors of local noise and spatial resolution that incorporate dependencies of the reconstruction algorithm on patient anatomy, x-ray technique, and geometry. These image property predictors serve as inputs to a task-based performance metric defined by detectability index, which is optimized with respect to the orbital parameters of data acquisition. We investigate the framework of the task-driven trajectory design in several examples to examine the dependence of optimal source-detector trajectories on the imaging task (or tasks), including location and spatial-frequency dependence. A variety of multitask objectives are also investigated, and the advantages to imaging performance are quantified in simulation studies.

Predicting image properties in penalized-likelihood reconstructions of flat-panel CBCT

PURPOSE

Model-based iterative reconstruction (MBIR) algorithms such as penalized-likelihood (PL) methods exhibit data-dependent and shift-variant properties. Image quality predictors have been derived to prospectively estimate local noise and spatial resolution, facilitating both system hardware design and tuning of reconstruction methods. However, current MBIR image quality predictors rely on idealized system models, ignoring physical blurring effects and noise correlations found in real systems. In this work, we develop and validate a new set of predictors using a physical system model specific to flat-panel cone-beam CT (FP-CBCT).

METHODS

Physical models appropriate for integration with MBIR analysis are developed and parameterized to represent nonidealities in FP projection data including focal spot blur, scintillator blur, detector aperture effect, and noise correlations. Flat-panel-specific predictors for local spatial resolution and local noise properties in PL reconstructions are developed based on these realistic physical models. Estimation accuracy of conventional (idealized) and FP-specific predictors is investigated and validated against experimental CBCT measurements using specialized phantoms.

RESULTS

Validation studies show that flat-panel-specific predictors can accurately estimate the local spatial resolution and noise properties, while conventional predictors show significant deviations in the magnitude and scale of the spatial resolution and local noise. The proposed predictors show accurate estimations over a range of imaging conditions including varying x-ray technique and regularization strength. The conventional spatial resolution prediction is sharper than ground truth. Using conventional spatial resolution predictor, the full width at half maximum (FWHM) of local point spread function (PSF) is underestimated by 0.2 mm. This mismatch is mostly eliminated in FP-specific prediction. The general shape and amplitude of local noise power spectrum (NPS) FP-specific predictions are consistent with measurement, while the conventional predictions underestimated the noise level by 70%.

CONCLUSION

The proposed image quality predictors permit accurate estimation of local spatial resolution and noise properties for PL reconstruction, accounting for dependencies on the system geometry, x-ray technique, and patient-specific anatomy in real FP-CBCT. Such tools enable prospective analysis of image quality for a range of goals including novel system and acquisition design, adaptive and task-driven imaging, and tuning of MBIR for robust and reliable behavior.

Regularization strategies in statistical image reconstruction of low-dose x-ray CT: A review

Statistical image reconstruction (SIR) methods have shown potential to substantially improve the image quality of low-dose x-ray computed tomography (CT) as compared to the conventional filtered back-projection (FBP) method. According to the maximum a posteriori (MAP) estimation, the SIR methods are typically formulated by an objective function consisting of two terms: (a) a data-fidelity term that models imaging geometry and physical detection processes in projection data acquisition, and (b) a regularization term that reflects prior knowledge or expectations of the characteristics of the to-be-reconstructed image. SIR desires accurate system modeling of data acquisition, while the regularization term also has a strong influence on the quality of reconstructed images. A variety of regularization strategies have been proposed for SIR in the past decades, based on different assumptions, models, and prior knowledge. In this paper, we review the conceptual and mathematical bases of these regularization strategies and briefly illustrate their efficacies in SIR of low-dose CT.

Spatial Resolution and Noise Prediction in Flat-Panel Cone-Beam CT Penalized-likelihood Reconstruction

Purpose

Model based iterative reconstruction (MBIR) algorithms such as penalized-likelihood (PL) methods have data-dependent and shift-variant image properties. Predictors of local reconstructed noise and resolution have found application in a number of methods that seek to understand, control, and optimize CT data acquisition and reconstruction parameters in a prospective fashion (as opposed to studies based on exhaustive evaluation). However, previous MBIR prediction methods have relied on idealized system models. In this work, we develop and validate new predictors using accurate physical models specific to flat-panel CT systems.

Methods

Novel predictors for estimation of local spatial resolution and noise properties are developed for PL reconstruction that include a physical model for blur and correlated noise in flat-panel cone-beam CT (CBCT) acquisitions. Prospective predictions (e.g., without reconstruction) of local point spread function and and local noise power spectrum (NPS) model are applied, compared, and validated using a flat-panel CBCT test bench.

Results

Comparisons between prediction and physical measurements show excellent agreement for both spatial resolution and noise properties. In comparison, traditional prediction methods (that ignore blur/correlation found in flat-panel data) fail to capture important data characteristics and show significant mismatch.

Conclusion

Novel image property predictors permit prospective assessment of flat-panel CBCT using MBIR. Such predictors enable standard and task-based performance assessments, and are well-suited to evaluation, control, and optimization of the CT imaging chain (e.g., x-ray technique, reconstruction parameters, novel data acquisition methods, etc.) for improved imaging performance and/or dose utilization.

Task-based statistical image reconstruction for high-quality cone-beam CT

Task-based analysis of medical imaging performance underlies many ongoing efforts in the development of new imaging systems. In statistical image reconstruction, regularization is often formulated in terms to encourage smoothness and/or sharpness (e.g. a linear, quadratic, or Huber penalty) but without explicit formulation of the task. We propose an alternative regularization approach in which a spatially varying penalty is determined that maximizes task-based imaging performance at every location in a 3D image. We apply the method to model-based image reconstruction (MBIR-viz., penalized weighted least-squares, PWLS) in cone-beam CT (CBCT) of the head, focusing on the task of detecting a small, low-contrast intracranial hemorrhage (ICH), and we test the performance of the algorithm in the context of a recently developed CBCT prototype for point-of-care imaging of brain injury. Theoretical predictions of local spatial resolution and noise are computed via an optimization by which regularization (specifically, the quadratic penalty strength) is allowed to vary throughout the image to maximize local task-based detectability index ([Formula: see text]). Simulation studies and test-bench experiments were performed using an anthropomorphic head phantom. Three PWLS implementations were tested: conventional (constant) penalty; a certainty-based penalty derived to enforce constant point-spread function, PSF; and the task-based penalty derived to maximize local detectability at each location. Conventional (constant) regularization exhibited a fairly strong degree of spatial variation in [Formula: see text], and the certainty-based method achieved uniform PSF, but each exhibited a reduction in detectability compared to the task-based method, which improved detectability up to ~15%. The improvement was strongest in areas of high attenuation (skull base), where the conventional and certainty-based methods tended to over-smooth the data. The task-driven reconstruction method presents a promising regularization method in MBIR by explicitly incorporating task-based imaging performance as the objective. The results demonstrate improved ICH conspicuity and support the development of high-quality CBCT systems.

A theoretical signal processing framework for linear diffusion MRI: Implications for parameter estimation and experiment design

The data measured in diffusion MRI can be modeled as the Fourier transform of the Ensemble Average Propagator (EAP), a probability distribution that summarizes the molecular diffusion behavior of the spins within each voxel. This Fourier relationship is potentially advantageous because of the extensive theory that has been developed to characterize the sampling requirements, accuracy, and stability of linear Fourier reconstruction methods. However, existing diffusion MRI data sampling and signal estimation methods have largely been developed and tuned without the benefit of such theory, instead relying on approximations, intuition, and extensive empirical evaluation. This paper aims to address this discrepancy by introducing a novel theoretical signal processing framework for diffusion MRI. The new framework can be used to characterize arbitrary linear diffusion estimation methods with arbitrary q-space sampling, and can be used to theoretically evaluate and compare the accuracy, resolution, and noise-resilience of different data acquisition and parameter estimation techniques. The framework is based on the EAP, and makes very limited modeling assumptions. As a result, the approach can even provide new insight into the behavior of model-based linear diffusion estimation methods in contexts where the modeling assumptions are inaccurate. The practical usefulness of the proposed framework is illustrated using both simulated and real diffusion MRI data in applications such as choosing between different parameter estimation methods and choosing between different q-space sampling schemes.

Direct parametric reconstruction in dynamic PET myocardial perfusion imaging: in vivo studies

Dynamic PET myocardial perfusion imaging (MPI) used in conjunction with tracer kinetic modeling enables the quantification of absolute myocardial blood flow (MBF). However, MBF maps computed using the traditional indirect method (i.e. post-reconstruction voxel-wise fitting of kinetic model to PET time-activity-curves-TACs) suffer from poor signal-to-noise ratio (SNR). Direct reconstruction of kinetic parameters from raw PET projection data has been shown to offer parametric images with higher SNR compared to the indirect method. The aim of this study was to extend and evaluate the performance of a direct parametric reconstruction method using in vivo dynamic PET MPI data for the purpose of quantifying MBF. Dynamic PET MPI studies were performed on two healthy pigs using a Siemens Biograph mMR scanner. List-mode PET data for each animal were acquired following a bolus injection of ~7-8 mCi of 18F-flurpiridaz, a myocardial perfusion agent. Fully-3D dynamic PET sinograms were obtained by sorting the coincidence events into 16 temporal frames covering ~5 min after radiotracer administration. Additionally, eight independent noise realizations of both scans-each containing 1/8th of the total number of events-were generated from the original list-mode data. Dynamic sinograms were then used to compute parametric maps using the conventional indirect method and the proposed direct method. For both methods, a one-tissue compartment model accounting for spillover from the left and right ventricle blood-pools was used to describe the kinetics of 18F-flurpiridaz. An image-derived arterial input function obtained from a TAC taken in the left ventricle cavity was used for tracer kinetic analysis. For the indirect method, frame-by-frame images were estimated using two fully-3D reconstruction techniques: the standard ordered subset expectation maximization (OSEM) reconstruction algorithm on one side, and the one-step late maximum a posteriori (OSL-MAP) algorithm on the other side, which incorporates a quadratic penalty function. The parametric images were then calculated using voxel-wise weighted least-square fitting of the reconstructed myocardial PET TACs. For the direct method, parametric images were estimated directly from the dynamic PET sinograms using a maximum a posteriori (MAP) parametric reconstruction algorithm which optimizes an objective function comprised of the Poisson log-likelihood term, the kinetic model and a quadratic penalty function. Maximization of the objective function with respect to each set of parameters was achieved using a preconditioned conjugate gradient algorithm with a specifically developed pre-conditioner. The performance of the direct method was evaluated by comparing voxel- and segment-wise estimates of [Formula: see text], the tracer transport rate (ml · min-1 · ml-1), to those obtained using the indirect method applied to both OSEM and OSL-MAP dynamic reconstructions. The proposed direct reconstruction method produced [Formula: see text] maps with visibly lower noise than the indirect method based on OSEM and OSL-MAP reconstructions. At normal count levels, the direct method was shown to outperform the indirect method based on OSL-MAP in the sense that at matched level of bias, reduced regional noise levels were obtained. At lower count levels, the direct method produced [Formula: see text] estimates with significantly lower standard deviation across noise realizations than the indirect method based on OSL-MAP at matched bias level. In all cases, the direct method yielded lower noise and standard deviation than the indirect method based on OSEM. Overall, the proposed direct reconstruction offered a better bias-variance tradeoff than the indirect method applied to either OSEM and OSL-MAP. Direct parametric reconstruction as applied to in vivo dynamic PET MPI data is therefore a promising method for producing MBF maps with lower variance.

Task-driven optimization of CT tube current modulation and regularization in model-based iterative reconstruction

Tube current modulation (TCM) is routinely adopted on diagnostic CT scanners for dose reduction. Conventional TCM strategies are generally designed for filtered-backprojection (FBP) reconstruction to satisfy simple image quality requirements based on noise. This work investigates TCM designs for model-based iterative reconstruction (MBIR) to achieve optimal imaging performance as determined by a task-based image quality metric. Additionally, regularization is an important aspect of MBIR that is jointly optimized with TCM, and includes both the regularization strength that controls overall smoothness as well as directional weights that permits control of the isotropy/anisotropy of the local noise and resolution properties. Initial investigations focus on a known imaging task at a single location in the image volume. The framework adopts Fourier and analytical approximations for fast estimation of the local noise power spectrum (NPS) and modulation transfer function (MTF)-each carrying dependencies on TCM and regularization. For the single location optimization, the local detectability index (d') of the specific task was directly adopted as the objective function. A covariance matrix adaptation evolution strategy (CMA-ES) algorithm was employed to identify the optimal combination of imaging parameters. Evaluations of both conventional and task-driven approaches were performed in an abdomen phantom for a mid-frequency discrimination task in the kidney. Among the conventional strategies, the TCM pattern optimal for FBP using a minimum variance criterion yielded a worse task-based performance compared to an unmodulated strategy when applied to MBIR. Moreover, task-driven TCM designs for MBIR were found to have the opposite behavior from conventional designs for FBP, with greater fluence assigned to the less attenuating views of the abdomen and less fluence to the more attenuating lateral views. Such TCM patterns exaggerate the intrinsic anisotropy of the MTF and NPS as a result of the data weighting in MBIR. Directional penalty design was found to reinforce the same trend. The task-driven approaches outperform conventional approaches, with the maximum improvement in d' of 13% given by the joint optimization of TCM and regularization. This work demonstrates that the TCM optimal for MBIR is distinct from conventional strategies proposed for FBP reconstruction and strategies optimal for FBP are suboptimal and may even reduce performance when applied to MBIR. The task-driven imaging framework offers a promising approach for optimizing acquisition and reconstruction for MBIR that can improve imaging performance and/or dose utilization beyond conventional imaging strategies.

Task-Driven Orbit Design and Implementation on a Robotic C-Arm System for Cone-Beam CT

PURPOSE

This work applies task-driven optimization to the design of non-circular orbits that maximize imaging performance for a particular imaging task. First implementation of task-driven imaging on a clinical robotic C-arm system is demonstrated, and a framework for orbit calculation is described and evaluated.

METHODS

We implemented a task-driven imaging framework to optimize orbit parameters that maximize detectability index d'. This framework utilizes a specified Fourier domain task function and an analytical model for system spatial resolution and noise. Two experiments were conducted to test the framework. First, a simple task was considered consisting of frequencies lying entirely on the f_z-axis (e.g., discrimination of structures oriented parallel to the central axial plane), and a "circle + arc" orbit was incorporated into the framework as a means to improve sampling of these frequencies, and thereby increase task-based detectability. The orbit was implemented on a robotic C-arm (Artis Zeego, Siemens Healthcare). A second task considered visualization of a cochlear implant simulated within a head phantom, with spatial frequency response emphasizing high-frequency content in the (f_y , f_z ) plane of the cochlea. An optimal orbit was computed using the task-driven framework, and the resulting image was compared to that for a circular orbit.

RESULTS

For the f_z -axis task, the circle + arc orbit was shown to increase d' by a factor of 1.20, with an improvement of 0.71 mm in a 3D edge-spread measurement for edges located far from the central plane and a decrease in streak artifacts compared to a circular orbit. For the cochlear implant task, the resulting orbit favored complementary views of high tilt angles in a 360° orbit, and d' was increased by a factor of 1.83.

CONCLUSIONS

This work shows that a prospective definition of imaging task can be used to optimize source-detector orbit and improve imaging performance. The method was implemented for execution of non-circular, task-driven orbits on a clinical robotic C-arm system. The framework is sufficiently general to include both acquisition parameters (e.g., orbit, kV, and mA selection) and reconstruction parameters (e.g., a spatially varying regularizer).

Fast Variance Prediction for Iteratively Reconstructed CT Images With Locally Quadratic Regularization

Predicting noise properties of iteratively reconstructed CT images is useful for analyzing reconstruction methods; for example, local noise power spectrum (NPS) predictions may be used to quantify the detectability of an image feature, to design regularization methods, or to determine dynamic tube current adjustment during a CT scan. This paper presents a method for fast prediction of reconstructed image variance and local NPS for statistical reconstruction methods using quadratic or locally quadratic regularization. Previous methods either require impractical computation times to generate an approximate map of the variance of each reconstructed voxel, or are restricted to specific CT geometries. Our method can produce a variance map of the entire image, for locally shift-invariant CT geometries with sufficiently fine angular sampling, using a computation time comparable to a single back-projection. The method requires only the projection data to be used in the reconstruction, not a reconstruction itself, and is reasonably accurate except near image edges where edge-preserving regularization behaves highly nonlinearly. We evaluate the accuracy of our method using reconstructions of both simulated CT data and real CT scans of a thorax phantom.

Fast analytical approach of application specific dose efficient spectrum selection for diagnostic CT imaging and PET attenuation correction

Computed tomography (CT) has been used for a variety of applications, two of which include diagnostic imaging and attenuation correction for PET or SPECT imaging. Ideally, the x-ray tube spectrum should be optimized for the specific application to minimize the patient radiation dose while still providing the necessary information. In this study, we proposed a projection-based analytic approach for the analysis of contrast, noise, and bias. Dose normalized contrast to noise ratio (CNRD), inverse noise normalized by dose (IND) and bias are used as evaluation metrics to determine the optimal x-ray spectrum. Our simulation investigated the dose efficiency of the x-ray spectrum ranging from 40 kVp to 200 kVp. Water cylinders with diameters of 15 cm, 24 cm, and 35 cm were used in the simulation to cover a variety of patient sizes. The effects of electronic noise and pre-patient copper filtration were also evaluated. A customized 24 cm CTDI-like phantom with 13 mm diameter inserts filled with iodine (10 mg ml^-1), tantalum (10 mg ml^-1), water, and PMMA was measured with both standard (1.5 mGy) and ultra-low (0.2 mGy) dose to verify the simulation results at tube voltages of 80, 100, 120, and 140 kVp. For contrast-enhanced diagnostic imaging, the simulation results indicated that for high dose without filtration, the optimal kVp for water contrast is approximately 100 kVp for a 15 cm water cylinder. However, the 60 kVp spectrum produces the highest CNRD for bone and iodine. The optimal kVp for tantalum has two selections: approximately 50 and 100 kVp. The kVp that maximizes CNRD increases when the object size increases. The trend in the CTDI phantom measurements agrees with the simulation results, which also agrees with previous studies. Copper filtration improved the dose efficiency for water and tantalum, but reduced the iodine and bone dose efficiency in a clinically-relevant range (70-140 kVp). Our study also shows that for CT-based attenuation correction applications for PET or SPECT, a higher-kVp spectrum with copper filtration is preferable. This method is developed based on filter back projection and does not require image reconstruction or Monte Carlo dose estimates; thus, it could potentially be used for patient-specific and task-based on-the-fly protocol optimization.

Task-Driven Tube Current Modulation and Regularization Design in Computed Tomography with Penalized-Likelihood Reconstruction

PURPOSE

This work applies task-driven optimization to design CT tube current modulation and directional regularization in penalized-likelihood (PL) reconstruction. The relative performance of modulation schemes commonly adopted for filtered-backprojection (FBP) reconstruction were also evaluated for PL in comparison.

METHODS

We adopt a task-driven imaging framework that utilizes a patient-specific anatomical model and information of the imaging task to optimize imaging performance in terms of detectability index (d'). This framework leverages a theoretical model based on implicit function theorem and Fourier approximations to predict local spatial resolution and noise characteristics of PL reconstruction as a function of the imaging parameters to be optimized. Tube current modulation was parameterized as a linear combination of Gaussian basis functions, and regularization was based on the design of (directional) pairwise penalty weights for the 8 in-plane neighboring voxels. Detectability was optimized using a covariance matrix adaptation evolutionary strategy algorithm. Task-driven designs were compared to conventional tube current modulation strategies for a Gaussian detection task in an abdomen phantom.

RESULTS

The task-driven design yielded the best performance, improving d' by ~20% over an unmodulated acquisition. Contrary to FBP, PL reconstruction using automatic exposure control and modulation based on minimum variance (in FBP) performed worse than the unmodulated case, decreasing d' by 16% and 9%, respectively.

CONCLUSIONS

This work shows that conventional tube current modulation schemes suitable for FBP can be suboptimal for PL reconstruction. Thus, the proposed task-driven optimization provides additional opportunities for improved imaging performance and dose reduction beyond that achievable with conventional acquisition and reconstruction.

Theoretical Analysis of Penalized Maximum-Likelihood Patlak Parametric Image Reconstruction in Dynamic PET for Lesion Detection

Detecting cancerous lesions is a major clinical application of emission tomography. In a previous work, we studied penalized maximum-likelihood (PML) image reconstruction for lesion detection in static PET. Here we extend our theoretical analysis of static PET reconstruction to dynamic PET. We study both the conventional indirect reconstruction and direct reconstruction for Patlak parametric image estimation. In indirect reconstruction, Patlak parametric images are generated by first reconstructing a sequence of dynamic PET images, and then performing Patlak analysis on the time activity curves (TACs) pixel-by-pixel. In direct reconstruction, Patlak parametric images are estimated directly from raw sinogram data by incorporating the Patlak model into the image reconstruction procedure. PML reconstruction is used in both the indirect and direct reconstruction methods. We use a channelized Hotelling observer (CHO) to assess lesion detectability in Patlak parametric images. Simplified expressions for evaluating the lesion detectability have been derived and applied to the selection of the regularization parameter value to maximize detection performance. The proposed method is validated using computer-based Monte Carlo simulations. Good agreements between the theoretical predictions and the Monte Carlo results are observed. Both theoretical predictions and Monte Carlo simulation results show the benefit of the indirect and direct methods under optimized regularization parameters in dynamic PET reconstruction for lesion detection, when compared with the conventional static PET reconstruction.

Three-dimensional imaging of human stem cells using soft X-ray tomography

Three-dimensional imaging of human stem cells using transmission soft X-ray tomography (SXT) is presented for the first time. Major organelle types--nuclei, nucleoli, mitochondria, lysosomes and vesicles--were discriminated at approximately 50 nm spatial resolution without the use of contrast agents, on the basis of measured linear X-ray absorption coefficients and comparison of the size and shape of structures to transmission electron microscopy (TEM) images. In addition, SXT was used to visualize the distribution of a cell surface protein using gold-labelled antibody staining. We present the strengths of SXT, which include excellent spatial resolution (intermediate between that of TEM and light microscopy), the lack of the requirement for fixative or contrast agent that might perturb cellular morphology or produce imaging artefacts, and the ability to produce three-dimensional images of cells without microtome sectioning. Possible applications to studying the differentiation of human stem cells are discussed.

Object Specific Trajectory Optimization for Industrial X-ray Computed Tomography

In industrial settings, X-ray computed tomography scans are a common tool for inspection of objects. Often the object can not be imaged using standard circular or helical trajectories because of constraints in space or time. Compared to medical applications the variance in size and materials is much larger. Adapting the acquisition trajectory to the object is beneficial and sometimes inevitable. There are currently no sophisticated methods for this adoption. Typically the operator places the object according to his best knowledge. We propose a detectability index based optimization algorithm which determines the scan trajectory on the basis of a CAD-model of the object. The detectability index is computed solely from simulated projections for multiple user defined features. By adapting the features the algorithm is adapted to different imaging tasks. Performance of simulated and measured data was qualitatively and quantitatively assessed.The results illustrate that our algorithm not only allows more accurate detection of features, but also delivers images with high overall quality in comparison to standard trajectory reconstructions. This work enables to reduce the number of projections and in consequence scan time by introducing an optimization algorithm to compose an object specific trajectory.

Prospective regularization design in prior-image-based reconstruction

Prior-image-based reconstruction (PIBR) methods leveraging patient-specific anatomical information from previous imaging studies and/or sequences have demonstrated dramatic improvements in dose utilization and image quality for low-fidelity data. However, a proper balance of information from the prior images and information from the measurements is required (e.g. through careful tuning of regularization parameters). Inappropriate selection of reconstruction parameters can lead to detrimental effects including false structures and failure to improve image quality. Traditional methods based on heuristics are subject to error and sub-optimal solutions, while exhaustive searches require a large number of computationally intensive image reconstructions. In this work, we propose a novel method that prospectively estimates the optimal amount of prior image information for accurate admission of specific anatomical changes in PIBR without performing full image reconstructions. This method leverages an analytical approximation to the implicitly defined PIBR estimator, and introduces a predictive performance metric leveraging this analytical form and knowledge of a particular presumed anatomical change whose accurate reconstruction is sought. Additionally, since model-based PIBR approaches tend to be space-variant, a spatially varying prior image strength map is proposed to optimally admit changes everywhere in the image (eliminating the need to know change locations a priori). Studies were conducted in both an ellipse phantom and a realistic thorax phantom emulating a lung nodule surveillance scenario. The proposed method demonstrated accurate estimation of the optimal prior image strength while achieving a substantial computational speedup (about a factor of 20) compared to traditional exhaustive search. Moreover, the use of the proposed prior strength map in PIBR demonstrated accurate reconstruction of anatomical changes without foreknowledge of change locations in phantoms where the optimal parameters vary spatially by an order of magnitude or more. In a series of studies designed to explore potential unknowns associated with accurate PIBR, optimal prior image strength was found to vary with attenuation differences associated with anatomical change but exhibited only small variations as a function of the shape and size of the change. The results suggest that, given a target change attenuation, prospective patient-, change-, and data-specific customization of the prior image strength can be performed to ensure reliable reconstruction of specific anatomical changes.

Multipinhole SPECT helical scan parameters and imaging volume

PURPOSE

The authors developed SPECT imaging capability on an animal PET scanner using a multiple-pinhole collimator and step-and-shoot helical data acquisition protocols. The objective of this work was to determine the preferred helical scan parameters, i.e., the angular and axial step sizes, and the imaging volume, that provide optimal imaging performance.

METHODS

The authors studied nine helical scan protocols formed by permuting three rotational and three axial step sizes. These step sizes were chosen around the reference values analytically calculated from the estimated spatial resolution of the SPECT system and the Nyquist sampling theorem. The nine helical protocols were evaluated by two figures-of-merit: the sampling completeness percentage (SCP) and the root-mean-square (RMS) resolution. SCP was an analytically calculated numerical index based on projection sampling. RMS resolution was derived from the reconstructed images of a sphere-grid phantom.

RESULTS

The RMS resolution results show that (1) the start and end pinhole planes of the helical scheme determine the axial extent of the effective field of view (EFOV), and (2) the diameter of the transverse EFOV is adequately calculated from the geometry of the pinhole opening, since the peripheral region beyond EFOV would introduce projection multiplexing and consequent effects. The RMS resolution results of the nine helical scan schemes show optimal resolution is achieved when the axial step size is the half, and the angular step size is about twice the corresponding values derived from the Nyquist theorem. The SCP results agree in general with that of RMS resolution but are less critical in assessing the effects of helical parameters and EFOV.

CONCLUSIONS

The authors quantitatively validated the effective FOV of multiple pinhole helical scan protocols and proposed a simple method to calculate optimal helical scan parameters.

Alternating dual updates algorithm for X-ray CT reconstruction on the GPU

Model-based image reconstruction (MBIR) for X-ray computed tomography (CT) offers improved image quality and potential low-dose operation, but has yet to reach ubiquity in the clinic. MBIR methods form an image by solving a large statistically motivated optimization problem, and the long time it takes to numerically solve this problem has hampered MBIR's adoption. We present a new optimization algorithm for X-ray CT MBIR based on duality and group coordinate ascent that may converge even with approximate updates and can handle a wide range of regularizers, including total variation (TV). The algorithm iteratively updates groups of dual variables corresponding to terms in the cost function; these updates are highly parallel and map well onto the GPU. Although the algorithm stores a large number of variables, the "working size" for each of the algorithm's steps is small and can be efficiently streamed to the GPU while other calculations are being performed. The proposed algorithm converges rapidly on both real and simulated data and shows promising parallelization over multiple devices.

Quantum noise properties of CT images with anatomical textured backgrounds across reconstruction algorithms: FBP and SAFIRE

PURPOSE

Quantum noise properties of CT images are generally assessed using simple geometric phantoms with uniform backgrounds. Such phantoms may be inadequate when assessing nonlinear reconstruction or postprocessing algorithms. The purpose of this study was to design anatomically informed textured phantoms and use the phantoms to assess quantum noise properties across two clinically available reconstruction algorithms, filtered back projection (FBP) and sinogram affirmed iterative reconstruction (SAFIRE).

METHODS

Two phantoms were designed to represent lung and soft-tissue textures. The lung phantom included intricate vessel-like structures along with embedded nodules (spherical, lobulated, and spiculated). The soft tissue phantom was designed based on a three-dimensional clustered lumpy background with included low-contrast lesions (spherical and anthropomorphic). The phantoms were built using rapid prototyping (3D printing) technology and, along with a uniform phantom of similar size, were imaged on a Siemens SOMATOM Definition Flash CT scanner and reconstructed with FBP and SAFIRE. Fifty repeated acquisitions were acquired for each background type and noise was assessed by estimating pixel-value statistics, such as standard deviation (i.e., noise magnitude), autocorrelation, and noise power spectrum. Noise stationarity was also assessed by examining the spatial distribution of noise magnitude. The noise properties were compared across background types and between the two reconstruction algorithms.

RESULTS

In FBP and SAFIRE images, noise was globally nonstationary for all phantoms. In FBP images of all phantoms, and in SAFIRE images of the uniform phantom, noise appeared to be locally stationary (within a reasonably small region of interest). Noise was locally nonstationary in SAFIRE images of the textured phantoms with edge pixels showing higher noise magnitude compared to pixels in more homogenous regions. For pixels in uniform regions, noise magnitude was reduced by an average of 60% in SAFIRE images compared to FBP. However, for edge pixels, noise magnitude ranged from 20% higher to 40% lower in SAFIRE images compared to FBP. SAFIRE images of the lung phantom exhibited distinct regions with varying noise texture (i.e., noise autocorrelation/power spectra).

CONCLUSIONS

Quantum noise properties observed in uniform phantoms may not be representative of those in actual patients for nonlinear reconstruction algorithms. Anatomical texture should be considered when evaluating the performance of CT systems that use such nonlinear algorithms.

Edge-preserving image denoising via group coordinate descent on the GPU

Image denoising is a fundamental operation in image processing, and its applications range from the direct (photographic enhancement) to the technical (as a subproblem in image reconstruction algorithms). In many applications, the number of pixels has continued to grow, while the serial execution speed of computational hardware has begun to stall. New image processing algorithms must exploit the power offered by massively parallel architectures like graphics processing units (GPUs). This paper describes a family of image denoising algorithms well-suited to the GPU. The algorithms iteratively perform a set of independent, parallel 1D pixel-update subproblems. To match GPU memory limitations, they perform these pixel updates in-place and only store the noisy data, denoised image, and problem parameters. The algorithms can handle a wide range of edge-preserving roughness penalties, including differentiable convex penalties and anisotropic total variation. Both algorithms use the majorize-minimize framework to solve the 1D pixel update subproblem. Results from a large 2D image denoising problem and a 3D medical imaging denoising problem demonstrate that the proposed algorithms converge rapidly in terms of both iteration and run-time.

Regularization designs for uniform spatial resolution and noise properties in statistical image reconstruction for 3-D X-ray CT

Statistical image reconstruction methods for X-ray computed tomography (CT) provide improved spatial resolution and noise properties over conventional filtered back-projection (FBP) reconstruction, along with other potential advantages such as reduced patient dose and artifacts. Conventional regularized image reconstruction leads to spatially variant spatial resolution and noise characteristics because of interactions between the system models and the regularization. Previous regularization design methods aiming to solve such issues mostly rely on circulant approximations of the Fisher information matrix that are very inaccurate for undersampled geometries like short-scan cone-beam CT. This paper extends the regularization method proposed in to 3-D cone-beam CT by introducing a hypothetical scanning geometry that helps address the sampling properties. The proposed regularization designs were compared with the original method in with both phantom simulation and clinical reconstruction in 3-D axial X-ray CT. The proposed regularization methods yield improved spatial resolution or noise uniformity in statistical image reconstruction for short-scan axial cone-beam CT.

Evaluation of penalty design in penalized maximum-likelihood image reconstruction for lesion detection

Detecting cancerous lesions is a major clinical application in emission tomography. Previously, we developed a method to design a shift-variant quadratic penalty function in penalized maximum-likelihood (PML) image reconstruction to improve the lesion detectability. We used a multiview channelized Hotelling observer (mvCHO) to assess the lesion detectability in three-dimensional images and validated the penalty design using computer simulations. In this study, we evaluate the benefit of the proposed penalty function for lesion detection using real patient data and artificial lesions. A high-count real patient dataset with no identifiable tumor inside the field of view is used as the background data. A Na-22 point source is scanned in air at variable locations and the point source data are superimposed onto the patient data as artificial lesions after being attenuated by the patient body. Independent Poisson noise is introduced to the high-count sinograms to generate 200 pairs of lesion-present and lesion-absent datasets, each mimicking a 5-min scan. Lesion detectability is assessed using a mvCHO and a human observer two-alternative forced choice (2AFC) experiment. The results show improvements in lesion detection by the proposed method compared with the conventional first-order quadratic penalty function and a total variation (TV) edge-preserving penalty function.

Chemical structure and morphology of dorsal root ganglion neurons from naive and inflamed mice

Fourier transform infrared spectromicroscopy provides label-free imaging to detect the spatial distribution of the characteristic functional groups in proteins, lipids, phosphates, and carbohydrates simultaneously in individual DRG neurons. We have identified ring-shaped distributions of lipid and/or carbohydrate enrichment in subpopulations of neurons which has never before been reported. These distributions are ring-shaped within the cytoplasm and are likely representative of the endoplasmic reticulum. The prevalence of chemical ring subtypes differs between large- and small-diameter neurons. Peripheral inflammation increased the relative lipid content specifically in small-diameter neurons, many of which are nociceptive. Because many small-diameter neurons express an ion channel involved in inflammatory pain, transient receptor potential ankyrin 1 (TRPA1), we asked whether this increase in lipid content occurs in TRPA1-deficient (knock-out) neurons. No statistically significant change in lipid content occurred in TRPA1-deficient neurons, indicating that the inflammation-mediated increase in lipid content is largely dependent on TRPA1. Because TRPA1 is known to mediate mechanical and cold sensitization that accompanies peripheral inflammation, our findings may have important implications for a potential role of lipids in inflammatory pain.

dPIRPLE: a joint estimation framework for deformable registration and penalized-likelihood CT image reconstruction using prior images

Sequential imaging studies are conducted in many clinical scenarios. Prior images from previous studies contain a great deal of patient-specific anatomical information and can be used in conjunction with subsequent imaging acquisitions to maintain image quality while enabling radiation dose reduction (e.g., through sparse angular sampling, reduction in fluence, etc). However, patient motion between images in such sequences results in misregistration between the prior image and current anatomy. Existing prior-image-based approaches often include only a simple rigid registration step that can be insufficient for capturing complex anatomical motion, introducing detrimental effects in subsequent image reconstruction. In this work, we propose a joint framework that estimates the 3D deformation between an unregistered prior image and the current anatomy (based on a subsequent data acquisition) and reconstructs the current anatomical image using a model-based reconstruction approach that includes regularization based on the deformed prior image. This framework is referred to as deformable prior image registration, penalized-likelihood estimation (dPIRPLE). Central to this framework is the inclusion of a 3D B-spline-based free-form-deformation model into the joint registration-reconstruction objective function. The proposed framework is solved using a maximization strategy whereby alternating updates to the registration parameters and image estimates are applied allowing for improvements in both the registration and reconstruction throughout the optimization process. Cadaver experiments were conducted on a cone-beam CT testbench emulating a lung nodule surveillance scenario. Superior reconstruction accuracy and image quality were demonstrated using the dPIRPLE algorithm as compared to more traditional reconstruction methods including filtered backprojection, penalized-likelihood estimation (PLE), prior image penalized-likelihood estimation (PIPLE) without registration, and prior image penalized-likelihood estimation with rigid registration of a prior image (PIRPLE) over a wide range of sampling sparsity and exposure levels.

Task-based detectability in CT image reconstruction by filtered backprojection and penalized likelihood estimation

PURPOSE

Nonstationarity is an important aspect of imaging performance in CT and cone-beam CT (CBCT), especially for systems employing iterative reconstruction. This work presents a theoretical framework for both filtered-backprojection (FBP) and penalized-likelihood (PL) reconstruction that includes explicit descriptions of nonstationary noise, spatial resolution, and task-based detectability index. Potential utility of the model was demonstrated in the optimal selection of regularization parameters in PL reconstruction.

METHODS

Analytical models for local modulation transfer function (MTF) and noise-power spectrum (NPS) were investigated for both FBP and PL reconstruction, including explicit dependence on the object and spatial location. For FBP, a cascaded systems analysis framework was adapted to account for nonstationarity by separately calculating fluence and system gains for each ray passing through any given voxel. For PL, the point-spread function and covariance were derived using the implicit function theorem and first-order Taylor expansion according to Fessler ["Mean and variance of implicitly defined biased estimators (such as penalized maximum likelihood): Applications to tomography," IEEE Trans. Image Process. 5(3), 493-506 (1996)]. Detectability index was calculated for a variety of simple tasks. The model for PL was used in selecting the regularization strength parameter to optimize task-based performance, with both a constant and a spatially varying regularization map.

RESULTS

Theoretical models of FBP and PL were validated in 2D simulated fan-beam data and found to yield accurate predictions of local MTF and NPS as a function of the object and the spatial location. The NPS for both FBP and PL exhibit similar anisotropic nature depending on the pathlength (and therefore, the object and spatial location within the object) traversed by each ray, with the PL NPS experiencing greater smoothing along directions with higher noise. The MTF of FBP is isotropic and independent of location to a first order approximation, whereas the MTF of PL is anisotropic in a manner complementary to the NPS. Task-based detectability demonstrates dependence on the task, object, spatial location, and smoothing parameters. A spatially varying regularization "map" designed from locally optimal regularization can improve overall detectability beyond that achievable with the commonly used constant regularization parameter.

CONCLUSIONS

Analytical models for task-based FBP and PL reconstruction are predictive of nonstationary noise and resolution characteristics, providing a valuable framework for understanding and optimizing system performance in CT and CBCT.

A PET system design by using mixed detectors: resolution properties

We investigate a cylindrical positron emission tomography (PET) system design strategy that employs two groups of detectors with different resolutions. The reason for considering this strategy is the observation that in many tasks one would want a higher resolution in a targeted region, which contains lesions or organs of interest, than that in the rest of the subject. Although one can design a PET system to meet the highest resolution required by the imaging task, this is not cost efficient because the superior resolution outside the target region is not needed. To address this issue, investigators have proposed the concept of an insert, in which a high-resolution detector (HRD) is inserted into a parent PET system to locally increase the image resolution. In this paper, we examine an alternative strategy in which the system is made of one arc of normal-resolution detectors with respect to, for example, whole-body imaging and one arc of HRDs. By using Monte Carlo simulations, we study the resolution properties of this system design and examine how they are affected by the location and size of the HRD arc. Our results show that the region obtained by connecting the edges of the HRD arc to the center of the field-of-view (FOV) can have significantly better resolution than that in the rest of the FOV, as well as better resolution uniformity.

Efficient determination of the uncertainty for the optimization of SPECT system design: a subsampled fisher information matrix

System designs in single photon emission tomography (SPECT) can be evaluated based on the fundamental trade-off between bias and variance that can be achieved in the reconstruction of emission tomograms. This trade off can be derived analytically using the Cramer-Rao type bounds, which imply the calculation and the inversion of the Fisher information matrix (FIM). The inverse of the FIM expresses the uncertainty associated to the tomogram, enabling the comparison of system designs. However, computing, storing and inverting the FIM is not practical with 3-D imaging systems. In order to tackle the problem of the computational load in calculating the inverse of the FIM, a method based on the calculation of the local impulse response and the variance, in a single point, from a single row of the FIM, has been previously proposed for system design. However this approximation (circulant approximation) does not capture the global interdependence between the variables in shift-variant systems such as SPECT, and cannot account e.g., for data truncation or missing data. Our new formulation relies on subsampling the FIM. The FIM is calculated over a subset of voxels arranged in a grid that covers the whole volume. Every element of the FIM at the grid points is calculated exactly, accounting for the acquisition geometry and for the object. This new formulation reduces the computational complexity in estimating the uncertainty, but nevertheless accounts for the global interdependence between the variables, enabling the exploration of design spaces hindered by the circulant approximation. The graphics processing unit accelerated implementation of the algorithm reduces further the computation times, making the algorithm a good candidate for real-time optimization of adaptive imaging systems. This paper describes the subsampled FIM formulation and implementation details. The advantages and limitations of the new approximation are explored, in comparison with the circulant approximation, in the context of design optimization of a parallel-hole collimator SPECT system and of an adaptive imaging system (similar to the commercially available D-SPECT).

Evaluation of PET quantification accuracy in vivo. Comparison of measured FDG concentration in the bladder with urine samples

Quantitative positron emission tomography (PET) requires accurate scanner calibration, which is commonly performed using phantoms. It is not clear to what extent this procedure ensures quantitatively correct results in vivo, since certain conditions differ between phantom and patient scans.

AIM

We, therefore, have evaluated the actual quantification accuracy in vivo of PET under clinical routine conditions.

PATIENTS, METHODS

We determined the activity concentration in the bladder in patients undergoing routine [18F]FDG whole body investigations with three different PET scanners (Siemens ECAT EXACT HR+ PET: n = 21; Siemens Biograph 16 PET/CT: n = 16; Philips Gemini-TF PET/CT: n = 19). Urine samples were collected immediately after scan. Activity concentration in the samples was determined in well counters cross-calibrated against the respective scanner. The PET (bladder) to well counter (urine sample) activity concentration ratio was determined.

RESULTS

Activity concentration in the bladder (PET) was systematically lower than in the urine samples (well counter). The patient-averaged PET to well counter ratios for the investigated scanners are (mean ± SEM): 0.881 ± 0.015 (ECAT HR+), 0.898 ± 0.024 (Biograph 16), 0.932 ± 0.024 (Gemini-TF). These values correspond to underestimates by PET of 11.9%, 10.2%, and 6.8%, respectively.

CONCLUSIONS

The investigated PET systems consistently underestimate activity concentration in the bladder. The comparison of urine samples with PET scans of the bladder is a straightforward means for in vivo evaluation of the expectable quantification accuracy. The method might be interesting for multi-center trials, for additional quality assurance in PET and for investigation of PET/MR systems for which clear proof of sufficient quantitative accuracy in vivo is still missing.

MAP reconstruction for Fourier rebinned TOF-PET data

Time-of-flight (TOF) information improves the signal-to-noise ratio in positron emission tomography (PET). The computation cost in processing TOF-PET sinograms is substantially higher than for nonTOF data because the data in each line of response is divided among multiple TOF bins. This additional cost has motivated research into methods for rebinning TOF data into lower dimensional representations that exploit redundancies inherent in TOF data. We have previously developed approximate Fourier methods that rebin TOF data into either three-dimensional (3D) nonTOF or 2D nonTOF formats. We refer to these methods respectively as FORET-3D and FORET-2D. Here we describe maximum a posteriori (MAP) estimators for use with FORET rebinned data. We first derive approximate expressions for the variance of the rebinned data. We then use these results to rescale the data so that the variance and mean are approximately equal allowing us to use the Poisson likelihood model for MAP reconstruction. MAP reconstruction from these rebinned data uses a system matrix in which the detector response model accounts for the effects of rebinning. Using these methods we compare the performance of FORET-2D and 3D with TOF and nonTOF reconstructions using phantom and clinical data. Our phantom results show a small loss in contrast recovery at matched noise levels using FORET compared to reconstruction from the original TOF data. Clinical examples show FORET images that are qualitatively similar to those obtained from the original TOF-PET data but with a small increase in variance at matched resolution. Reconstruction time is reduced by a factor of 5 and 30 using FORET3D+MAP and FORET2D+MAP respectively compared to 3D TOF MAP, which makes these methods attractive for clinical applications.

Regularization design in penalized maximum-likelihood image reconstruction for lesion detection in 3D PET

Detecting cancerous lesions is a major clinical application in emission tomography. In previous work, we have studied penalized maximum-likelihood (PML) image reconstruction for the detection task and proposed a method to design a shift-invariant quadratic penalty function to maximize detectability of a lesion at a known location in a two dimensional image. Here we extend the regularization design to maximize detectability of lesions at unknown locations in fully 3D PET. We used a multiview channelized Hotelling observer (mvCHO) to assess the lesion detectability in 3D images to mimic the condition where a human observer examines three orthogonal views of a 3D image for lesion detection. We derived simplified theoretical expressions that allow fast prediction of the detectability of a 3D lesion. The theoretical results were used to design the regularization in PML reconstruction to improve lesion detectability. We conducted computer-based Monte Carlo simulations to compare the optimized penalty with the conventional penalty for detecting lesions of various sizes. Only true coincidence events were simulated. Lesion detectability was also assessed by two human observers, whose performances agree well with that of the mvCHO. Both the numerical observer and human observer results showed a statistically significant improvement in lesion detection by using the proposed penalty function compared to using the conventional penalty function.

Quantitative statistical methods for image quality assessment

Quantitative measures of image quality and reliability are critical for both qualitative interpretation and quantitative analysis of medical images. While, in theory, it is possible to analyze reconstructed images by means of Monte Carlo simulations using a large number of noise realizations, the associated computational burden makes this approach impractical. Additionally, this approach is less meaningful in clinical scenarios, where multiple noise realizations are generally unavailable. The practical alternative is to compute closed-form analytical expressions for image quality measures. The objective of this paper is to review statistical analysis techniques that enable us to compute two key metrics: resolution (determined from the local impulse response) and covariance. The underlying methods include fixed-point approaches, which compute these metrics at a fixed point (the unique and stable solution) independent of the iterative algorithm employed, and iteration-based approaches, which yield results that are dependent on the algorithm, initialization, and number of iterations. We also explore extensions of some of these methods to a range of special contexts, including dynamic and motion-compensated image reconstruction. While most of the discussed techniques were developed for emission tomography, the general methods are extensible to other imaging modalities as well. In addition to enabling image characterization, these analysis techniques allow us to control and enhance imaging system performance. We review practical applications where performance improvement is achieved by applying these ideas to the contexts of both hardware (optimizing scanner design) and image reconstruction (designing regularization functions that produce uniform resolution or maximize task-specific figures of merit).

Characterization of statistical prior image constrained compressed sensing (PICCS): II. Application to dose reduction

PURPOSE

The ionizing radiation imparted to patients during computed tomography exams is raising concerns. This paper studies the performance of a scheme called dose reduction using prior image constrained compressed sensing (DR-PICCS). The purpose of this study is to characterize the effects of a statistical model of x-ray detection in the DR-PICCS framework and its impact on spatial resolution.

METHODS

Both numerical simulations with known ground truth and in vivo animal dataset were used in this study. In numerical simulations, a phantom was simulated with Poisson noise and with varying levels of eccentricity. Both the conventional filtered backprojection (FBP) and the PICCS algorithms were used to reconstruct images. In PICCS reconstructions, the prior image was generated using two different denoising methods: a simple Gaussian blur and a more advanced diffusion filter. Due to the lack of shift-invariance in nonlinear image reconstruction such as the one studied in this paper, the concept of local spatial resolution was used to study the sharpness of a reconstructed image. Specifically, a directional metric of image sharpness, the so-called pseudopoint spread function (pseudo-PSF), was employed to investigate local spatial resolution.

RESULTS

In the numerical studies, the pseudo-PSF was reduced from twice the voxel width in the prior image down to less than 1.1 times the voxel width in DR-PICCS reconstructions when the statistical model was not included. At the same noise level, when statistical weighting was used, the pseudo-PSF width in DR-PICCS reconstructed images varied between 1.5 and 0.75 times the voxel width depending on the direction along which it was measured. However, this anisotropy was largely eliminated when the prior image was generated using diffusion filtering; the pseudo-PSF width was reduced to below one voxel width in that case. In the in vivo study, a fourfold improvement in CNR was achieved while qualitatively maintaining sharpness; images also had a qualitatively more uniform noise spatial distribution when including a statistical model.

CONCLUSIONS

DR-PICCS enables to reconstruct CT images with lower noise than FBP and the loss of spatial resolution can be mitigated to a large extent. The introduction of statistical modeling in DR-PICCS may improve some noise characteristics, but it also leads to anisotropic spatial resolution properties. A denoising method, such as the directional diffusion filtering, has been demonstrated to reduce anisotropy in spatial resolution effectively when it was combined with DR-PICCS with statistical modeling.

3D spectral imaging with synchrotron Fourier transform infrared spectro-microtomography

We report Fourier transform infrared spectro-microtomography, a nondestructive three-dimensional imaging approach that reveals the distribution of distinctive chemical compositions throughout an intact biological or materials sample. The method combines mid-infrared absorption contrast with computed tomographic data acquisition and reconstruction to enhance chemical and morphological localization by determining a complete infrared spectrum for every voxel (millions of spectra determined per sample).

Parameter optimization of relaxed Ordered Subsets Pre-computed Back Projection (BP) based Penalized-Likelihood (OS-PPL) reconstruction in limited-angle X-ray tomography

This paper presents a two-step strategy to provide a quality-predictable image reconstruction. A Pre-computed Back Projection based Penalized-Likelihood (PPL) method is proposed in the strategy to generate consistent image quality. To solve PPL efficiently, relaxed Ordered Subsets (OS) is applied. A training sets based evaluation is performed to quantify the effect of the undetermined parameters in OS, which lets the results as consistent as possible with the theoretical one.

Modeling and Control of Nonstationary Noise Characteristics in Filtered-Backprojection and Penalized Likelihood Image Reconstruction

Purpose

Nonstationarity of CT noise presents a major challenge to the assessment of image quality. This work presents models for imaging performance in both filtered backprojection (FBP) and penalized likelihood (PL) reconstruction that describe not only the dependence on the imaging chain but also the dependence on the object as well as the nonstationary characteristics of the signal and noise. The work furthermore demonstrates the ability to impart control over the imaging process by adjusting reconstruction parameters to exploit nonstationarity in a manner advantageous to a particular imaging task.

Methods

A cascaded systems analysis model was used to model the local noise-power spectrum (NPS) and modulation transfer function (MTF) for FBP reconstruction, with locality achieved by separate calculation of fluence and system gain for each view as a function of detector location. The covariance and impulse response function for PL reconstruction (quadratic penalty) were computed using the implicit function theorem and Taylor expansion. Detectability index was calculated under the assumption of local stationarity to show the variation in task-dependent image quality throughout the image for simple and complex, heterogeneous objects. Control of noise magnitude and correlation was achieved by applying a spatially varying roughness penalty in PL reconstruction in a manner that improved overall detectability.

Results

The models provide a foundation for task-based imaging performance assessment in FBP and PL image reconstruction. For both FBP and PL, noise is anisotropic and varies in a manner dependent on the path length of each view traversing the object. The anisotropy in turn affects task performance, where detectability is enhanced or diminished depending on the frequency content of the task relative to that of the NPS. Spatial variation of the roughness penalty can be exploited to control noise magnitude and correlation (and hence detectability).

Conclusions

Nonstationarity of image noise is a significant effect that can be modeled in both FBP and PL image reconstruction. Prevalent spatial-frequency-dependent metrics of spatial resolution and noise can be analyzed under assumptions of local stationarity, providing a means to analyze imaging performance as a function of location throughout the image. Knowledgeable selection of a spatially-varying roughness penalty in PL can potentially improve local noise and spatial resolution in a manner tuned to a particular imaging task.

Direct 4-D PET list mode parametric reconstruction with a novel EM algorithm

The production of images of kinetic parameters is often the ultimate goal of positron emission tomography (PET) imaging. The indirect method of PET parametric imaging, also called the frame-based method (FM), is performed by fitting the time-activity curve (TAC) for each voxel with an appropriate compartment model after image reconstruction. The indirect method is simple and easily implemented, however, it usually leads to some loss of accuracy or precision, due to the use of two separate steps. This paper presents a direct 4-D method for producing 3-D images of kinetic parameters from list mode PET data. In this application, the TAC for each voxel is described by a one-tissue compartment model (1T). Extending previous EM algorithms, a new spatiotemporal complete data space was introduced to optimize the maximum likelihood function. This leads to a straightforward closed-form parametric image update equation. This method was implemented by extending the current list mode platform MOLAR to produce a parametric algorithm PMOLAR-1T. Using an ordered subset approach, qualitative and quantitative evaluations were performed using 2-D (x, t) and 4-D (x, y, z, t) simulated list mode data based on brain receptor tracers and also with a human brain study. Comparisons with the indirect method showed that the proposed direct method can lead to accurate estimation of the parametric image values with reduced variance, especially at low count levels. In the 2-D test, the direct method showed similar bias to the frame-based method but with variance reduction of 23%-60%. In the 4-D test, bias values of both methods were no more than 4% and the direct method had lower variability (coefficient of variation reduction of 0%-64% compared to the frame-based method) at the normal count level. The direct method had a larger reduction in variability (27%-81%) and lower bias (1%-5% for 4-D and 1%-19% for FM) at low count levels. The results in the human brain study are similar with PMOLAR-1T showing lower noise than FM.

Human amnion epithelial cells induced to express functional cystic fibrosis transmembrane conductance regulator

Cystic fibrosis, an autosomal recessive disorder caused by a mutation in a gene encoding the cystic fibrosis transmembrane conductance regulator (CFTR), remains a leading cause of childhood respiratory morbidity and mortality. The respiratory consequences of cystic fibrosis include the generation of thick, tenacious mucus that impairs lung clearance, predisposing the individual to repeated and persistent infections, progressive lung damage and shortened lifespan. Currently there is no cure for cystic fibrosis. With this in mind, we investigated the ability of human amnion epithelial cells (hAECs) to express functional CFTR. We found that hAECs formed 3-dimensional structures and expressed the CFTR gene and protein after culture in Small Airway Growth Medium (SAGM). We also observed a polarized CFTR distribution on the membrane of hAECs cultured in SAGM, similar to that observed in polarized airway cells in vivo. Further, hAECs induced to express CFTR possessed functional iodide/chloride (I^−/Cl⁻) ion channels that were inhibited by the CFTR-inhibitor CFTR-172, indicating the presence of functional CFTR ion channels. These data suggest that hAECs may be a promising source for the development of a cellular therapy for cystic fibrosis.

Spatially regularized T(1) estimation from variable flip angles MRI

PURPOSE

To develop efficient algorithms for fast voxel-by-voxel quantification of tissue longitudinal relaxation time (T(1)) from variable flip angles magnetic resonance images (MRI) to reduce voxel-level noise without blurring tissue edges.

METHODS

T(1) estimations regularized by total variation (TV) and quadratic penalty are developed to measure T(1) from fast variable flip angles MRI and to reduce voxel-level noise without decreasing the accuracy of the estimates. First, a quadratic surrogate for a log likelihood cost function of T(1) estimation is derived based upon the majorization principle, and then the TV-regularized surrogate function is optimized by the fast iterative shrinkage thresholding algorithm. A fast optimization algorithm for the quadratically regularized T(1) estimation is also presented. The proposed methods are evaluated by the simulated and experimental MR data.

RESULTS

The means of the T(1) values in the simulated brain data estimated by the conventional, TV-regularized, and quadratically regularized methods have less than 3% error from the true T(1) in both GM and WM tissues with image noise up to 9%. The relative standard deviations (SDs) of the T(1) values estimated by the conventional method are more than 12% and 15% when the images have 7% and 9% noise, respectively. In comparison, the TV-regularized and quadratically regularized methods are able to suppress the relative SDs of the estimated T(1) to be less than 2% and 3%, respectively, regardless of the image noise level. However, the quadratically regularized method tends to overblur the edges compared to the TV-regularized method.

CONCLUSIONS

The spatially regularized methods improve quality of T(1) estimation from multiflip angles MRI. Quantification of dynamic contrast-enhanced MRI can benefit from the high quality measurement of native T(1).

Spatial resolution properties of motion-compensated tomographic image reconstruction methods

Many motion-compensated image reconstruction (MCIR) methods have been proposed to correct for subject motion in medical imaging. MCIR methods incorporate motion models to improve image quality by reducing motion artifacts and noise. This paper analyzes the spatial resolution properties of MCIR methods and shows that nonrigid local motion can lead to nonuniform and anisotropic spatial resolution for conventional quadratic regularizers. This undesirable property is akin to the known effects of interactions between heteroscedastic log-likelihoods (e.g., Poisson likelihood) and quadratic regularizers. This effect may lead to quantification errors in small or narrow structures (such as small lesions or rings) of reconstructed images. This paper proposes novel spatial regularization design methods for three different MCIR methods that account for known nonrigid motion. We develop MCIR regularization designs that provide approximately uniform and isotropic spatial resolution and that match a user-specified target spatial resolution. Two-dimensional PET simulations demonstrate the performance and benefits of the proposed spatial regularization design methods.