Spatial resolution properties of penalized-likelihood image reconstruction: space-invariant tomographs

Noise-matched total-likelihood-based bilateral filter: Experimental feasibility in a benchtop photon-counting CBCT system

PURPOSE

Material decomposition induces substantial noise in basis images and their synthesized computed tomography (CT) images. A likelihood-based bilateral filter was previously developed as a neighborhood filter that effectively reduces noise. However, this method is sensitive to image contrast, and the noise texture needs improvement. It is also necessary to address how to optimally combine filtered basis images to synthesize CT images. This study addressed these issues by introducing total likelihood and a noise-matched condition.

METHODS

The experimental feasibility of the proposed method was demonstrated in a benchtop photon-counting CT (PCCT) system using the following steps: (1) A calibration process for forward modeling, (2) maximum likelihood (ML)-based material decomposition, which is accurate but suffers from substantial noise, (3) noise reduction by applying a total-likelihood-based filter, and (4) CT image synthesis using the noise-matched condition. The proposed method was compared with conventional neighborhood filters and statistical iterative reconstruction with edge-preserving regularization.

RESULTS

The local noise and task-based modulation transfer function (TTF) were analyzed using a test phantom, and the proposed method was found to preserve the spatial resolution better than the other methods, especially in low-contrast regions. In the chicken leg experiment, the proposed method improved the fine structures and background textures in the denoised images and exhibited superior properties in analyzing the noise power spectrum.

CONCLUSION

The proposed method is effective and computationally efficient for noise reduction in PCCT and can potentially replace conventional iterative edge-preserved regularization approaches.

Refining penalty parameter selection in whole-body PET image reconstruction for lung cancer patients using the cross-validation log-likelihood method

Objective.Penalty parameters in penalized likelihood positron emission tomography (PET) reconstruction are typically determined empirically. The cross-validation log-likelihood (CVLL) method has been introduced to optimize these parameters by maximizing a CVLL function, which assesses the likelihood of reconstructed images using one subset of a list-mode dataset based on another subset. This study aims to validate the efficacy of the CVLL method in whole-body imaging for cancer patients using a conventional clinical PET scanner.Approach.Fifteen lung cancer patients were injected with 243.7 ± 23.8 MBq of [18F]FDG and underwent a 22 min PET scan on a Biograph mCT PET/CT scanner, starting at 60 ± 5 min post-injection. The PET list-mode data were partitioned by subsampling without replacement, with 20 minutes of data for image reconstruction using an in-house ordered subset expectation maximization algorithm and the remaining 2 minutes of data for cross-validation. Two penalty parameters, penalty strengthβand Fair penalty function parameterδ, were subjected to optimization. Whole-body images were reconstructed, and CVLL values were computed across various penalty parameter combinations. The optimal image corresponding to the maximum CVLL value was selected by a grid search for each patient.Main results.Theδvalue required to maximize the CVLL value was notably small (⩽10-6in this study). The influences of voxel size and scan duration on image optimization were investigated. A correlation analysis revealed a significant inverse relationship between optimalβand scan count level, with a correlation coefficient of -0.68 (p-value = 3.5 × 10-5). The optimal images selected by the CVLL method were compared with those chosen by two radiologists based on their diagnostic preferences. Differences were observed in the selection of optimal images.Significance.This study demonstrates the feasibility of incorporating the CVLL method into routine imaging protocols, potentially allowing for a wide range of combinations of injected radioactivity amounts and scan durations in modern PET imaging.

RT-SRTS: Angle-agnostic real-time simultaneous 3D reconstruction and tumor segmentation from single X-ray projection

Radiotherapy is one of the primary treatment methods for tumors, but the organ movement caused by respiration limits its accuracy. Recently, 3D imaging from a single X-ray projection has received extensive attention as a promising approach to address this issue. However, current methods can only reconstruct 3D images without directly locating the tumor and are only validated for fixed-angle imaging, which fails to fully meet the requirements of motion control in radiotherapy. In this study, a novel imaging method RT-SRTS is proposed which integrates 3D imaging and tumor segmentation into one network based on multi-task learning (MTL) and achieves real-time simultaneous 3D reconstruction and tumor segmentation from a single X-ray projection at any angle. Furthermore, the attention enhanced calibrator (AEC) and uncertain-region elaboration (URE) modules have been proposed to aid feature extraction and improve segmentation accuracy. The proposed method was evaluated on fifteen patient cases and compared with three state-of-the-art methods. It not only delivers superior 3D reconstruction but also demonstrates commendable tumor segmentation results. Simultaneous reconstruction and segmentation can be completed in approximately 70 ms, significantly faster than the required time threshold for real-time tumor tracking. The efficacies of both AEC and URE have also been validated in ablation studies. The code of work is available at https://github.com/ZywooSimple/RT-SRTS.

The SNR of time-of-flight positron emission tomography data for joint reconstruction of the activity and attenuation images

Objective.Measurement of the time-of-flight (TOF) difference of each coincident pair of photons increases the effective sensitivity of positron emission tomography (PET). Many authors have analyzed the benefit of TOF for quantification and hot spot detection in the reconstructed activity images. However, TOF not only improves the effective sensitivity, it also enables the joint reconstruction of the tracer concentration and attenuation images. This can be used to correct for errors in CT- or MR-derived attenuation maps, or to apply attenuation correction without the help of a second modality. This paper presents an analysis of the effect of TOF on the variance of the jointly reconstructed attenuation and (attenuation corrected) tracer concentration images.Approach.The analysis is performed for PET systems that have a distribution of possibly non-Gaussian TOF-kernels, and includes the conventional Gaussian TOF-kernel as a special case. Non-Gaussian TOF-kernels are often observed in novel detector designs, which make use of two (or more) different mechanisms to convert the incoming 511 keV photon to optical photons. The analytical result is validated with a simple 2D simulation.Main results.We show that if two different TOF-kernels are equivalent for image reconstruction with known attenuation, then they are also equivalent for joint reconstruction of the activity and the attenuation images. The variance increase in the activity, caused by also jointly reconstructing the attenuation image, vanishes when the TOF-resolution approaches perfection.Significance.These results are of interest for PET detector development and for the development of stand-alone PET systems.

Characterization and Assessment of Projection Probability Density Function and Enhanced Sampling in Self-Collimation SPECT

We have recently reported a self-collimation SPECT (SC-SPECT) design concept that constructs sensitive detectors in a multi-ring interspaced mosaic architecture to simultaneously improve system spatial resolution and sensitivity. In this work, through numerical and Monte-Carlo simulation studies, we investigate this new design concept by analyzing its projection probability density functions (PPDF) and the effects of enhanced sampling, i.e. having rotational and translational object movements during imaging. We first quantitatively characterize PPDFs by their widths and edge slopes. Then we compare the PPDFs of an SC-SPECT and a series of multiple-pinhole SPECT (MPH-SPECT) systems and assess the impact of PPDFs - combined with enhanced sampling - on image contrast recovery coefficient and variance through phantom studies. We show the PPDFs of SC- SPECT have steeper edges and a wider range of width, and these attributes enable SC-SPECT to achieve better performance.

The SNR of Positron Emission Data With Gaussian and Non-Gaussian Time-of-Flight Kernels, With Application to Prompt Photon Coincidence

It is well known that measurement of the time-of-flight (TOF) increases the information provided by coincident events in positron emission tomography (PET). This information increase propagates through the reconstruction and improves the signal-to-noise ratio in the reconstructed images. Takehiro Tomitani has analytically computed the gain in variance in the reconstructed image, provided by a particular TOF resolution, for the center of a uniform disk and for a Gaussian TOF kernel. In this paper we extend this result, by computing the signal-to-noise ratio (SNR) contributed by individual coincidence events for two different tasks. One task is the detection of a hot spot in the center of a uniform cylinder. The second one is the same as that considered by Tomitani, i.e. the reconstruction of the central voxel in the image of a uniform cylinder. In addition, we extend the computation to non-Gaussian TOF kernels. It is found that a modification of the TOF-kernel changes the SNR for both tasks in almost exactly the same way. The proposed method can be used to compare TOF-systems with different and possibly event-dependent TOF-kernels, as encountered when prompt photons, such as Cherenkov photons are present, or when the detector is composed of different scintillators. The method is validated with simple 2D simulations and illustrated by applying it to PET detectors producing optical photons with event-dependent timing characteristics.

Linearized Analysis of Noise and Resolution for DL-Based Image Generation

Deep-learning (DL) based CT image generation methods are often evaluated using RMSE and SSIM. By contrast, conventional model-based image reconstruction (MBIR) methods are often evaluated using image properties such as resolution, noise, bias. Calculating such image properties requires time consuming Monte Carlo (MC) simulations. For MBIR, linearized analysis using first order Taylor expansion has been developed to characterize noise and resolution without MC simulations. This inspired us to investigate if linearization can be applied to DL networks to enable efficient characterization of resolution and noise. We used FBPConvNet as an example DL network and performed extensive numerical evaluations, including both computer simulations and real CT data. Our results showed that network linearization works well under normal exposure settings. For such applications, linearization can characterize image noise and resolutions without running MC simulations. We provide with this work the computational tools to implement network linearization. The efficiency and ease of implementation of network linearization can hopefully popularize the physics-related image quality measures for DL applications. Our methodology is general; it allows flexible compositions of DL nonlinear modules and linear operators such as filtered-backprojection (FBP). For the latter, we develop a generic method for computing the covariance images that is needed for network linearization.

Image quality models for 2D and 3D x-ray imaging systems: A perspective vignette

Image quality models based on cascaded systems analysis and task-based imaging performance were an important aspect of the emergence of 2D and 3D digital x-ray systems over the last 25 years. This perspective vignette offers cursory review of such developments and personal insights that may not be obvious within previously published scientific literature. The vignette traces such models to the mid-1990s, when flat-panel x-ray detectors were emerging as a new base technology for digital radiography and benefited from the rigorous, objective characterization of imaging performance gained from such models. The connection of models for spatial resolution and noise to spatial-frequency-dependent descriptors of imaging task provided a useful framework for system optimization that helped to accelerate the development of new technologies to first clinical use. Extension of the models to new technologies and applications is also described, including dual-energy imaging, photon-counting detectors, phase contrast imaging, tomosynthesis, cone-beam CT, 3D image reconstruction, and image registration.

Design Optimization of Spatial-Spectral Filters for Cone-Beam CT Material Decomposition

Spectral CT has shown promise for high-sensitivity quantitative imaging and material decomposition. This work presents a new device called a spatial-spectral filter (SSF) which consists of a tiled array of filter materials positioned near the x-ray source that is used to modulate the spectral shape of the x-ray beam. The filter is moved to obtain projection data that is sparse in each spectral channel. To process this sparse data, we employ a one-step direct model-based material decomposition (MBMD) to reconstruct basis material density images directly from the SSF CT data. To evaluate different possible SSF designs, we define a new Fisher-information-based predictive image quality metric called separability index which characterizes the ability of a spectral CT system to distinguish between the signals from two or more materials. This spectral CT performance metric can be used to optimize spectral CT system design. We conducted simulation-based design optimization study to find optimized combinations of filter materials, filter thicknesses, filter widths, and source settings. Finally, we present MBMD results using simulated SSF CT measurements from the optimized designs to demonstrate the ability to reconstruct basis material density images and to show the benefits of the optimized designs. Our results indicate that optimizing SSF CT for separability leads to high-performance at material discrimination tasks.

Source-detector trajectory optimization in cone-beam computed tomography: a comprehensive review on today’s state-of-the-art

Cone-beam computed tomography (CBCT) imaging is becoming increasingly important for a wide range of applications such as image-guided surgery, image-guided radiation therapy as well as diagnostic imaging such as breast and orthopaedic imaging. The potential benefits of non-circular source-detector trajectories was recognized in early work to improve the completeness of CBCT sampling and extend the field of view (FOV). Another important feature of interventional imaging is that prior knowledge of patient anatomy such as a preoperative CBCT or prior CT is commonly available. This provides the opportunity to integrate such prior information into the image acquisition process by customized CBCT source-detector trajectories. Such customized trajectories can be designed in order to optimize task-specific imaging performance, providing intervention or patient-specific imaging settings. The recently developed robotic CBCT C-arms as well as novel multi-source CBCT imaging systems with additional degrees of freedom provide the possibility to largely expand the scanning geometries beyond the conventional circular source-detector trajectory. This recent development has inspired the research community to innovate enhanced image quality by modifying image geometry, as opposed to hardware or algorithms. The recently proposed techniques in this field facilitate image quality improvement, FOV extension, radiation dose reduction, metal artifact reduction as well as 3D imaging under kinematic constraints. Because of the great practical value and the increasing importance of CBCT imaging in image-guided therapy for clinical and preclinical applications as well as in industry, this paper focuses on the review and discussion of the available literature in the CBCT trajectory optimization field. To the best of our knowledge, this paper is the first study that provides an exhaustive literature review regarding customized CBCT algorithms and tries to update the community with the clarification of in-depth information on the current progress and future trends.

Quantitative measurements of emphysema in ultra-high resolution computed tomography using model-based iterative reconstruction in comparison to that using hybrid iterative reconstruction

The percentage of low attenuation volume ratio (LAVR), which is measured using computed tomography (CT), is an index of the severity of emphysema. For LAVR evaluation, ultra-high-resolution (U-HR) CT images are useful. To improve the image quality of U-HRCT, iterative reconstruction is used. There are two types of iterative reconstruction: hybrid iterative reconstruction (HIR) and model-based iterative reconstruction (MBIR). In this study, we physically and clinically evaluated U-HR images reconstructed with HIR and MBIR, and demonstrated the usefulness of U-HR images with MBIR for quantitative measurements of emphysema. Both images were reconstructed with a slice thickness of 0.25 mm and an image matrix size of 1024 × 1024 pixels. For physical evaluation, the modulation transfer function (MTF) and noise power spectrum (NPS) of HIR and MBIR were compared. For clinical evaluation, LAVR calculated from HIR and MBIR were compared using the Wilcoxon matched-pairs signed-rank test. In addition, the correlation between LAVR and forced expiratory volume in one second (FEV₁%) was evaluated using the Spearman rank correlation test. The MTFs of HIR and MBIR were comparable. The NPS of MBIR was lower than that of HIR. The mean LAVR values calculated from HIR and MBIR were 19.5 ± 12.6% and 20.4 ± 11.7%, respectively (p = 0.84). The correlation coefficients between LAVR and FEV₁% that were taken from HIR and MBIR were 0.64 and 0.74, respectively (p < 0.01). MBIR is more useful than HIR for the quantitative measurements of emphysema with U-HR images.

Combined diffusion-relaxometry microstructure imaging: Current status and future prospects

Microstructure imaging seeks to noninvasively measure and map microscopic tissue features by pairing mathematical modeling with tailored MRI protocols. This article reviews an emerging paradigm that has the potential to provide a more detailed assessment of tissue microstructure-combined diffusion-relaxometry imaging. Combined diffusion-relaxometry acquisitions vary multiple MR contrast encodings-such as b-value, gradient direction, inversion time, and echo time-in a multidimensional acquisition space. When paired with suitable analysis techniques, this enables quantification of correlations and coupling between multiple MR parameters-such as diffusivity, T 1 , T 2 , and T 2 ∗ . This opens the possibility of disentangling multiple tissue compartments (within voxels) that are indistinguishable with single-contrast scans, enabling a new generation of microstructural maps with improved biological sensitivity and specificity.

Optimizing constrained reconstruction in magnetic resonance imaging for signal detection

Constrained reconstruction in magnetic resonance imaging (MRI) allows the use of prior information through constraints to improve reconstructed images. These constraints often take the form of regularization terms in the objective function used for reconstruction. Constrained reconstruction leads to images which appear to have fewer artifacts than reconstructions without constraints but because the methods are typically nonlinear, the reconstructed images have artifacts whose structure is hard to predict. In this work, we compared different methods of optimizing the regularization parameter using a total variation (TV) constraint in the spatial domain and sparsity in the wavelet domain for one-dimensional (2.56×) undersampling using variable density undersampling. We compared the mean squared error (MSE), structural similarity (SSIM), L-curve and the area under the receiver operating characteristic (AUC) using a linear discriminant for detecting a small and a large signal. We used a signal-known-exactly task with varying backgrounds in a simulation where the anatomical variation was the major source of clutter for the detection task. Our results show that the AUC dependence on regularization parameters varies with the imaging task (i.e. the signal being detected). The choice of regularization parameters for MSE, SSIM, L-curve and AUC were similar. We also found that a model-based reconstruction including TV and wavelet sparsity did slightly better in terms of AUC than just enforcing data consistency but using these constraints resulted in much better MSE and SSIM. These results suggest that the increased performance in MSE and SSIM over-estimate the improvement in detection performance for the tasks in this paper. The MSE and SSIM metrics show a big difference in performance where the difference in AUC is small. To our knowledge, this is the first time that signal detection with varying backgrounds has been used to optimize constrained reconstruction in MRI.

Local perturbation responses and checkerboard tests: Characterization tools for nonlinear MRI methods

PURPOSE

Modern methods for MR image reconstruction, denoising, and parameter mapping are becoming increasingly nonlinear, black-box, and at risk of "hallucination." These trends mean that traditional tools for judging confidence in an image (visual quality assessment, point-spread functions (PSFs), g-factor maps, etc.) are less helpful than before. This paper describes and evaluates an approach that can help with assessing confidence in images produced by arbitrary nonlinear methods.

THEORY AND METHODS

We propose to characterize nonlinear methods by examining the images they produce before and after applying controlled perturbations to the measured data. This results in functions known as local perturbation responses (LPRs) that can provide useful insight into sensitivity, spatial resolution, and aliasing characteristics. LPRs can be viewed as generalizations of classical PSFs, and are are very flexible-they can be applied to arbitary nonlinear methods and arbitrary datasets across a range of different reconstruction, denoising, and parameter mapping applications. Importantly, LPRs do not require a ground truth image.

RESULTS

Impulse-based and checkerboard-pattern LPRs are demonstrated in image reconstruction and denoising scenarios. We observe that these LPRs provide insights into spatial resolution, signal leakage, and aliasing that are not available with other methods. We also observe that popular reference-based image quality metrics (eg, mean-squared error and structural similarity) do not always correlate with good LPR characteristics.

CONCLUSIONS

LPRs are a useful tool that can be used to characterize and assess confidence in nonlinear MR methods, and provide insights that are distinct from and complementary to existing quality assessments.

Location and direction dependence in the 3D MTF for a high-resolution CT system

PURPOSE

The purpose of this study was to quantify location and direction-dependent variations in the 3D modulation transfer function (MTF) of a high-resolution CT scanner with selectable focal spot sizes and resolution modes.

METHODS

The Aquilion Precision CT scanner (Canon Medical Systems) has selectable 0.25 mm or 0.5 mm detectors (by binning) in both the axial (x-y) and detector array width (z) directions. For the x-y and z orientations, detectors are configured (x-y) = 0.5 mm/(z) = 0.5 mm for normal resolution (NR), 0.25/0.5 mm for high resolution (HR), and 0.25/0.25 mm for super high resolution (SHR). Six focal spots (FS1-FS6) range in size from 0.4 (x-y) × 0.5 mm (z) for FS1 to 1.6 × 1.4 mm for FS6. Phantoms fabricated from spherical objects were positioned at radial distances of 0, 4.0, 7.5, 11.0, 14.5, and 18.5 cm. Axial and helical acquisitions were utilized and reconstructed using filtered back projection with the FC18 "Body," FC30 "Bone," and FC81 "Bone Sharp" kernels. The reconstructions were used to measure a 1D slice of the 3D MTF by oversampling the 3D ESF in the axial plane [MTF(f_r ); φ = 0°)], 45° out of the axial plane [MTF(f_r ); φ = 45°)], in the longitudinal direction [MTF(f_r ); φ = 80°)], and along the radial and azimuthal directions within the axial plane.

RESULTS

The MTF(f_r ); φ = 45°) drops to 10% (f₁₀ ) at 1.20, 1.45, and 2.06 mm^-1 for NR, HR, and SHR, respectively, for a helical acquisition with FS1, FC30, and r = 4 cm from the isocenter. The MTF(f_r ); φ = 45°) includes contributions of both the axial-plane MTF (f₁₀  = 1.10, 2.04, and 2.01 mm^-1 ) and the longitudinal MTF (f₁₀  = 1.17, 1.18, and 1.82 mm^-1 ) for the NR, HR, and SHR modes, respectively. For SHR, the axial scan mode showed a 15-25% improvement over helical mode in the longitudinal resolution. Helical pitch, ranging from 0.569 to 1.381, did not appreciably affect the 3D resolution (<2%). The radial MTFs across the axial field of view (FOV) showed dependencies on the focal spot length in z; for example, for SHR with FS2 (0.6 × 0.6 mm), f₁₀ at  r = 11 cm was within 17% of the value at r = 4 cm, but for SHR with FS3 (0.6 × 1.3), the reduction in f₁₀ was 46% from 4 to 11 cm from the isocenter. The azimuthal MTF also decreased as r increased but less so for longer gantry rotation times and smaller focal spot dimensions in the axial plane. The longitudinal MTF was minimally affected (<11%) by position in the FOV and was principally affected by the focal spot length in the z-dimension.

CONCLUSIONS

The 3D MTF was measured throughout the FOV of a high-resolution CT scanner, quantifying the advantages of different resolution modes and focal spot sizes on the axial-plane and longitudinal MTF. Reconstruction kernels were shown to impact axial-plane resolution, imparting non-isotropic 3D resolution characteristics. Focal spot size (both in x-y and in z) and gantry rotation time play important roles in preserving the high-resolution characteristics throughout the field of view for this new high-resolution CT scanner technology.

Accelerated 3D image reconstruction with a morphological pyramid and noise-power convergence criterion

Model-based iterative reconstruction (MBIR) for cone-beam CT (CBCT) offers better noise-resolution tradeoff and image quality than analytical methods for acquisition protocols with low x-ray dose or limited data, but with increased computational burden that poses a drawback to routine application in clinical scenarios. This work develops a comprehensive framework for acceleration of MBIR in the form of penalized weighted least squares optimized with ordered subsets separable quadratic surrogates. The optimization was scheduled on a set of stages forming a morphological pyramid varying in voxel size. Transition between stages was controlled with a convergence criterion based on the deviation between the mid-band noise power spectrum (NPS) measured on a homogeneous region of the evolving reconstruction and that expected for the converged image, computed with an analytical model that used projection data and the reconstruction parameters. A stochastic backprojector was developed by introducing a random perturbation to the sampling position of each voxel for each ray in the reconstruction within a voxel-based backprojector, breaking the deterministic pattern of sampling artifacts when combined with an unmatched Siddon forward projector. This fast, forward and backprojector pair were included into a multi-resolution reconstruction strategy to provide support for objects partially outside of the field of view. Acceleration from ordered subsets was combined with momentum accumulation stabilized with an adaptive technique that automatically resets the accumulated momentum when it diverges noticeably from the current iteration update. The framework was evaluated with CBCT data of a realistic abdomen phantom acquired on an imaging x-ray bench and with clinical CBCT data from an angiography robotic C-arm (Artis Zeego, Siemens Healthineers, Forchheim, Germany) acquired during a liver embolization procedure. Image fidelity was assessed with the structural similarity index (SSIM) computed with a converged reconstruction. The accelerated framework provided accurate reconstructions in 60 s (SSIM = 0.97) and as little as 27 s (SSIM = 0.94) for soft-tissue evaluation. The use of simple forward and backprojectors resulted in 9.3× acceleration. Accumulation of momentum provided extra ∼3.5× acceleration with stable convergence for 6-30 subsets. The NPS-driven morphological pyramid resulted in initial faster convergence, achieving similar SSIM with 1.5× lower runtime than the single-stage optimization. Acceleration of MBIR to provide reconstruction time compatible with clinical applications is feasible via architectures that integrate algorithmic acceleration with approaches to provide stable convergence, and optimization schedules that maximize convergence speed.

High-Resolution Oscillating Steady-State fMRI Using Patch-Tensor Low-Rank Reconstruction

The goals of fMRI acquisition include high spatial and temporal resolutions with a high signal to noise ratio (SNR). Oscillating Steady-State Imaging (OSSI) is a new fMRI acquisition method that provides large oscillating signals with the potential for high SNR, but does so at the expense of spatial and temporal resolutions. The unique oscillation pattern of OSSI images makes it well suited for high-dimensional modeling. We propose a patch-tensor low-rank model to exploit the local spatial-temporal low-rankness of OSSI images. We also develop a practical sparse sampling scheme with improved sampling incoherence for OSSI. With an alternating direction method of multipliers (ADMM) based algorithm, we improve OSSI spatial and temporal resolutions with a factor of 12 acquisition acceleration and 1.3 mm isotropic spatial resolution in prospectively undersampled experiments. The proposed model yields high temporal SNR with more activation than other low-rank methods. Compared to the standard grad- ient echo (GRE) imaging with the same spatial-temporal resolution, 3D OSSI tensor model reconstruction demonstrates 2 times higher temporal SNR with 2 times more functional activation.

Multidimensional correlation spectroscopic imaging of exponential decays: From theoretical principles to in vivo human applications

Multiexponential modeling of relaxation or diffusion MR signal decays is a popular approach for estimating and spatially mapping different microstructural tissue compartments. While this approach can be quite powerful, it is also limited by the fact that one-dimensional multiexponential modeling is an ill-posed inverse problem with substantial ambiguities. In this article, we present an overview of a recent multidimensional correlation spectroscopic imaging approach to this problem. This approach helps to alleviate ill-posedness by making advantageous use of multidimensional contrast encoding (e.g., 2D diffusion-relaxation encoding or 2D relaxation-relaxation encoding) combined with a regularized spatial-spectral estimation procedure. Theoretical calculations, simulations, and experimental results are used to illustrate the benefits of this approach relative to classical methods. In addition, we demonstrate an initial proof-of-principle application of this kind of approach to in vivo human MRI experiments.

CHARACTERIZATION OF TWO CT SYSTEMS USING A CHANNELIZED HOTELLING OBSERVER AND NPS METRIC

We investigated the performances of two computed tomography (CT) systems produced by the same manufacturers (Somatom Flash and Edge Siemens) with different detector technologies (Ultrafast Ceramic and Stellar) and different generation of iterative reconstruction (IR) algorithms (SAFIRE and ADMIRE). A homemade phantom was scanned and the images were reconstructed with filtered back-projection (FBP) and IR algorithms. In terms of image quality, the performances of the systems were checked using the low-contrast detectability, evaluated by a Channelized Hotelling Observer (CHO), and the noise power spectrum (NPS). The analysis with CHO showed the best performance of Edge respect to Flash system for both FBP and IR algorithms. This better behavior, which reaches 20%, has been ascribed to the Stellar detector. From the NPS analysis, the noise reduction due to Stellar detector was 57%, moreover ADMIRE algorithm preserves a more traditional CT image texture appearance versus SAFIRE due to a lower NPS peak shift.

Bootstrap-Optimised Regularised Image Reconstruction for Emission Tomography

In emission tomography, iterative image reconstruction from noisy measured data usually results in noisy images, and so regularisation is often used to compensate for noise. However, in practice, an appropriate, automatic and precise specification of the strength of regularisation for image reconstruction from a given noisy measured dataset remains unresolved. Existing approaches are either empirical approximations with no guarantee of generalisation, or else are computationally intensive cross-validation methods requiring full reconstructions for a limited set of preselected regularisation strengths. In contrast, we propose a novel methodology embedded within iterative image reconstruction, using one or more bootstrapped replicates of the measured data for precise optimisation of the regularisation. The approach uses a conventional unregularised iterative update of a current image estimate from the noisy measured data, and then also uses the bootstrap replicate to obtain a bootstrap update of the current image estimate. The method then seeks the regularisation hyperparameters which, when applied to the bootstrap update of the image, lead to a best fit of the regularised bootstrap update to the conventional measured data update. This corresponds to estimating the degree of regularisation needed in order to map the noisy update to a model of the mean of an ensemble of noisy updates. For a given regularised objective function (e.g. penalised likelihood), no hyperparameter selection or tuning is required. The method is demonstrated for positron emission tomography (PET) data at different noise levels, and delivers near-optimal reconstructions (in terms of reconstruction error) without any knowledge of the ground truth, nor any form of training data.

Image domain multi-material decomposition using single energy CT

Multi-material decomposition (MMD) technique decomposes the CT images into basis material images and has been promising in clinical practice for material composition quantification within the human body. MMD could be implemented using the image data acquired from spectral CT or its special case, dual-energy CT (DECT) while the spectral CT data acquisition usually requires a hardware modification. In this paper, we propose an image domain MMD method using single energy CT (SECT). The proposed objective function applies a least square data fidelity term to enforce the minimization between the linear combination of decomposed material image and the measured SECT image, and an edge-preserving (EP) regularization term to meet the piecewise constant property of the material image. We apply the optimization transfer principle to form a pixel-wise separable quadratic surrogate (PWSQS) function in each iteration to decrease the objective function. The pixelwise direct inversion method assisted by the two-material assumption (TMA) is applied to obtain a good initial value. The proposed method is evaluated using a digital phantom, a Catphan phantom and the clinical data. A low-pass filtration method is implemented for a comparison purpose. In the phantom study, the proposed TMA method achieves high volume fraction accuracy (VFA) of 79.64% and the proposed EP method further increases the VFA by 15.56% and decreases the decomposition standard deviation (STD) by 81.51% compared with the TMA method. At the comparable noise level, the proposed EP method increases spatial resolution by an overall factor of 1.01 when the modulation transfer function magnitude is decreased to 50% compared with the low-pass filtration method. In clinical data study, the virtual non-contrast image generated by the proposed method achieves the root-mean-squared-relative error of 2.93% compared with the contrast-free ground-truth image.

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.

Image Reconstruction: From Sparsity to Data-adaptive Methods and Machine Learning

The field of medical image reconstruction has seen roughly four types of methods. The first type tended to be analytical methods, such as filtered back-projection (FBP) for X-ray computed tomography (CT) and the inverse Fourier transform for magnetic resonance imaging (MRI), based on simple mathematical models for the imaging systems. These methods are typically fast, but have suboptimal properties such as poor resolution-noise trade-off for CT. A second type is iterative reconstruction methods based on more complete models for the imaging system physics and, where appropriate, models for the sensor statistics. These iterative methods improved image quality by reducing noise and artifacts. The FDA-approved methods among these have been based on relatively simple regularization models. A third type of methods has been designed to accommodate modified data acquisition methods, such as reduced sampling in MRI and CT to reduce scan time or radiation dose. These methods typically involve mathematical image models involving assumptions such as sparsity or low-rank. A fourth type of methods replaces mathematically designed models of signals and systems with data-driven or adaptive models inspired by the field of machine learning. This paper focuses on the two most recent trends in medical image reconstruction: methods based on sparsity or low-rank models, and data-driven methods based on machine learning techniques.

Joint B0 and image estimation integrated with model based reconstruction for field map update and distortion correction in prostate diffusion MRI

In prostate Diffusion Weighted MRI, differences in susceptibility values exist at the interface between the prostate and rectal-air. This can result in off-resonance magnetic field leading to geometric distortions including signal stretching and signal pile-up in the reconstructed images. Using a set of EPI data acquired with blip-up and blip-down phase encoding gradient directions, model based reconstruction has recently been proposed that can correct these distortions by using a B0 field estimated from a separate B0 scan. However, change in the size of the rectal air region across time can occur that can result in a mismatch of the B0 field to the EPI scan. Also, the measured B0 field itself can be erroneous in regions of low Signal to Noise ratio around the prostate rectal air interface. In this work, using a set of single shot EPI data acquired with blip-up and blip-down phase encoding gradient directions, a novel joint model based reconstruction is proposed that can account for changes in the off resonance effects between the B0 and EPI scans. For ten prostate patients, using a measured B0 field as an initial B0 estimate, on a 5-point scale (1-5) image quality scores evaluated by an experienced radiologist, the proposed framework achieved scores of 3.50 ± 0.85 and 3.40 ± 0.51 for b-values of 0 and 500 s/mm2, respectively compared to 3.40 ± 0.70 and 3.30 ± 0.67 for model based reconstruction. The proposed framework is also capable of estimating a distortion corrected EPI image even without an initial B0 field estimate in situations where a separate B0 scan cannot be obtained due to time constraint.

A deep learning reconstruction framework for X-ray computed tomography with incomplete data

As a powerful imaging tool, X-ray computed tomography (CT) allows us to investigate the inner structures of specimens in a quantitative and nondestructive way. Limited by the implementation conditions, CT with incomplete projections happens quite often. Conventional reconstruction algorithms are not easy to deal with incomplete data. They are usually involved with complicated parameter selection operations, also sensitive to noise and time-consuming. In this paper, we reported a deep learning reconstruction framework for incomplete data CT. It is the tight coupling of the deep learning U-net and CT reconstruction algorithm in the domain of the projection sinograms. The U-net estimated results are not the artifacts caused by the incomplete data, but the complete projection sinograms. After training, this framework is determined and can reconstruct the final high quality CT image from a given incomplete projection sinogram. Taking the sparse-view and limited-angle CT as examples, this framework has been validated and demonstrated with synthetic and experimental data sets. Embedded with CT reconstruction, this framework naturally encapsulates the physical imaging model of CT systems and is easy to be extended to deal with other challenges. This work is helpful to push the application of the state-of-the-art deep learning techniques in the field of CT.

Sparsity promoting regularization for effective noise suppression in SPECT image reconstruction

The purpose of this research is to develop an advanced reconstruction method for low-count, hence high-noise, single-photon emission computed tomography (SPECT) image reconstruction. It consists of a novel reconstruction model to suppress noise while conducting reconstruction and an efficient algorithm to solve the model. A novel regularizer is introduced as the nonconvex denoising term based on the approximate sparsity of the image under a geometric tight frame transform domain. The deblurring term is based on the negative log-likelihood of the SPECT data model. To solve the resulting nonconvex optimization problem a preconditioned fixed-point proximity algorithm (PFPA) is introduced. We prove that under appropriate assumptions, PFPA converges to a local solution of the optimization problem at a global O ( 1 / k ) convergence rate. Substantial numerical results for simulation data are presented to demonstrate the superiority of the proposed method in denoising, suppressing artifacts and reconstruction accuracy. We simulate noisy 2D SPECT data from two phantoms: hot Gaussian spheres on random lumpy warm background, and the anthropomorphic brain phantom, at high- and low-noise levels (64k and 90k counts, respectively), and reconstruct them using PFPA. We also perform limited comparative studies with selected competing state-of-the-art total variation (TV) and higher-order TV (HOTV) transform-based methods, and widely used post-filtered maximum-likelihood expectation-maximization. We investigate imaging performance of these methods using: contrast-to-noise ratio (CNR), ensemble variance images (EVI), background ensemble noise (BEN), normalized mean-square error (NMSE), and channelized hotelling observer (CHO) detectability. Each of the competing methods is independently optimized for each metric. We establish that the proposed method outperforms the other approaches in all image quality metrics except NMSE where it is matched by HOTV. The superiority of the proposed method is especially evident in the CHO detectability tests results. We also perform qualitative image evaluation for presence and severity of image artifacts where it also performs better in terms of suppressing 'staircase' artifacts, as compared to TV methods. However, edge artifacts on high-contrast regions persist. We conclude that the proposed method may offer a powerful tool for detection tasks in high-noise SPECT imaging.

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.

Improved statistical efficiency of simultaneous multi-slice fMRI by reconstruction with spatially adaptive temporal smoothing

We introduce an approach to reconstruction of simultaneous multi-slice (SMS)-fMRI data that improves statistical efficiency. The method incorporates regularization to adjust temporal smoothness in a spatially varying, encoding-dependent manner, reducing the g-factor noise amplification per temporal degree of freedom. This results in a net improvement in tSNR and GLM efficiency, where the efficiency gain can be derived analytically as a function of the encoding and reconstruction parameters. Residual slice leakage and aliasing is limited when fMRI signal energy is dominated by low frequencies. Analytical predictions, simulated and experimental results demonstrate a marked improvement in statistical efficiency in the temporally regularized reconstructions compared to conventional slice-GRAPPA reconstructions, particularly in central brain regions. Furthermore, experimental results confirm that residual slice leakage and aliasing errors are not noticeably increased compared to slice-GRAPPA reconstruction. This approach to temporally regularized image reconstruction in SMS-fMRI improves statistical power, and allows for explicit choice of reconstruction parameters by directly assessing their impact on noise variance per degree of freedom.

Convolutional Analysis Operator Learning: Acceleration and Convergence

Convolutional operator learning is gaining attention in many signal processing and computer vision applications. Learning kernels has mostly relied on so-called patch-domain approaches that extract and store many overlapping patches across training signals. Due to memory demands, patch-domain methods have limitations when learning kernels from large datasets - particularly with multi-layered structures, e.g., convolutional neural networks - or when applying the learned kernels to high-dimensional signal recovery problems. The so-called convolution approach does not store many overlapping patches, and thus overcomes the memory problems particularly with careful algorithmic designs; it has been studied within the "synthesis" signal model, e.g., convolutional dictionary learning. This paper proposes a new convolutional analysis operator learning (CAOL) framework that learns an analysis sparsifying regularizer with the convolution perspective, and develops a new convergent Block Proximal Extrapolated Gradient method using a Majorizer (BPEG-M) to solve the corresponding block multi-nonconvex problems. To learn diverse filters within the CAOL framework, this paper introduces an orthogonality constraint that enforces a tight-frame filter condition, and a regularizer that promotes diversity between filters. Numerical experiments show that, with sharp majorizers, BPEG-M significantly accelerates the CAOL convergence rate compared to the state-of-the-art block proximal gradient (BPG) method. Numerical experiments for sparse-view computational tomography show that a convolutional sparsifying regularizer learned via CAOL significantly improves reconstruction quality compared to a conventional edge-preserving regularizer. Using more and wider kernels in a learned regularizer better preserves edges in reconstructed images.

Image reconstruction for interrupted-beam x-ray CT on diagnostic clinical scanners

Low-dose x-ray CT is a major research area with high clinical impact. Compressed sensing using view-based sparse sampling and sparsity-promoting regularization has shown promise in simulations, but these methods can be difficult to implement on diagnostic clinical CT scanners since the x-ray beam cannot be switched on and off rapidly enough. An alternative to view-based sparse sampling is interrupted-beam sparse sampling. SparseCT is a recently-proposed interrupted-beam scheme that achieves sparse sampling by blocking a portion of the beam using a multislit collimator (MSC). The use of an MSC necessitates a number of modifications to the standard compressed sensing reconstruction pipeline. In particular, we find that SparseCT reconstruction is feasible within a model-based image reconstruction framework that incorporates data fidelity weighting to consider penumbra effects and source jittering to consider the effect of partial source obstruction. Here, we present these modifications and demonstrate their application in simulations and real-world prototype scans. In simulations compared to conventional low-dose acquisitions, SparseCT is able to achieve smaller normalized root-mean square differences and higher structural similarity measures on two reduction factors. In prototype experiments, we successfully apply our reconstruction modifications and maintain image resolution at quarter-dose reduction level. The SparseCT design requires only small hardware modifications to current diagnostic clinical scanners, opening up new possibilities for CT dose reduction.

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).

Prior-Guided Metal Artifact Reduction for Iterative X-Ray Computed Tomography

High-attenuation materials pose significant challenges to computed tomographic imaging. Formed of high mass-density and high atomic number elements, they cause more severe beam hardening and scattering artifacts than do water-like materials. Pre-corrected line-integral density measurements are no longer linearly proportional to the path lengths, leading to reconstructed image suffering from streaking artifacts extending from metal, often along highest-density directions. In this paper, a novel prior-based iterative approach is proposed to reduce metal artifacts. It combines the superiority of statistical methods with the benefits of sinogram completion methods to estimate and correct metal-induced biases. Preliminary results show minimized residual artifacts and significantly improved image quality.

Local response prediction in model-based CT material decomposition

Spectral CT is an emerging modality that permits material decomposition and density estimation through the use of energy-dependent information in measurements. Direct model-based material decomposition algorithms have been developed that incorporate statistical models and advanced regularization schemes to improve density estimates and lower exposure requirements. However, understanding and control of the relationship between regularization and image properties is complex with interactions between spectral channels and material bases. In particular, regularization in one material basis can affect the image properties of other material bases, and vice versa. In this work, we derived a closed-form set of local impulse responses for the solutions to a general, regularized, model-based material decomposition (MBMD) objective. These predictors quantify both the spatial resolution in each material image as well as the influence of regularization of one material basis on other material images. This information can be used prospectively to tune regularization parameters for specific imaging goals.

Generalized Prediction Framework for Reconstructed Image Properties using Neural Networks

Model-based reconstruction (MBR) algorithms in CT have demonstrated superior dose-image quality tradeoffs compared to traditional analytical methods. However, the nonlinear and data-dependent nature of these algorithms pose significant challenges for performance evaluation and parameter optimization. To address these challenges, this work presents an analysis framework for quantitative and predictive modeling of image properties in general nonlinear MBR algorithms. We propose to characterize the reconstructed appearance of arbitrary stimuli by the generalized system response function that accounts for dependence on the imaging conditions, reconstruction parameters, object, and the stimulus itself (size, contrast, location). We estimate this nonlinear function using a multilayer perceptron neural network by providing input and output pairs that samples the range of imaging parameters of interest. The feasibility of this approach was demonstrated for predicting the appearance of a spiculated lesion reconstructed by a penalized-likelihood objective with a Huber penalty in a physical phantom as a function of its location and reconstruction parameters β and δ. The generalized system response functions predicted from the trained neural network show good agreement with those computed from mean reconstructions, proving the ability of the framework in mapping out the nonlinear function for combinations of imaging parameters not present in the training data. We demonstrated utility of the framework to achieve desirable (e.g., non-blocky) lesion appearance in arbitrary locations in the phantom without the need for performing actual reconstructions. The proposed prediction framework permits efficient and quantifiable performance evaluations to provide robust control and understanding of image properties for general classes of nonlinear MBR algorithms.

Sparse sampling and reconstruction for an optoacoustic ultrasound volumetric hand-held probe

Accurate anatomical localization of functional information is the main goal of hybridizing optoacoustic and ultrasound imaging, with the promise of early stage diagnosis and disease pathophysiology. Optoacoustic integration to ultrasound is a relatively mature technique for clinical two-dimensional imaging, however the complexity of biological samples places particular demands for volumetric measurement and reconstruction. This integration is a multi-fold challenge that is mainly associated with the system geometry, the sampling and beam quality. In this study, we evaluated the design geometry for the sparse ultrasonic hand-held probe that is popularly associated with three-dimensional imaging of anatomical deformation, to incorporate the three-dimensional optoacoustic physiological information. We explored the imaging performance of three unconventional annular geometries; namely, segmented, spiral, and circular geometries. To avoid bias evaluation, two classes of analytical and model-based algorithms were used. The superior performance of the segmented annular array for recovery of the true object is demonstrated. Along with the model-based approach, this geometry offers spatial invariant resolution for the optoacoustic mode for the given field of view.The analytical approach, on the other hand, is computationally less expensive and is the method of choice for ultrasound imaging. Our design can potentially evolve into a valuable diagnostic tool, particularly for vascular-related disease.

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.

Optimization-Based Image Reconstruction From Low-Count, List-Mode TOF-PET Data

OBJECTIVE

We investigate an optimization-based approach to image reconstruction from list-mode data in digital time-of-flight (TOF) positron emission tomography (PET) imaging.

METHOD

In the study, the image to be reconstructed is designed as a solution to a convex, non-smooth optimization program, and a primal-dual algorithm is developed for image reconstruction by solving the optimization program. The algorithm is first applied to list-mode TOF-PET data of a typical count level from physical phantoms and a human subject. Subsequently, we explore the algorithm's potential for image reconstruction in low-dose and/or fast TOF-PET imaging of practical interest by applying the algorithm to list-mode TOF-PET data of different, low-count levels from the same physical phantoms and human subject.

RESULTS

Visual inspection and quantitative-metric analysis reveal that the optimization reconstruction approach investigated can yield images with enhanced spatial and contrast resolution, suppressed image noise, and increased axial volume coverage over the reference images obtained with a standard clinical reconstruction algorithm especially for low-dose TOF-PET data.

SIGNIFICANCE

The optimization-based reconstruction approach can be exploited for yielding insights into potential quality upper bound of reconstructed images in, and design of scanning protocols of, TOF-PET imaging of practical significance.

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 Analysis and Design for Prior-Image-Based X-Ray CT Reconstruction

Prior-image-based reconstruction (PIBR) methods have demonstrated great potential for radiation dose reduction in computed tomography applications. PIBR methods take advantage of shared anatomical information between sequential scans by incorporating a patient-specific prior image into the reconstruction objective function, often as a form of regularization. However, one major challenge with PIBR methods is how to optimally determine the prior image regularization strength which balances anatomical information from the prior image with data fitting to the current measurements. Too little prior information yields limited improvements over traditional model-based iterative reconstruction, while too much prior information can force anatomical features from the prior image not supported by the measurement data, concealing true anatomical changes. In this paper, we develop quantitative measures of the bias associated with PIBR. This bias exhibits as a fractional reconstructed contrast of the difference between the prior image and current anatomy, which is quite different from traditional reconstruction biases that are typically quantified in terms of spatial resolution or artifacts. We have derived an analytical relationship between the PIBR bias and prior image regularization strength and illustrated how this relationship can be used as a predictive tool to prospectively determine prior image regularization strength to admit specific kinds of anatomical change in the reconstruction. Because bias is dependent on local statistics, we further generalized shift-variant prior image penalties that permit uniform (shift invariant) admission of anatomical changes across the imaging field of view. We validated the mathematical framework in phantom studies and compared bias predictions with estimates based on brute force exhaustive evaluation using numerous iterative reconstructions across regularization values. The experimental results demonstrate that the proposed analytical approach can predict the bias-regularization relationship accurately, allowing for prospective determination of the prior image regularization strength in PIBR. Thus, the proposed approach provides an important tool for controlling image quality of PIBR methods in a reliable, robust, and efficient fashion.

Image quality and dose characteristics for an O-arm intraoperative imaging system with model-based image reconstruction

PURPOSE

To assess the imaging performance and radiation dose characteristics of the O-arm CBCT imaging system (Medtronic Inc., Littleton MA) and demonstrate the potential for improved image quality and reduced dose via model-based image reconstruction (MBIR).

METHODS

Two main studies were performed to investigate previously unreported characteristics of the O-arm system. First is an investigation of dose and 3D image quality achieved with filtered back-projection (FBP) - including enhancements in geometric calibration, handling of lateral truncation and detector saturation, and incorporation of an isotropic apodization filter. Second is implementation of an MBIR algorithm based on Huber-penalized likelihood estimation (PLH) and investigation of image quality improvement at reduced dose. Each study involved measurements in quantitative phantoms as a basis for analysis of contrast-to-noise ratio and spatial resolution as well as imaging of a human cadaver to test the findings under realistic imaging conditions.

RESULTS

View-dependent calibration of system geometry improved the accuracy of reconstruction as quantified by the full-width at half maximum of the point-spread function - from 0.80 to 0.65 mm - and yielded subtle but perceptible improvement in high-contrast detail of bone (e.g., temporal bone). Standard technique protocols for the head and body imparted absorbed dose of 16 and 18 mGy, respectively. For low-to-medium contrast (<100 HU) imaging at fixed spatial resolution (1.3 mm edge-spread function) and fixed dose (6.7 mGy), PLH improved CNR over FBP by +48% in the head and +35% in the body. Evaluation at different dose levels demonstrated 30% increase in CNR at 62% of the dose in the head and 90% increase in CNR at 50% dose in the body.

CONCLUSIONS

A variety of improvements in FBP implementation (geometric calibration, truncation and saturation effects, and isotropic apodization) offer the potential for improved image quality and reduced radiation dose on the O-arm system. Further gains are possible with MBIR, including improved soft-tissue visualization, low-dose imaging protocols, and extension to methods that naturally incorporate prior information of patient anatomy and/or surgical instrumentation.

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.

Assessing uncertainties in x-ray single-particle three-dimensional reconstruction

Modern technology for producing extremely bright and coherent x-ray laser pulses provides the possibility to acquire a large number of diffraction patterns from individual biological nanoparticles, including proteins, viruses, and DNA. These two-dimensional diffraction patterns can be practically reconstructed and retrieved down to a resolution of a few angstroms. In principle, a sufficiently large collection of diffraction patterns will contain the required information for a full three-dimensional reconstruction of the biomolecule. The computational methodology for this reconstruction task is still under development and highly resolved reconstructions have not yet been produced. We analyze the expansion-maximization-compression scheme, the current state of the art approach for this very challenging application, by isolating different sources of resolution-limiting factors. Through numerical experiments on synthetic data we evaluate their respective impact. We reach conclusions of relevance for handling actual experimental data, and we also point out certain improvements to the underlying estimation algorithm. We also introduce a practically applicable computational methodology in the form of bootstrap procedures for assessing reconstruction uncertainty in the real data case. We evaluate the sharpness of this approach and argue that this type of procedure will be critical in the near future when handling the increasing amount of data.