Mean and variance of implicitly defined biased estimators (such as penalized maximum likelihood): applications to tomography

Cramér-Rao Bound Optimized Subspace Reconstruction in Quantitative MRI

OBJECTIVE

We extend the traditional framework for estimating subspace bases in quantitative MRI that maximize the preserved signal energy to additionally preserve the Cramér-Rao bound (CRB) of the biophysical parameters and, ultimately, improve accuracy and precision in the quantitative maps.

METHODS

To this end, we introduce an approximate compressed CRB based on orthogonalized versions of the signal's derivatives with respect to the model parameters. This approximation permits singular value decomposition (SVD)-based minimization of both the CRB and signal losses during compression.

RESULTS

Compared to the traditional SVD approach, the proposed method better preserves the CRB across all biophysical parameters with minimal cost to the preserved signal energy, leading to reduced bias and variance of the parameter estimates in simulation. In vivo, improved accuracy and precision are observed in two quantitative neuroimaging applications.

CONCLUSION

The proposed method permits subspace reconstruction with a more compact basis, thereby offering significant computational savings.

SIGNIFICANCE

Efficient subspace reconstruction facilitates the validation and translation of advanced quantitative MRI techniques, e.g., magnetization transfer and diffusion.

Bias-reduced neural networks for parameter estimation in quantitative MRI

PURPOSE

To develop neural network (NN)-based quantitative MRI parameter estimators with minimal bias and a variance close to the Cramér-Rao bound.

THEORY AND METHODS

We generalize the mean squared error loss to control the bias and variance of the NN's estimates, which involves averaging over multiple noise realizations of the same measurements during training. Bias and variance properties of the resulting NNs are studied for two neuroimaging applications.

RESULTS

In simulations, the proposed strategy reduces the estimates' bias throughout parameter space and achieves a variance close to the Cramér-Rao bound. In vivo, we observe good concordance between parameter maps estimated with the proposed NNs and traditional estimators, such as nonlinear least-squares fitting, while state-of-the-art NNs show larger deviations.

CONCLUSION

The proposed NNs have greatly reduced bias compared to those trained using the mean squared error and offer significantly improved computational efficiency over traditional estimators with comparable or better accuracy.

Fast time-resolved micro-CT imaging of pharmaceutical tablets: Insights into water uptake and disintegration

We use dynamic micro-computed tomography (micro-CT) with a high temporal resolution to visualize water penetration through the porous network of immediate-release pharmaceutical solid tablets and characterize dynamic swelling and disintegration mechanisms. We process the micro-CT images using two theoretical scenarios that reflect different paths of pore structure evolution: a scenario where tablet porosity remains constant during the swelling process and a scenario where the tablet porosity progressively diminishes and eventually closes during the swelling process. We calculate the time evolution of the volume of water absorbed by the tablet and, specifically, absorbed by the excipients and the pore structure, as well as the formation and evolution of cracks. In turn, the three-dimensional disintegration pattern of the tablets is reconstructed. Restricting attention to the limiting scenario where tablet porosity is assumed fixed during the swelling process, we couple liquid penetration due to capillary pressure described by the Lucas-Washburn theory with the first-order swelling kinetics of the excipients to provide a physical interpretation of the experimental observations. We estimate model parameters that are in agreement with values reported in the literature, and we demonstrate that water penetration is dominated by intra-particle porosity rather than inter-particle porosity.

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.

Motion-compensated scheme for sequential scanned statistical iterative dual-energy CT reconstruction

Objective.Dual-energy computed tomography (DECT) has been widely used to reconstruct numerous types of images due its ability to better discriminate tissue properties. Sequential scanning is a popular dual-energy data acquisition method as it requires no specialized hardware. However, patient motion between two sequential scans may lead to severe motion artifacts in DECT statistical iterative reconstructions (SIR) images. The objective is to reduce the motion artifacts in such reconstructions.Approach.We propose a motion-compensation scheme that incorporates a deformation vector field into any DECT SIR. The deformation vector field is estimated via the multi-modality symmetric deformable registration method. The precalculated registration mapping and its inverse or adjoint are then embedded into each iteration of the iterative DECT algorithm.Main results.Results from a simulated and clinical case show that the proposed framework is capable of reducing motion artifacts in DECT SIRs. Percentage mean square errors in regions of interest in the simulated and clinical cases were reduced from 4.6% to 0.5% and 6.8% to 0.8%, respectively. A perturbation analysis was then performed to determine errors in approximating the continuous deformation by using the deformation field and interpolation. Our findings show that errors in our method are mostly propagated through the target image and amplified by the inverse matrix of the combination of the Fisher information and Hessian of the penalty term.Significance.We have proposed a novel motion-compensation scheme to incorporate a 3D registration method into the joint statistical iterative DECT algorithm in order to reduce motion artifacts caused by inter-scan motion, and successfully demonstrate that interscan motion corrections can be integrated into the DECT SIR process, enabling accurate imaging of radiological quantities on conventional SECT scanners, without significant loss of either computational efficiency or accuracy.

Advanced data analysis in inertial confinement fusion and high energy density physics

Bayesian analysis enables flexible and rigorous definition of statistical model assumptions with well-characterized propagation of uncertainties and resulting inferences for single-shot, repeated, or even cross-platform data. This approach has a strong history of application to a variety of problems in physical sciences ranging from inference of particle mass from multi-source high-energy particle data to analysis of black-hole characteristics from gravitational wave observations. The recent adoption of Bayesian statistics for analysis and design of high-energy density physics (HEDP) and inertial confinement fusion (ICF) experiments has provided invaluable gains in expert understanding and experiment performance. In this Review, we discuss the basic theory and practical application of the Bayesian statistics framework. We highlight a variety of studies from the HEDP and ICF literature, demonstrating the power of this technique. Due to the computational complexity of multi-physics models needed to analyze HEDP and ICF experiments, Bayesian inference is often not computationally tractable. Two sections are devoted to a review of statistical approximations, efficient inference algorithms, and data-driven methods, such as deep-learning and dimensionality reduction, which play a significant role in enabling use of the Bayesian framework. We provide additional discussion of various applications of Bayesian and machine learning methods that appear to be sparse in the HEDP and ICF literature constituting possible next steps for the community. We conclude by highlighting community needs, the resolution of which will improve trust in data-driven methods that have proven critical for accelerating the design and discovery cycle in many application areas.

On Ambiguity in Linear Inverse Problems: Entrywise Bounds on Nearly Data-Consistent Solutions and Entrywise Condition Numbers

Ill-posed linear inverse problems appear frequently in various signal processing applications. It can be very useful to have theoretical characterizations that quantify the level of ill-posedness for a given inverse problem and the degree of ambiguity that may exist about its solution. Traditional measures of ill-posedness, such as the condition number of a matrix, provide characterizations that are global in nature. While such characterizations can be powerful, they can also fail to provide full insight into situations where certain entries of the solution vector are more or less ambiguous than others. In this work, we derive novel theoretical lower- and upper-bounds that apply to individual entries of the solution vector, and are valid for all potential solution vectors that are nearly data-consistent. These bounds are agnostic to the noise statistics and the specific method used to solve the inverse problem, and are also shown to be tight. In addition, our results also lead us to introduce an entrywise version of the traditional condition number, which provides a substantially more nuanced characterization of scenarios where certain elements of the solution vector are less sensitive to perturbations than others. Our results are illustrated in an application to magnetic resonance imaging reconstruction, and we include discussions of practical computation methods for large-scale inverse problems, connections between our new theory and the traditional Cramér-Rao bound under statistical modeling assumptions, and potential extensions to cases involving constraints beyond just data-consistency.

Semi-mechanistic reduced order model of pharmaceutical tablet dissolution for enabling Industry 4.0 manufacturing systems

We propose a generalization of the Weibull dissolution model, referred to as generalized Weibull dissolution model, that seamlessly captures all three fractional dissolution rates experimentally observed in pharmaceutical solid tablets, namely decreasing, increasing, and non-monotonic rates. This is in contrast to traditional reduced order models, which capture at most two fractional dissolution rates and, thus, are not suitable for a wide range of product formulations hindering, for example, the adoption of knowledge management in the context of Industry 4.0. We extend the generalized Weibull dissolution model further to capture the relationship between critical process parameters (CPPs), critical materials attributes (CMAs), and dissolution profile to, in turn, facilitate real-time release testing (RTRT) and quality-by-control (QbC) strategies. Specifically, we endow the model with multivariate rational polynomials that interpolate the mechanistic limiting behavior of tablet dissolution as CPPs and CMAs approach certain values of physical significance (such as the upper and lower bounds of tablet porosity or lubrication conditions), thus the semi-mechanistic nature of the reduced order model. Restricting attention to direct compaction and using various case studies from the literature, we demonstrate the versatility and the capability of the semi-mechanistic ROM to estimate changes in dissolution due to process disturbances in tablet weight, porosity, lubrication conditions (i.e., the total amount of shear strain imparted during blending), and moisture content in the powder blend. In all of the cases considered in this work, the estimations of the model are in remarkable agreement with experimental data.

Probabilistic deconvolution of PET images using informed priors

Purpose

We present a probabilistic approach to medical image analysis that requires, and makes use of, explicit prior information provided by a medical expert. Depending on the choice of prior model the method can be used for image enhancement, analysis, and segmentation.

Methods

The methodology is based on a probabilistic approach to medical image analysis, that allows integration of 1) arbitrarily complex prior information (for which realizations can be generated), 2) information about a convolution operator of the imaging system, and 3) information about the noise in the reconstructed image into a posterior probability density. The method was demonstrated on positron emission tomography (PET) images obtained from a phantom and a patient with lung cancer. The likelihood model (multivariate log-normal) and the convolution operator were derived from phantom data. Two examples of prior information were used to show the potential of the method. The extended Metropolis-Hastings algorithm, a Markov chain Monte Carlo method, was used to generate realizations of the posterior distribution of the tracer activity concentration.

Results

A set of realizations from the posterior was used as the base of a quantitative PET image analysis. The mean and variance of activity concentrations were computed, as well as the probability of high tracer uptake and statistics on the size and activity concentration of high uptake regions. For both phantom and in vivo images, the estimated images of mean activity concentrations appeared to have reduced noise levels, and a sharper outline of high activity regions, as compared to the original PET. The estimated variance of activity concentrations was high at the edges of high activity regions.

Conclusions

The methodology provides a probabilistic approach for medical image analysis that explicitly takes into account medical expert knowledge as prior information. The presented first results indicate the potential of the method to improve the detection of small lesions. The methodology allows for a probabilistic measure of the size and activity level of high uptake regions, with possible long-term perspectives for early detection of cancer, as well as treatment, planning, and follow-up.

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.

On bias, variance, overfitting, gold standard and consensus in single-particle analysis by cryo-electron microscopy

Cryo-electron microscopy (cryoEM) has become a well established technique to elucidate the 3D structures of biological macromolecules. Projection images from thousands of macromolecules that are assumed to be structurally identical are combined into a single 3D map representing the Coulomb potential of the macromolecule under study. This article discusses possible caveats along the image-processing path and how to avoid them to obtain a reliable 3D structure. Some of these problems are very well known in the community. These may be referred to as sample-related (such as specimen denaturation at interfaces or non-uniform projection geometry leading to underrepresented projection directions). The rest are related to the algorithms used. While some have been discussed in depth in the literature, such as the use of an incorrect initial volume, others have received much less attention. However, they are fundamental in any data-analysis approach. Chiefly among them, instabilities in estimating many of the key parameters that are required for a correct 3D reconstruction that occur all along the processing workflow are referred to, which may significantly affect the reliability of the whole process. In the field, the term overfitting has been coined to refer to some particular kinds of artifacts. It is argued that overfitting is a statistical bias in key parameter-estimation steps in the 3D reconstruction process, including intrinsic algorithmic bias. It is also shown that common tools (Fourier shell correlation) and strategies (gold standard) that are normally used to detect or prevent overfitting do not fully protect against it. Alternatively, it is proposed that detecting the bias that leads to overfitting is much easier when addressed at the level of parameter estimation, rather than detecting it once the particle images have been combined into a 3D map. Comparing the results from multiple algorithms (or at least, independent executions of the same algorithm) can detect parameter bias. These multiple executions could then be averaged to give a lower variance estimate of the underlying parameters.

A probabilistic approach to tomography and adjoint state methods, with an application to full waveform inversion in medical ultrasound

Bayesian methods are a popular research direction for inverse problems. There are a variety of techniques available to solve Bayes' equation, each with their own strengths and limitations. Here, we discuss stochastic variational inference (SVI), which solves Bayes' equation using gradient-based methods. This is important for applications which are time-limited (e.g. medical tomography) or where solving the forward problem is expensive (e.g. adjoint methods). To evaluate the use of SVI in both these contexts, we apply it to ultrasound tomography of the brain using full-waveform inversion (FWI). FWI is a computationally expensive adjoint method for solving the ultrasound tomography inverse problem, and we demonstrate that SVI can be used to find a no-cost estimate of the pixel-wise variance of the sound-speed distribution using a mean-field Gaussian approximation. In other words, we show experimentally that it is possible to estimate the pixel-wise uncertainty of the sound-speed reconstruction using SVI and a common approximation which is already implicit in other types of iterative reconstruction. Uncertainty estimates have a variety of uses in adjoint methods and tomography. As an illustrative example, we focus on the use of uncertainty for image quality assessment. This application is not limiting; our variance estimator has effectively no computational cost and we expect that it will have applications in fields such as non-destructive testing or aircraft component design where uncertainties may not be routinely estimated.

Analytical covariance estimation for iterative CT reconstruction methods

Covariance of reconstruction images are useful to analyze the magnitude and correlation of noise in the evaluation of systems and reconstruction algorithms. The covariance estimation requires a big number of image samples that are hard to acquire in reality. A covariance propagation method from projection by a few noisy realizations is studied in this work. Based on the property of convergent points of cost funtions, the proposed method is composed of three steps, (1) construct a relationship between the covariance of projection and corresponding reconstruction from cost functions at its convergent point, (2) simplify the covariance relationship constructed in (1) by introducing an approximate gradient of penalties, and (3) obtain an analytical covariance estimation according to the simplified relationship in (2). Three approximation methods for step (2) are studied: the linear approximation of the gradient of penalties (LAM), the Taylor apprximation (TAM), and the mixture of LAM and TAM (MAM). TV and qGGMRF penalized weighted least square methods are experimented on. Results from statistical methods are used as reference. Under the condition of unstable 2nd derivative of penalties such as TV, the covariance image estimated by LAM accords to reference well but of smaller values, while the covarianc estimation by TAM is quite off. Under the conditon of relatively stable 2nd derivative of penalties such as qGGMRF, TAM performs well and LAM is again with a negative bias in magnitude. MAM gives a best performance under both conditions by combining LAM and TAM. Results also show that only one noise realization is enough to obtain reasonable covariance estimation analytically, which is important for practical usage. This work suggests the necessity and a new way to estimate the covariance for non-quadratically penalized reconstructions. Currently, the proposed method is computationally expensive for large size reconstructions.Computational efficiency is our future work to focus.

Measurement uncertainty evaluation procedures and applications for various types of multichannel rotating-element spectroscopic ellipsometers

A universal measurement uncertainty evaluation procedure is required for different types of multichannel rotating-element spectroscopic ellipsometers (RE-SEs) used in modern semiconductor industry. Herein, an improved uncertainty evaluation procedure, based on the universal measurement model functions and implicit function theorem, is introduced for unknown optical parameters of a sample. In addition, we develop a measurement standard instrument that can solve the error problems related to the basic principles of the multichannel RE-SEs used in the industrial field and present an example of applying the proposed uncertainty evaluation method to this standard instrument. Accordingly, the measurement performance for several types of real-time RE-SEs can be quantitatively compared. It can also be used for standardization, instrumentation, and measurement optimization.

Reducing residual-motion artifacts in iterative 3D CBCT reconstruction in image-guided radiation therapy

PURPOSE

Recent evaluations of a 3D iterative cone-beam computed tomography (iCBCT) reconstruction method available on Varian radiation treatment devices demonstrated that iCBCT provides superior image quality when compared to analytical Feldkamp-Davis-Kress (FDK) method. However, iCBCT employs statistical penalized likelihood (PL) that is known to be highly sensitive to inconsistencies due to physiological motion occurring during the acquisition. We propose a computationally inexpensive extension of iCBCT addressing this deficiency.

METHODS

During the iterative process, the gradients of PL are modified to avoid the generation of motion-related artifacts. To assess the impact of this modification, we propose a motion simulation generating CBCT projections of a moving anatomy together with artifact-free images used as ground truth. Contrast-to-noise ratio and power spectra of difference images are computed to quantify the impact of the motion on reconstructed CBCT volumes as well as the effect of the proposed modification.

RESULTS

Using both simulated and clinical data, it is shown that the motion of patient's abdominal wall during the acquisition results in artifacts that can be quantified as low-frequency components in volumes reconstructed with iCBCT. Further, a quantitative evaluation demonstrates that the proposed modification of PL reduces these low-frequency components. While preserving the advantages of PL, it effectively suppresses the propagation of motion-related artifacts into clinically important regions, thus increasing the motion resiliency of iCBCT.

CONCLUSIONS

The proposed modified iterative reconstruction method significantly improves the quality of CBCT images of anatomies suffering from residual motion.

Time of Flight in Perspective: Instrumental and Computational Aspects of Time Resolution in Positron Emission Tomography

The first time-of-flight positron emission tomography (TOF-PET) scanners were developed as early as in the 1980s. However, the poor light output and low detection efficiency of TOF-capable detectors available at the time limited any gain in image quality achieved with these TOF-PET scanners over the traditional non-TOF PET scanners. The discovery of LSO and other Lu-based scintillators revived interest in TOF-PET and led to the development of a second generation of scanners with high sensitivity and spatial resolution in the mid-2000s. The introduction of the silicon photomultiplier (SiPM) has recently yielded a third generation of TOF-PET systems with unprecedented imaging performance. Parallel to these instrumentation developments, much progress has been made in the development of image reconstruction algorithms that better utilize the additional information provided by TOF. Overall, the benefits range from a reduction in image variance (SNR increase), through allowing joint estimation of activity and attenuation, to better reconstructing data from limited angle systems. In this work, we review these developments, focusing on three broad areas: 1) timing theory and factors affecting the time resolution of a TOF-PET system; 2) utilization of TOF information for improved image reconstruction; and 3) quantification of the benefits of TOF compared to non-TOF PET. Finally, we offer a brief outlook on the TOF-PET developments anticipated in the short and longer term. Throughout this work, we aim to maintain a clinically driven perspective, treating TOF as one of multiple (and sometimes competitive) factors that can aid in the optimization of PET imaging performance.

Reconstruction, analysis and interpretation of posterior probability distributions of PET images, using the posterior bootstrap

The uncertainty of reconstructed PET images remains difficult to assess and to interpret for the use in diagnostic and quantification tasks. Here we provide (1) an easy-to-use methodology for uncertainty assessment for almost any Bayesian model in PET reconstruction from single datasets and (2) a detailed analysis and interpretation of produced posterior image distributions. We apply a recent posterior bootstrap framework to the PET image reconstruction inverse problem and obtain simple parallelizable algorithms based on random weights and on existing maximuma posteriori(MAP) (posterior maximum) optimization-based algorithms. Posterior distributions are produced, analyzed and interpreted for several common Bayesian models. Their relationship with the distribution of the MAP image estimate over multiple dataset realizations is exposed. The coverage properties of posterior distributions are validated. More insight is obtained for the interpretation of posterior distributions in order to open the way for including uncertainty information into diagnostic and quantification tasks.

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.

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.

Uncertainty analysis of MR-PET image registration for precision neuro-PET imaging

Accurate regional brain quantitative PET measurements, particularly when using partial volume correction, rely on robust image registration between PET and MR images. We argue here that the precision, and hence the uncertainty, of MR-PET image registration is mainly driven by the registration implementation and the quality of PET images due to their lower resolution and higher noise compared to the structural MR images. We propose a dedicated uncertainty analysis for quantifying the precision of MR-PET registration, centred around the bootstrap resampling of PET list-mode events to generate multiple PET image realisations with different noise (count) levels. The effects of PET image reconstruction parameters, such as the use of attenuation and scatter corrections and different number of iterations, on the precision and accuracy of MR-PET registration were investigated. In addition, the performance of four software packages with their default settings for rigid inter-modality image registration were considered: NiftyReg, Vinci, FSL and SPM. Four distinct PET image distributions made of two early time frames (similar to cortical FDG) and two late frames using two amyloid PET dynamic acquisitions of one amyloid positive and one amyloid negative participants were investigated. For the investigated four PET frames, the biggest impact on the uncertainty was observed between registration software packages (up to 10-fold difference in precision) followed by the reconstruction parameters. On average, the lowest uncertainty for different PET frames and brain regions was observed with SPM and two iterations of fully quantitative image reconstruction. The observed uncertainty for the varying PET count-level (from 5% to 60%) was slightly lower than for the reconstruction parameters. We also observed that the registration uncertainty in quantitative PET analysis depends on amyloid status of the considered PET frames, with increased uncertainty (up to three times) when using post-reconstruction partial volume correction. This analysis is applicable for PET data obtained from either PET/MR or PET/CT scanners.

PET imaging of neurotransmission using direct parametric reconstruction

Receptor ligand-based dynamic Positron Emission Tomography (PET) permits the measurement of neurotransmitter release in the human brain. For single-scan paradigms, the conventional method of estimating changes in neurotransmitter levels relies on fitting a pharmacokinetic model to activity concentration histories extracted after PET image reconstruction. However, due to the statistical fluctuations of activity concentration data at the voxel scale, parametric images computed using this approach often exhibit low signal-to-noise ratio, impeding characterization of neurotransmitter release. Numerous studies have shown that direct parametric reconstruction (DPR) approaches, which combine image reconstruction and kinetic analysis in a unified framework, can improve the signal-to-noise ratio of parametric mapping. However, there is little experience with DPR in imaging of neurotransmission and the performance of the approach in this application has not been evaluated before in humans. In this report, we present and evaluate a DPR methodology that computes 3-D distributions of ligand transport, binding potential (BP_ND) and neurotransmitter release magnitude (γ) from a dynamic sequence of PET sinograms. The technique employs the linear simplified reference region model (LSRRM) of Alpert et al. (2003), which represents an extension of the simplified reference region model that incorporates time-varying binding parameters due to radioligand displacement by release of neurotransmitter. Estimation of parametric images is performed by gradient-based optimization of a Poisson log-likelihood function incorporating LSRRM kinetics and accounting for the effects of head movement, attenuation, detector sensitivity, random and scattered coincidences. A ¹¹C-raclopride simulation study showed that the proposed approach substantially reduces the bias and variance of voxel-wise γ estimates as compared to standard methods. Moreover, simulations showed that detection of release could be made more reliable and/or conducted using a smaller sample size using the proposed DPR estimator. Likewise, images of BP_ND computed using DPR had substantially improved bias and variance properties. Application of the method in human subjects was demonstrated using ¹¹C-raclopride dynamic scans and a reward task, confirming the improved quality of the estimated parametric images using the proposed approach.

Cone-beam CT for imaging of the head/brain: Development and assessment of scanner prototype and reconstruction algorithms

PURPOSE

Our aim was to develop a high-quality, mobile cone-beam computed tomography (CBCT) scanner for point-of-care detection and monitoring of low-contrast, soft-tissue abnormalities in the head/brain, such as acute intracranial hemorrhage (ICH). This work presents an integrated framework of hardware and algorithmic advances for improving soft-tissue contrast resolution and evaluation of its technical performance with human subjects.

METHODS

Four configurations of a CBCT scanner prototype were designed and implemented to investigate key aspects of hardware (including system geometry, antiscatter grid, bowtie filter) and technique protocols. An integrated software pipeline (c.f., a serial cascade of algorithms) was developed for artifact correction (image lag, glare, beam hardening and x-ray scatter), motion compensation, and three-dimensional image (3D) reconstruction [penalized weighted least squares (PWLS), with a hardware-specific statistical noise model]. The PWLS method was extended in this work to accommodate multiple, independently moving regions with different resolution (to address both motion compensation and image truncation). Imaging performance was evaluated quantitatively and qualitatively with 41 human subjects in the neurosciences critical care unit (NCCU) at our institution.

RESULTS

The progression of four scanner configurations exhibited systematic improvement in the quality of raw data by variations in system geometry (source-detector distance), antiscatter grid, and bowtie filter. Quantitative assessment of CBCT images in 41 subjects demonstrated: ~70% reduction in image nonuniformity with artifact correction methods (lag, glare, beam hardening, and scatter); ~40% reduction in motion-induced streak artifacts via the multi-motion compensation method; and ~15% improvement in soft-tissue contrast-to-noise ratio (CNR) for PWLS compared to filtered backprojection (FBP) at matched resolution. Each of these components was important to improve contrast resolution for point-of-care cranial imaging.

CONCLUSIONS

This work presents the first application of a high-quality, point-of-care CBCT system for imaging of the head/ brain in a neurological critical care setting. Hardware configuration iterations and an integrated software pipeline for artifacts correction and PWLS reconstruction mitigated artifacts and noise to achieve image quality that could be valuable for point-of-care detection and monitoring of a variety of intracranial abnormalities, including ICH and hydrocephalus.

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.

Simplified Statistical Image Reconstruction for X-ray CT With Beam-Hardening Artifact Compensation

CT images are often affected by beam-hardening artifacts due to the polychromatic nature of the X-ray spectra. These artifacts appear in the image as cupping in homogeneous areas and as dark bands between dense regions such as bones. This paper proposes a simplified statistical reconstruction method for X-ray CT based on Poisson statistics that accounts for the non-linearities caused by beam hardening. The main advantages of the proposed method over previous algorithms are that it avoids the preliminary segmentation step, which can be tricky, especially for low-dose scans, and it does not require knowledge of the whole source spectrum, which is often unknown. Each voxel attenuation is modeled as a mixture of bone and soft tissue by defining density-dependent tissue fractions and maintaining one unknown per voxel. We approximate the energy-dependent attenuation corresponding to different combinations of bone and soft tissues, the so-called beam-hardening function, with the 1D function corresponding to water plus two parameters that can be tuned empirically. Results on both simulated data with Poisson sinogram noise and two rodent studies acquired with the ARGUS/CT system showed a beam hardening reduction (both cupping and dark bands) similar to analytical reconstruction followed by post-processing techniques but with reduced noise and streaks in cases with a low number of projections, as expected for statistical image reconstruction.

OEDIPUS: An Experiment Design Framework for Sparsity-Constrained MRI

This paper introduces a new estimation-theoretic framework for experiment design in the context of MR image reconstruction under sparsity constraints. The new framework is called OEDIPUS (Oracle-based Experiment Design for Imaging Parsimoniously Under Sparsity constraints) and is based on combining the constrained Cramér-Rao bound with classical experiment design techniques. Compared to popular random sampling approaches, OEDIPUS is fully deterministic and automatically tailors the sampling pattern to the specific imaging context of interest (i.e., accounting for coil geometry, anatomy, image contrast, etc.). OEDIPUS-based experiment designs are evaluated using retrospectively subsampled in vivo MRI data in several different contexts. The results demonstrate that OEDIPUS-based experiment designs have some desirable characteristics relative to conventional MRI sampling approaches.

Performance Analysis for Nonlinear Tomographic Data Processing

Image quality analysis of nonlinear algorithms is challenging due to numerous dependencies on the imaging system, algorithmic parameters, object, and stimulus. In particular, traditional notions of linearity and local linearity are of limited utility when the system response is dependent on the stimulus itself. In this work, we analyze the performance of nonlinear systems using perturbation response - the difference between the mean output with and without a stimulus, and introduce a new metric to examine variation of the responses in individual images. We applied the analysis to four algorithms with different degrees of nonlinearity for a spherical stimulus of varying contrast. For model-based reconstruction methods [penalized-likelihood (PL) reconstruction with a quadratic penalty and a Huber penalty], perturbation response analysis reaffirmed known trends in terms of object- and location-dependence. For a CNN denoising network, the response exhibits highly nonlinear behavior as the contrast increases - from the stimulus completely disappearing, to appearing at the right contrast but smaller in size, to being fully admitted by the algorithm. Furthermore, the variation metric for PL reconstruction with a Huber penalty and the CNN network reveals high variation at the edge of the stimulus, i.e., perturbation response computed from the mean images is a smoothed version of individual responses due to "jitter" in edges. This behavior suggests that the mean response alone may not be representative of performance in individual images and image quality metrics traditionally defined based on the mean response may be inappropriate for certain nonlinear algorithms. This work demonstrates the potential utility of perturbation response and response variation in the analysis and optimization of nonlinear imaging algorithms.

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.

Artificial Neural Network Enhanced Bayesian PET Image Reconstruction

In positron emission tomography (PET) image reconstruction, the Bayesian framework with various regularization terms has been implemented to constrain the radio tracer distribution. Varying the regularizing weight of a maximum a posteriori (MAP) algorithm specifies a lower bound of the tradeoff between variance and spatial resolution measured from the reconstructed images. The purpose of this paper is to build a patch-based image enhancement scheme to reduce the size of the unachievable region below the bound and thus to quantitatively improve the Bayesian PET imaging. We cast the proposed enhancement as a regression problem which models a highly nonlinear and spatial-varying mapping between the reconstructed image patches and an enhanced image patch. An artificial neural network model named multilayer perceptron (MLP) with backpropagation was used to solve this regression problem through learning from examples. Using the BrainWeb phantoms, we simulated brain PET data at different count levels of different subjects with and without lesions. The MLP was trained using the image patches reconstructed with a MAP algorithm of different regularization parameters for one normal subject at a certain count level. To evaluate the performance of the trained MLP, reconstructed images from other simulations and two patient brain PET imaging data sets were processed. In every testing cases, we demonstrate that the MLP enhancement technique improves the noise and bias tradeoff compared with the MAP reconstruction using different regularizing weights thus decreasing the size of the unachievable region defined by the MAP algorithm in the variance/resolution plane.

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.

Experimental study to optimize configurations of PCD Spectral CT

BACKGROUND

High dose efficiency of photon counting detector based spectral CT (PCD-SCT) and its value in some clinical diagnosis have been well acknowledged. However, it has not been widely adopted in practical use for medical diagnosis and security inspection.

OBJECTIVE

To evaluate the influence on PCD-SCT from multiple aspects including the number of energy channels, k-edge materials, energy thresholding, basis functions in spectral information decomposition, and the combined optimal setting for these parameters and configurations.

METHODS

Basis material decomposition after spatial reconstruction is applied for PCD-SCT. A "one-step" synthesis method, merging decomposition with synthesis, is proposed to obtain virtual monochromatic images. An I-RMSE is computed using the bias part of I-RMSE to describe the difference of a synthesized signal from ground truth and the standard deviation part of I-RMSE to express the noise level. In addition, virtual monochromatic images commonly used in the medical area are also synthesized. Both numerical simulations and practical experiments are conducted for validation.

RESULTS

Results indicated that the I-RMSE for matters significantly reduced with an increased number of energy channels compared with dual-energy channel. The maximum reduction is 6% for triple-, 18% for quadruple-and 24% for quintuple-energy, respectively. However, the improvement is not linear, and also slows down after the number of energy channels reaches a certain number. Contrast agents of high concentration can introduce up to 50% error to surrounding matters. Moreover, different energy partitions influence the total error, which demonstrates the necessity of energy threshold optimization. Last, the optimal basis-material combination varies according to targeted imaging matters and the interested monochromatic energies.

CONCLUSIONS

Gain from more energy channels could be significant with the increase of energy channel number. Introduction of contrast agents in scanned objects will increase overall error in spectral CT imaging. Energy thresholding optimization is beneficial for information recovery. Moreover, the choice of basis materials could also be important to obtain low noise results. With these studies of the effect from various configurations for PCD-SCT, one may optimize the configuration of PCD-SCT accordingly.

Optimization of an Adaptive SPECT System with the Scanning Linear Estimator

A method for optimization of an adaptive Single Photon Emission Computed Tomography (SPECT) system is presented. Adaptive imaging systems can quickly change their hardware configuration in response to data being generated in order to improve image quality for a specific task. In this work we simulate an adaptive SPECT system and propose a method for finding the adaptation that maximizes the performance on a signal estimation task. To start with, a simulated object model containing a spherical signal is imaged with a scout configuration. A Markov-Chain Monte Carlo (MCMC) technique utilizes the scout data to generate an ensemble of possible objects consistent with the scout data. This object ensemble is imaged by numerous simulated hardware configurations and for each system estimates of signal activity, size and location are calculated via the Scanning Linear Estimator (SLE). A figure of merit, based on a Modified Dice Index (MDI), quantifies the performance of each imaging configuration and it allows for optimization of the adaptive SPECT. This figure of merit is calculated by multiplying two terms: the first term uses the definition of the Dice similarity index to determine the percent of overlap between the actual and the estimated spherical signal, the second term utilizes an exponential function that measures the squared error for the activity estimate. The MDI combines the error in estimates of activity, size, and location, in one convenient metric and it allows for simultaneous optimization of the SPECT system with respect to all the estimated signal parameters. The results of our optimizations indicate that the adaptive system performs better than a non-adaptive one in conditions where the diagnostic scan has a low photon count - on the order of thousand photons per projection. In a statistical study, we optimized the SPECT system for one hundred unique objects and demonstrated that the average MDI on an estimation task is 0.84 for the adaptive system and 0.65 for the non-adaptive system.

Task-Driven Optimization of Fluence Field and Regularization for Model-Based Iterative Reconstruction in Computed Tomography

This paper presents a joint optimization of dynamic fluence field modulation (FFM) and regularization in quadratic penalized-likelihood reconstruction that maximizes a task-based imaging performance metric. We adopted a task-driven imaging framework for prospective designs of the imaging parameters. A maxi-min objective function was adopted to maximize the minimum detectability index ( ) throughout the image. The optimization algorithm alternates between FFM (represented by low-dimensional basis functions) and local regularization (including the regularization strength and directional penalty weights). The task-driven approach was compared with three FFM strategies commonly proposed for FBP reconstruction (as well as a task-driven TCM strategy) for a discrimination task in an abdomen phantom. The task-driven FFM assigned more fluence to less attenuating anteroposterior views and yielded approximately constant fluence behind the object. The optimal regularization was almost uniform throughout image. Furthermore, the task-driven FFM strategy redistribute fluence across detector elements in order to prescribe more fluence to the more attenuating central region of the phantom. Compared with all strategies, the task-driven FFM strategy not only improved minimum by at least 17.8%, but yielded higher over a large area inside the object. The optimal FFM was highly dependent on the amount of regularization, indicating the importance of a joint optimization. Sample reconstructions of simulated data generally support the performance estimates based on computed . The improvements in detectability show the potential of the task-driven imaging framework to improve imaging performance at a fixed dose, or, equivalently, to provide a similar level of performance at reduced dose.

Pixel-wise estimation of noise statistics on iterative CT reconstruction from a single scan

PURPOSE

As iterative CT reconstruction continues to advance, the spatial distribution of noise standard deviation (STD) and accurate noise power spectrum (NPS) on the reconstructed CT images become important for method evaluation as well as optimization of algorithm parameters. Using a single CT scan, we propose a practical method for pixel-wise calculation of noise statistics on an iteratively reconstructed CT image, which enables accurate calculation of noise STD for each pixel and NPS.

METHOD

We first derive the noise propagation from measured projections to an iteratively reconstructed CT image provided that the projection noise is known. We then show that the model of noise propagation remains approximately unchanged for extra simulated noise added on the measured projections. To compute the noise STD map and the NPS map on an iteratively reconstructed CT image from a single scan, we first iteratively reconstruct the CT image from the measured projections using an existing reconstruction algorithm. The same measured projections are added by different sets (a total of 32 sets in our implementation) of projection noise simulated from an estimated projection noise model, and are then used to iteratively reconstruct different CT images. The calculations of the noise STD map and the NPS map are finally performed on the entire stack of these different reconstruction images.

RESULTS

We evaluate our method on an anthropomorphic head phantom, and demonstrate the clinical utility on a set of head and neck patient CT data, using two iterative CT reconstruction algorithms: the penalized weighted least-square (PWLS) algorithm and the total-variation (TV) regularization. In the head phantom case, repeated scans are acquired to generate the ground truths of noise STD and NPS maps. Using only one single scan, the proposed method accurately calculates the noise STD maps with a root-mean-square error (RMSE) of less than 5HU. In the NPS map estimation, we compare the result of our proposed method with that of the conventional method which calculates the NPS maps on a uniform region of interest on one CT image. Our method outperforms the conventional method on the NPS map estimation with RMSE reduced by 92%. The implementation of the proposed method on the patient data successfully provides the noise STD values around complex structures and a high-quality NPS map.

CONCLUSION

The proposed method accurately calculates noise STD for each pixel and NPS on an iteratively reconstructed CT image, with no requirement of repeated CT scans. It provides a detailed evaluation of imaging performance of different iterative reconstruction methods on the same CT dataset.

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.

Denoising of polychromatic CT images based on their own noise properties

PURPOSE

Because of high diagnostic accuracy and fast scan time, computed tomography (CT) has been widely used in various clinical applications. Since the CT scan introduces radiation exposure to patients, however, dose reduction has recently been recognized as an important issue in CT imaging. However, low-dose CT causes an increase of noise in the image and thereby deteriorates the accuracy of diagnosis. In this paper, the authors develop an efficient denoising algorithm for low-dose CT images obtained using a polychromatic x-ray source. The algorithm is based on two steps: (i) estimation of space variant noise statistics, which are uniquely determined according to the system geometry and scanned object, and (ii) subsequent novel conversion of the estimated noise to Gaussian noise so that an existing high performance Gaussian noise filtering algorithm can be directly applied to CT images with non-Gaussian noise.

METHODS

For efficient polychromatic CT image denoising, the authors first reconstruct an image with the iterative maximum-likelihood polychromatic algorithm for CT to alleviate the beam-hardening problem. We then estimate the space-variant noise variance distribution on the image domain. Since there are many high performance denoising algorithms available for the Gaussian noise, image denoising can become much more efficient if they can be used. Hence, the authors propose a novel conversion scheme to transform the estimated space-variant noise to near Gaussian noise. In the suggested scheme, the authors first convert the image so that its mean and variance can have a linear relationship, and then produce a Gaussian image via variance stabilizing transform. The authors then apply a block matching 4D algorithm that is optimized for noise reduction of the Gaussian image, and reconvert the result to obtain a final denoised image. To examine the performance of the proposed method, an XCAT phantom simulation and a physical phantom experiment were conducted.

RESULTS

Both simulation and experimental results show that, unlike the existing denoising algorithms, the proposed algorithm can effectively reduce the noise over the whole region of CT images while preventing degradation of image resolution.

CONCLUSIONS

To effectively denoise polychromatic low-dose CT images, a novel denoising algorithm is proposed. Because this algorithm is based on the noise statistics of a reconstructed polychromatic CT image, the spatially varying noise on the image is effectively reduced so that the denoised image will have homogeneous quality over the image domain. Through a simulation and a real experiment, it is verified that the proposed algorithm can deliver considerably better performance compared to the existing denoising algorithms.

Modeling and Pre-Treatment of Photon-Starved CT Data for Iterative Reconstruction

An increasing number of X-ray CT procedures are being conducted with drastically reduced dosage, due at least in part to advances in statistical reconstruction methods that can deal more effectively with noise than can traditional techniques. As data become photon-limited, more detailed models are necessary to deal with count rates that drop to the levels of system electronic noise. We present two options for sinogram pre-treatment that can improve the performance of photon-starved measurements, with the intent of following with model-based image reconstruction. Both the local linear minimum mean-squared error (LLMMSE) filter and pointwise Bayesian restoration (PBR) show promise in extracting useful, quantitative information from very low-count data by reducing local bias while maintaining the lower noise variance of statistical methods. Results from clinical data demonstrate the potential of both techniques.

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.

Evaluation of lesion detectability in positron emission tomography when using a convergent penalized likelihood image reconstruction method

We have previously developed a convergent penalized likelihood (PL) image reconstruction algorithm using the relative difference prior (RDP) and showed that it achieves more accurate lesion quantitation compared to ordered subsets expectation maximization (OSEM). We evaluated the detectability of low-contrast liver and lung lesions using the PL-RDP algorithm compared to OSEM. We performed a two-alternative forced choice study using a channelized Hotelling observer model that was previously validated against human observers. Lesion detectability showed a stronger dependence on lesion size for PL-RDP than OSEM. Lesion detectability was improved using time-of-flight (TOF) reconstruction, with greater benefit for the liver compared to the lung and with increasing benefit for decreasing lesion size and contrast. PL detectability was statistically significantly higher than OSEM for 20 mm liver lesions when contrast was [Formula: see text] ([Formula: see text]), and TOF PL detectability was statistically significantly higher than TOF OSEM for 15 and 20 mm liver lesions with contrast [Formula: see text] and [Formula: see text], respectively. For all other cases, there was no statistically significant difference between PL and OSEM ([Formula: see text]). For the range of studied lesion properties, lesion detectability using PL-RDP was equivalent or improved compared to using OSEM.

Initial performance studies of a wearable brain positron emission tomography camera based on autonomous thin-film digital Geiger avalanche photodiode arrays

Using analytical and Monte Carlo modeling, we explored performance of a lightweight wearable helmet-shaped brain positron emission tomography (PET), or BET camera, based on thin-film digital Geiger avalanche photodiode arrays with Lutetium-yttrium oxyorthosilicate (LYSO) or [Formula: see text] scintillators for imaging in vivo human brain function of freely moving and acting subjects. We investigated a spherical cap BET and cylindrical brain PET (CYL) geometries with 250-mm diameter. We also considered a clinical whole-body (WB) LYSO PET/CT scanner. The simulated energy resolutions were 10.8% (LYSO) and 3.3% ([Formula: see text]), and the coincidence window was set at 2 ns. The brain was simulated as a water sphere of uniform F-18 activity with a radius of 100 mm. We found that BET achieved [Formula: see text] better noise equivalent count (NEC) performance relative to the CYL and [Formula: see text] than WB. For 10-mm-thick [Formula: see text] equivalent mass systems, LYSO (7-mm thick) had [Formula: see text] higher NEC than [Formula: see text]. We found that [Formula: see text] scintillator crystals achieved [Formula: see text] full-width-half-maximum spatial resolution without parallax errors. Additionally, our simulations showed that LYSO generally outperformed [Formula: see text] for NEC unless the timing resolution for [Formula: see text] was considerably smaller than that presently used for LYSO, i.e., well below 300 ps.

Mixed Confidence Estimation for Iterative CT Reconstruction

Dynamic (4D) CT imaging is used in a variety of applications, but the two major drawbacks of the technique are its increased radiation dose and longer reconstruction time. Here we present a statistical analysis of our previously proposed Mixed Confidence Estimation (MCE) method that addresses both these issues. This method, where framed iterative reconstruction is only performed on the dynamic regions of each frame while static regions are fixed across frames to a composite image, was proposed to reduce computation time. In this work, we generalize the previous method to describe any application where a portion of the image is known with higher confidence (static, composite, lower-frequency content, etc.) and a portion of the image is known with lower confidence (dynamic, targeted, etc). We show that by splitting the image space into higher and lower confidence components, MCE can lower the estimator variance in both regions compared to conventional reconstruction. We present a theoretical argument for this reduction in estimator variance and verify this argument with proof-of-principle simulations. We also propose a fast approximation of the variance of images reconstructed with MCE and confirm that this approximation is accurate compared to analytic calculations of and multi-realization image variance. This MCE method requires less computation time and provides reduced image variance for imaging scenarios where portions of the image are known with more certainty than others allowing for potentially reduced radiation dose and/or improved dynamic imaging.

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.

A novel approach to assess the treatment response using Gaussian random field in PET

PURPOSE

The assessment of early therapeutic response to anticancer therapy is vital for treatment planning and patient management in clinic. With the development of personal treatment plan, the early treatment response, especially before any anatomically apparent changes after treatment, becomes urgent need in clinic. Positron emission tomography (PET) imaging serves an important role in clinical oncology for tumor detection, staging, and therapy response assessment. Many studies on therapy response involve interpretation of differences between two PET images, usually in terms of standardized uptake values (SUVs). However, the quantitative accuracy of this measurement is limited. This work proposes a statistically robust approach for therapy response assessment based on Gaussian random field (GRF) to provide a statistically more meaningful scale to evaluate therapy effects.

METHODS

The authors propose a new criterion for therapeutic assessment by incorporating image noise into traditional SUV method. An analytical method based on the approximate expressions of the Fisher information matrix was applied to model the variance of individual pixels in reconstructed images. A zero mean unit variance GRF under the null hypothesis (no response to therapy) was obtained by normalizing each pixel of the post-therapy image with the mean and standard deviation of the pretherapy image. The performance of the proposed method was evaluated by Monte Carlo simulation, where XCAT phantoms (128(2) pixels) with lesions of various diameters (2-6 mm), multiple tumor-to-background contrasts (3-10), and different changes in intensity (6.25%-30%) were used. The receiver operating characteristic curves and the corresponding areas under the curve were computed for both the proposed method and the traditional methods whose figure of merit is the percentage change of SUVs. The formula for the false positive rate (FPR) estimation was developed for the proposed therapy response assessment utilizing local average method based on random field. The accuracy of the estimation was validated in terms of Euler distance and correlation coefficient.

RESULTS

It is shown that the performance of therapy response assessment is significantly improved by the introduction of variance with a higher area under the curve (97.3%) than SUVmean (91.4%) and SUVmax (82.0%). In addition, the FPR estimation serves as a good prediction for the specificity of the proposed method, consistent with simulation outcome with ∼1 correlation coefficient.

CONCLUSIONS

In this work, the authors developed a method to evaluate therapy response from PET images, which were modeled as Gaussian random field. The digital phantom simulations demonstrated that the proposed method achieved a large reduction in statistical variability through incorporating knowledge of the variance of the original Gaussian random field. The proposed method has the potential to enable prediction of early treatment response and shows promise for application to clinical practice. In future work, the authors will report on the robustness of the estimation theory for application to clinical practice of therapy response evaluation, which pertains to binary discrimination tasks at a fixed location in the image such as detection of small and weak lesion.

Performance of 3DOSEM and MAP algorithms for reconstructing low count SPECT acquisitions

PURPOSE

Low count single photon emission computed tomography (SPECT) is becoming more important in view of whole body SPECT and reduction of radiation dose. In this study, we investigated the performance of several 3D ordered subset expectation maximization (3DOSEM) and maximum a posteriori (MAP) algorithms for reconstructing low count SPECT images.

MATERIALS AND METHODS

Phantom experiments were conducted using the National Electrical Manufacturers Association (NEMA) NU2 image quality (IQ) phantom. The background compartment of the phantom was filled with varying concentrations of pertechnetate and indiumchloride, simulating various clinical imaging conditions. Images were acquired using a hybrid SPECT/CT scanner and reconstructed with 3DOSEM and MAP reconstruction algorithms implemented in Siemens Syngo MI.SPECT (Flash3D) and Hermes Hybrid Recon Oncology (Hyrid Recon 3DOSEM and MAP). Image analysis was performed by calculating the contrast recovery coefficient (CRC),percentage background variability (N%), and contrast-to-noise ratio (CNR), defined as the ratio between CRC and N%. Furthermore, image distortion is characterized by calculating the aspect ratio (AR) of ellipses fitted to the hot spheres. Additionally, the performance of these algorithms to reconstruct clinical images was investigated.

RESULTS

Images reconstructed with 3DOSEM algorithms demonstrated superior image quality in terms of contrast and resolution recovery when compared to images reconstructed with filtered-back-projection (FBP), OSEM and 2DOSEM. However, occurrence of correlated noise patterns and image distortions significantly deteriorated the quality of 3DOSEM reconstructed images. The mean AR for the 37, 28, 22, and 17mm spheres was 1.3, 1.3, 1.6, and 1.7 respectively. The mean N% increase in high and low count Flash3D and Hybrid Recon 3DOSEM from 5.9% and 4.0% to 11.1% and 9.0%, respectively. Similarly, the mean CNR decreased in high and low count Flash3D and Hybrid Recon 3DOSEM from 8.7 and 8.8 to 3.6 and 4.2, respectively. Regularization with smoothing priors could suppress these noise patterns at the cost of reduced image contrast. The mean N% was 6.4% and 6.8% for low count QSP and MRP MAP reconstructed images. Alternatively, regularization with an anatomical Bowhser prior resulted in sharp images with high contrast, limited image distortion, and low N% of 8.3% in low count images, although some image artifacts did occur. Analysis of clinical images suggested that the same effects occur in clinical imaging.

CONCLUSION

Image quality of low count SPECT acquisitions reconstructed with modern 3DOSEM algorithms is deteriorated by the occurrence of correlated noise patterns and image distortions. The artifacts observed in the phantom experiments can also occur in clinical imaging.