Deep learning (DL) based image processing methods have been successfully applied to low-dose x-ray images based on the assumption that the feature distribution of the training data is consistent with that of the test data. However, low-dose computed tomography (LDCT) images from different commercial scanners may contain different amounts and types of image noise, violating this assumption. Moreover, in the application of DL based image processing methods to LDCT, the feature distributions of LDCT images from simulation and clinical CT examination can be quite different. Therefore, the network models trained with simulated image data or LDCT images from one specific scanner may not work well for another CT scanner and image processing task. To solve such domain adaptation problem, in this study, a novel generative adversarial network (GAN) with noise encoding transfer learning (NETL), or GAN-NETL, is proposed to generate a paired dataset with a different noise style. Specifically, we proposed a method to perform noise encoding operator and incorporate it into the generator to extract a noise style. Meanwhile, with a transfer learning (TL) approach, the image noise encoding operator transformed the noise type of the source domain to that of the target domain for realistic noise generation. One public and two private datasets are used to evaluate the proposed method. Experiment results demonstrated the feasibility and effectiveness of our proposed GAN-NETL model in LDCT image synthesis. In addition, we conduct additional image denoising study using the synthesized clinical LDCT data, which verified the merit of the proposed synthesis in improving the performance of the DL based LDCT processing method.

The four-dimensional (4-D) eXtended CArdiac-Torso (XCAT) series of phantoms was developed to provide accurate computerized models of the human anatomy and physiology. The XCAT series encompasses a vast population of phantoms of varying ages from newborn to adult, each including parameterized models for the cardiac and respiratory motions. With great flexibility in the XCAT's design, any number of body sizes, different anatomies, cardiac or respiratory motions or patterns, patient positions and orientations, and spatial resolutions can be simulated. As such, the XCAT phantoms are gaining a wide use in biomedical imaging research. There they can provide a virtual patient base from which to quantitatively evaluate and improve imaging instrumentation, data acquisition, techniques, and image reconstruction and processing methods which can lead to improved image quality and more accurate clinical diagnoses. The phantoms have also found great use in radiation dosimetry, radiation therapy, medical device design, and even the security and defense industry. This review paper highlights some specific areas in which the XCAT phantoms have found use within biomedical imaging and other fields. From these examples, we illustrate the increasingly important role that computerized phantoms and computer simulation are playing in the research community.

We present a direct (noniterative) algorithm for 1-D quadratic data fitting with neighboring intensity differences penalized by the Huber function. Applications of such an algorithm include 1-D processing of medical signals, such as smoothing of tissue time concentration curves in kinetic data analysis or sinogram preprocessing, and using it as a subproblem solver for 2-D or 3-D image restoration and reconstruction. dynamic programming was used to develop the direct algorithm. The problem was reformulated as a sequence of univariate optimization problems, for , where is the number of data points. The solution to the univariate problem at index is parameterized by the solution at , except at . Solving the univariate optimization problem at yields the solution to each problem in the sequence using back-tracking. Computational issues and memory cost are discussed in detail. Two numerical studies, tissue concentration curve smoothing and sinogram preprocessing for image reconstruction, are used to validate the direct algorithm and illustrate its practical applications. In the example of 1-D curve smoothing, the efficiency of the direct algorithm is compared with four iterative methods: the iterative coordinate descent, Nesterov's accelerated gradient descent algorithm, FISTA, and an off-the-shelf second order method. The first two methods were applied to the primal problem, the others to the dual problem. The comparisons show that the direct algorithm outperforms all other methods by a significant factor, which rapidly grows with the curvature of the Huber function. The second example, sinogram preprocessing, showed that robustness and speed of the direct algorithm are maintained over a wide range of signal variations, and that noise and streaking artifacts could be reduced with almost no increase in computation time. We also outline how the proposed 1-D solver can be used for imaging applications.

Intrinsic or data-driven respiratory and cardiac motion detection often track the center-of-mass (COM) change in PET data to derive a motion gating signal. The effectiveness of this method depends on the contrast of the moving target to the relatively stationary background. The stationary background leads to a reduced COM displacement in PET data. Further, the COM calculated using axially truncated PET data is biased. To improve intrinsic motion detection for motion compensated image reconstruction, we use the time-of-flight (TOF) PET data of the original object f(x) to calculate the non-TOF PET data of a volume-of-interest (VOI) weighted object f(x)w(x) . The VOI-weighting w(x) can be chosen to reduce contribution from the stationary background. The reduced background in f(x)w(x) leads to an observed increase in the COM displacement. We also derive rebinning equations to obtain the exact axial COM using axially truncated PET data. To assess the quality of the motion gating signal, we analyze the variance property of the COM using different methods, including with(out) VOI weighting and with(out) compensation for axial data truncation. Analytical simulations, phantom and patient data demonstrate the effectiveness of the proposed approach in identifying the motion phase and in deriving a gating signal to be used for motion-compensated image reconstruction.

Statistical image reconstruction (SIR) is a promising approach to reducing radiation dose in clinical computerized tomography (CT) scans. Clinical CT scanners use energy-integrating detectors. The CT signal follows a compound Poisson distribution, its probability density function (PDF) does not have an analytical form hence cannot be used in an SIR method. The goal of this work is to quantify the effects of using an approximate statistical assumption in SIR methods for clinical CT applications. We apply a pseudo-Ideal Observer (pIO) to simulated CT projection data of the fanbeam geometry at different dose levels. The simulation models the polychromatic X-ray tube spectrum, the effects of the bowtie filter, and the energy-integrating detectors. The pIO uses a pseudo likelihood function (pLF) to calculate the pseudo likelihood ratio, which is the decision variable used by the pIO in a binary detection task. The pLF is an approximation to the true LF of the underlying data. The pIO has inferior performance than the IO unless the pLF coincides with the LF; this performance difference quantifies the closeness between the pseudo likelihood and the exact one. Using lesion detectability in a signal known exactly, background known exactly binary detection task as a figure-of-merit, our results show that at down to 0.1% of a reference tube current level I0, the pIO that uses a Poisson approximation, or a matched variance Gaussian approximation in either the transmission or the line integral domain, achieves 99% the performance of the IO. The constant variance Gaussian approximation has only 70%-80% of the IO performance. At tube currents lower than 0.1% I0, the performance difference is more substantial. We conclude that at current clinical dose levels, it is important to account for the mean-dependent variance in CT projection data in SIR problem formulation, the exact PDF of the CT signal is not as important.

This work is a continuation of our previous work on geometric calibration in the circular cone-beam geometry. It is well known that seven parameters completely describe such a geometry in either flat-panel X-ray computed tomography or single pinhole SPECT imaging. Previously we developed a graphical procedure to determine the detector in-plane rotation angle independently of the other six parameters. Using the discovered geometrical relationships, in this paper we determine the remaining six parameters using the cone-beam projections of a minimum of three point objects. Our method is analytical. It makes use of the parameters of the fitted ellipse from the calibration data. The parameter estimation is accurate in the noise-free case or when there is moderate projection data truncation or shorter calibration scan range ( ≤ 360°). We perform numerical evaluations to study the robustness of the proposed method under different projection noise levels and using different data acquisition ranges. Using a full 360° scan range, the estimation accuracy and precision of our method are comparable or superior to previous methods. Using a shorter acquisition range, there may be bias in the ellipse parameters obtained by simple algebraic fitting methods. This bias will propagate to the estimated geometric parameters. Such bias can be mostly eliminated by using a more sophisticated fitting algorithm. At the same noise level, the geometric parameter estimation accuracies are comparable, but the estimation precision degrades, as the acquisition range becomes shorter.

It is well known that seven parameters completely describe a circular cone-beam geometry in either flat-panel X-ray computed tomography (CT) or single pinhole SPECT imaging. This paper considers the problem of determining one of the seven parameters only, the detector in-plane rotation or twist angle η. We describe a graphical procedure that can determine η independently of all other six parameters from a geometric calibration scan of point objects. Our method is exact in the ideal noise-free case and is general in that the other two out-of-plane detector rotation angles θ and φ can be nonzero. The calibration scan typically needs at least two point objects and an even number of projection views over a full 360° data acquisition. Under certain conditions, projection data truncation or a short scan acquisition of 180° + fan angle can be accommodated without affecting the accuracy of the calibration result. The graphical method is equally applicable to rotational multipinhole SPECT geometry. In this case, the final result is averaged from the individual estimates considering each pinhole separately. We use computer simulations and a multipinhole SPECT experiment to demonstrate the accuracy and precision of the proposed method.

The 4D extended cardiac-torso (XCAT) phantom was developed to provide a realistic and flexible model of the human anatomy and cardiac and respiratory motions for use in medical imaging research. A prior limitation to the phantom was that it did not accurately simulate altered functions of the heart that result from cardiac pathologies such as coronary artery disease (CAD). We overcame this limitation in a previous study by combining the phantom with a finite-element (FE) mechanical model of the left ventricle (LV) capable of more realistically simulating regional defects caused by ischemia. In the present work, we extend this model giving it the ability to accurately simulate motion abnormalities caused by myocardial infarction (MI), a far more complex situation in terms of altered mechanics compared with the modeling of acute ischemia. The FE model geometry is based on high resolution CT images of a normal male subject. An anterior region was defined as infarcted and the material properties and fiber distribution were altered, according to the bio-physiological properties of two types of infarction, i.e., fibrous and remodeled infarction (30% thinner wall than fibrous case). Compared with the original, surface-based 4D beating heart model of the XCAT, where regional abnormalities are modeled by simply scaling down the motion in those regions, the FE model was found to provide a more accurate representation of the abnormal motion of the LV due to the effects of fibrous infarction as well as depicting the motion of remodeled infarction. In particular, the FE models allow for the accurate depiction of dyskinetic motion. The average circumferential strain results were found to be consistent with measured dyskinetic experimental results. Combined with the 4D XCAT phantom, the FE model can be used to produce realistic multimodality sets of imaging data from a variety of patients in which the normal or abnormal cardiac function is accurately represented.

Projection data incompleteness arises in many situations relevant to X-ray computed tomography (CT) imaging. We propose a penalized maximum likelihood statistical sinogram restoration approach that incorporates the Helgason-Ludwig (HL) consistency conditions to accommodate projection data incompleteness. Image reconstruction is performed by the filtered-backprojection (FBP) in a second step. In our problem formulation, the objective function consists of the log-likelihood of the X-ray CT data and a penalty term; the HL condition poses a linear constraint on the restored sinogram and can be implemented efficiently via fast Fourier transform (FFT) and inverse FFT. We derive an iterative algorithm that increases the objective function monotonically. The proposed algorithm is applied to both computer simulated data and real patient data. We study different factors in the problem formulation that affect the properties of the final FBP reconstructed images, including the data truncation level, the amount of prior knowledge on the object support, as well as different approximations of the statistical distribution of the available projection data. We also compare its performance with an analytical truncation artifacts reduction method. The proposed method greatly improves both the accuracy and the precision of the reconstructed images within the scan field-of-view, and to a certain extent recovers the truncated peripheral region of the object. The proposed method may also be applied in areas such as limited angle tomography, metal artifacts reduction, and sparse sampling imaging.

Recent work in the development of computerized phantoms has focused on the creation of ideal "hybrid" models that seek to combine the realism of a patient-based voxelized phantom with the flexibility of a mathematical or stylized phantom. We have been leading the development of such computerized phantoms for use in medical imaging research. This paper will summarize our developments dating from the original four-dimensional (4-D) Mathematical Cardiac-Torso (MCAT) phantom, a stylized model based on geometric primitives, to the current 4-D extended Cardiac-Torso (XCAT) and Mouse Whole-Body (MOBY) phantoms, hybrid models of the human and laboratory mouse based on state-of-the-art computer graphics techniques. This paper illustrates the evolution of computerized phantoms toward more accurate models of anatomy and physiology. This evolution was catalyzed through the introduction of nonuniform rational b-spline (NURBS) and subdivision (SD) surfaces, tools widely used in computer graphics, as modeling primitives to define a more ideal hybrid phantom. With NURBS and SD surfaces as a basis, we progressed from a simple geometrically based model of the male torso (MCAT) containing only a handful of structures to detailed, whole-body models of the male and female (XCAT) anatomies (at different ages from newborn to adult), each containing more than 9000 structures. The techniques we applied for modeling the human body were similarly used in the creation of the 4-D MOBY phantom, a whole-body model for the mouse designed for small animal imaging research. From our work, we have found the NURBS and SD surface modeling techniques to be an efficient and flexible way to describe the anatomy and physiology for realistic phantoms. Based on imaging data, the surfaces can accurately model the complex organs and structures in the body, providing a level of realism comparable to that of a voxelized phantom. In addition, they are very flexible. Like stylized models, they can easily be manipulated to model anatomical variations and patient motion. With the vast improvement in realism, the phantoms developed in our lab can be combined with accurate models of the imaging process (SPECT, PET, CT, magnetic resonance imaging, and ultrasound) to generate simulated imaging data close to that from actual human or animal subjects. As such, they can provide vital tools to generate predictive imaging data from many different subjects under various scanning parameters from which to quantitatively evaluate and improve imaging devices and techniques. From the MCAT to XCAT, we will demonstrate how NURBS and SD surface modeling have resulted in a major evolutionary advance in the development of computerized phantoms for imaging research.

The widespread availability of high-performance computing and accurate and realistic computer simulation techniques has stimulated the development of computational anthropomorphic models of both the anatomy and physiological functions of humans and laboratory animals. These simulation tools have been applied to different medical imaging modalities including ultrasound, single photon emission computed tomography, positron emission tomography, X-ray computed tomography, magnetic resonance imaging, optical imaging, and multimodality imaging with various combinations of the above. This paper reviews the fundamental and technical challenges and future directions of developing computational models of normal and abnormal human anatomy and physiological functions, with a particular focus on their applications to biomedical imaging and radiation dosimetry calculations. The combination of accurate and realistic computer generated models of human and laboratory animals, radiation sources and distributions, transport of radiation through biological tissues, characteristics of the imaging system, and physics of the image formation process allows accurate and realistic simulation of biomedical imaging data and radiation dose distributions that are ever closer to those obtained from clinical and experimental laboratory animal studies. These simulation tools and techniques will provide an increasingly important contribution and impact in the future of biomedical imaging and dosimetry calculations.

We consider electronic noise modeling in tomographic image reconstruction when the measured signal is the sum of a Gaussian distributed electronic noise component and another random variable whose log-likelihood function satisfies a certain linearity condition. Examples of such likelihood functions include the Poisson distribution and an exponential dispersion (ED) model that can approximate the signal statistics in integration mode X-ray detectors. We formulate the image reconstruction problem as a maximum-likelihood estimation problem. Using an expectation-maximization approach, we demonstrate that a reconstruction algorithm can be obtained following a simple substitution rule from the one previously derived without electronic noise considerations. To illustrate the applicability of the substitution rule, we present examples of a fully iterative reconstruction algorithm and a sinogram smoothing algorithm both in transmission CT reconstruction when the measured signal contains additive electronic noise. Our simulation studies show the potential usefulness of accurate electronic noise modeling in low-dose CT applications.

With continuing improvements in spatial resolution of positron emission tomography (PET) scanners, small patient movements during PET imaging become a significant source of resolution degradation. This work develops and investigates a comprehensive formalism for accurate motion-compensated reconstruction which at the same time is very feasible in the context of high-resolution PET. In particular, this paper proposes an effective method to incorporate presence of scattered and random coincidences in the context of motion (which is similarly applicable to various other motion correction schemes). The overall reconstruction framework takes into consideration missing projection data which are not detected due to motion, and additionally, incorporates information from all detected events, including those which fall outside the field-of-view following motion correction. The proposed approach has been extensively validated using phantom experiments as well as realistic simulations of a new mathematical brain phantom developed in this work, and the results for a dynamic patient study are also presented.

To further improve pinhole single photon emission computed tomography (SPECT) imaging, there have been increasing interests in the use of nonstandard collimator designs and/or acquisition geometries. Homogeneous coordinates provide a compact and convenient framework to unify the geometric descriptions of the projection operators for these different imaging geometries, which may facilitate the implementation of iterative reconstruction algorithms and the investigation of crucial geometric calibration problems in pinhole SPECT. In this work, these advantages were demonstrated through three examples, namely, multipinhole SPECT, pinhole SPECT with a helical scanning orbit, and pinhole SPECT with dual detectors. Specifically, we showed adaptable implementations of iterative image reconstruction algorithms and translatable strategies for efficient geometric calibrations through unifying projection operators of the aforementioned imaging geometries. Notably, the unified geometric descriptions of multipinhole and single pinhole projection operators allowed us to derive that one can effectively calibrate a multipinhole geometry using only two point sources without measuring their distance. Experimental studies were performed to demonstrate the validity of our approaches, which may be extended to other pinhole SPECT and cone-beam X-ray computed tomography imaging geometries.

Rotating multisegment slant-hole (RMSSH) single photon emission computed tomography (SPECT) is suitable for detecting small and low-contrast breast lesions since it has much higher detection efficiency than conventional SPECT with a parallel-hole collimator and can image the breast at a closer distance. Our RMSSH SPECT reconstruction extends a previous rotation-shear transformation-based method to include nonuniform attenuation and collimator-detector response (CDR) compensation. To evaluate our reconstruction method, we performed two phantom simulation studies with 1) an isolated breast and 2) a breast phantom attached to the body torso. The reconstructed RMSSH SPECT images with attenuation and CDR compensation showed improved quantitative accuracy and less image artifacts than without. To evaluate the clinical efficacy of RMSSH SPECT mammography, we used a simulation study to compare with planar scintimammography in terms of the signal-to-noise ratio (SNR) value of a breast lesion. The RMSSH SPECT reconstruction images showed higher SNR value than the planar scintimammography images and even more so as we applied compensation for attenuation and collimator detector response. We conclude that attenuation and CDR compensation provide RMSSH SPECT mammography images with improved quality and quantitative accuracy.

Receiver operating characteristic (ROC) analysis is well established in the evaluation of systems involving binary classification tasks. However, medical tests often require distinguishing among more than two diagnostic alternatives. The goal of this work was to develop an ROC analysis method for three-class classification tasks. Based on decision theory, we developed a method for three-class ROC analysis. In this method, the objects were classified by making the decision that provided the maximal utility relative to the other two. By making assumptions about the magnitudes of the relative utilities of incorrect decisions, we found a decision model that maximized the expected utility of the decisions when using log-likelihood ratios as decision variables. This decision model consists of a two-dimensional decision plane with log likelihood ratios as the axes and a decision structure that separates the plane into three regions. Moving the decision structure over the decision plane, which corresponds to moving the decision threshold in two-class ROC analysis, and computing the true class 1, 2, and 3 fractions defined a three-class ROC surface. We have shown that the resulting three-class ROC surface shares many features with the two-class ROC curve; i.e., using the log likelihood ratios as the decision variables results in maximal expected utility of the decisions, and the optimal operating point for a given diagnostic setting (set of relative utilities and disease prevalences) lies on the surface. The volume under the three-class surface (VUS) serves as a figure-of-merit to evaluate different data acquisition systems or image processing and reconstruction methods when the assumed utility constraints are relevant.

The four-dimensional (4-D) NURBS-based cardiac-torso (NCAT) phantom, which provides a realistic model of the normal human anatomy and cardiac and respiratory motions, is used in medical imaging research to evaluate and improve imaging devices and techniques, especially dynamic cardiac applications. One limitation of the phantom is that it lacks the ability to accurately simulate altered functions of the heart that result from cardiac pathologies such as coronary artery disease (CAD). The goal of this work was to enhance the 4-D NCAT phantom by incorporating a physiologically based, finite-element (FE) mechanical model of the left ventricle (LV) to simulate both normal and abnormal cardiac motions. The geometry of the FE mechanical model was based on gated high-resolution X-ray multislice computed tomography (MSCT) data of a healthy male subject. The myocardial wall was represented as a transversely isotropic hyperelastic material, with the fiber angle varying from -90 degrees at the epicardial surface, through 0 degrees at the midwall, to 90 degrees at the endocardial surface. A time-varying elastance model was used to simulate fiber contraction, and physiological intraventricular systolic pressure-time curves were applied to simulate the cardiac motion over the entire cardiac cycle. To demonstrate the ability of the FE mechanical model to accurately simulate the normal cardiac motion as well as the abnormal motions indicative of CAD, a normal case and two pathologic cases were simulated and analyzed. In the first pathologic model, a subendocardial anterior ischemic region was defined. A second model was created with a transmural ischemic region defined in the same location. The FE-based deformations were incorporated into the 4-D NCAT cardiac model through the control points that define the cardiac structures in the phantom which were set to move according to the predictions of the mechanical model. A simulation study was performed using the FE-NCAT combination to investigate how the differences in contractile function between the subendocardial and transmural infarcts manifest themselves in myocardial Single photon emission computed tomography (SPECT) images. The normal FE model produced strain distributions that were consistent with those reported in the literature and a motion consistent with that defined in the normal 4-D NCAT beating heart model based on tagged magnetic resonance imaging (MRI) data. The addition of a subendocardial ischemic region changed the average transmural circumferential strain from a contractile value of -0.09 to a tensile value of 0.02. The addition of a transmural ischemic region changed average circumferential strain to a value of 0.13, which is consistent with data reported in the literature. Model results demonstrated differences in contractile function between subendocardial and transmural infarcts and how these differences in function are documented in simulated myocardial SPECT images produced using the 4-D NCAT phantom. Compared with the original NCAT beating heart model, the FE mechanical model produced a more accurate simulation for the cardiac motion abnormalities. Such a model, when incorporated into the 4-D NCAT phantom, has great potential for use in cardiac imaging research. With its enhanced physiologically based cardiac model, the 4-D NCAT phantom can be used to simulate realistic, predictive imaging data of a patient population with varying whole-body anatomy and with varying healthy and diseased states of the heart that will provide a known truth from which to evaluate and improve existing and emerging 4-D imaging techniques used in the diagnosis of cardiac disease.

Partial volume (PV) effects degrade the quantitative accuracy of SPECT brain images. In this paper, we extended a PV compensation (PVC) method originally developed for brain PET, the geometric transfer matrix (GTM) method, to brain SPECT using iterative reconstruction-based compensations. In the GTM method a linear transform between the true regional activities and the measured results was assumed. Elements of the GTM were calculated by projecting and reconstructing maps with uniform regions representing different structures. However, with iterative reconstruction methods, especially when reconstruction-based compensation for detector response was applied, we found that it was important to treat the region maps as a perturbation to the reconstructed image in the estimation of the GTM. This modified method, termed perturbation-based GTM (pGTM) was evaluated using Monte Carlo (MC) simulated and experimentally acquired data. Results showed great improvement of the quantitative accuracy in brain SPECT imaging. For MC simulated data, PVC using pGTM reduced the underestimation of striatal activities from 30% to less than 1.2%. For experimental data, PVC using pGTM reduced the underestimation of striatal activities from 36% to less than 7.8%. The underestimation of the striatum to background activity ratio was also improved from 31% to 2.7%.

In this paper, we apply the channelized Hotelling observer (CHO) using a defect detection task to the optimization and evaluation of three-dimensional iterative reconstruction-based compensation methods for myocardial perfusion single-photon emission computed tomography (SPECT). We used a population of 24 mathematical cardiac-torso phantoms that realistically model the activity and attenuation distribution in three classes of patients: females, and males with flat diaphragms and raised diaphragms. Projection data were generated and subsequently reconstructed using methods based on the ordered subsets-expectation maximization (OSEM) algorithm. The methods evaluated included compensation for attenuation, detector response blurring, and scatter in various combinations. We applied the CHO to optimize the number of iterations for OSEM and the cutoff frequency and order of a three-dimensional postreconstruction Butterworth filter. Using the optimal parameters, we then compared the compensation methods. The index of comparison in these studies was the area under the receiver operating characteristics curve (AUC) for the CHO. We found that attenuation compensation with either detector response or scatter compensation gave statistically significant increases in the AUC compared to attenuation compensation alone. The greatest increase in the AUC occurred when all three compensations were applied. These results indicate that compensation for detector response and scatter, in addition to attenuation compensation, will improve defect detectability in myocardial SPECT images.

This paper describes a new Bayesian modeling and analysis method for emission computed tomography based on a novel multiscale framework. The class of multiscale priors has the interesting feature that the "non-informative" member yields the traditional maximum likelihood solution; other choices are made to reflect prior belief as to the smoothness of the unknown intensity. Remarkably, this Bayesian multiscale framework admits a novel maximum a posteriori (MAP) reconstruction procedure using an expectation-maximization (EM) algorithm, in which the EM update equations have simple, closed-form expressions. The potential of this new framework is assessed using the Zubal brain phantom and simulated SPECT studies.

In this work, we present a method for approximating constrained maximum entropy (ME) reconstructions of SPECT data with modifications to a block-iterative maximum a posteriori (MAP) algorithm. Maximum likelihood (ML)-based reconstruction algorithms require some form of noise smoothing. Constrained ME provides a more formal method of noise smoothing without requiring the user to select parameters. In the context of SPECT, constrained ME seeks the minimum-information image estimate among those whose projections are a given distance from the noisy measured data, with that distance determined by the magnitude of the Poisson noise. Images that meet the distance criterion are referred to as feasible images. We find that modeling of all principal degrading factors (attenuation, detector response, and scatter) in the reconstruction is critical because feasibility is not meaningful unless the projection model is as accurate as possible. Because the constrained ME solution is the same as a MAP solution for a particular value of the MAP weighting parameter, beta, the constrained ME solution can be found with a MAP algorithm if the correct value of beta is found. We show that the RBI-MAP algorithm, if used with a dynamic scheme for estimating beta, can approximate constrained ME solutions in 20 or fewer iterations. We compare results for various methods of achieving feasible images on a simulation of Tl-201 cardiac SPECT data. Results show that the RBI-MAP ME approximation provides images and quantitative estimates close to those from a slower algorithm that gives the true ME solution. Also, we find that the ME results have higher spatial resolution and greater high-frequency noise content than a feasibility-based stopping rule, feasibility-based low-pass filtering, and a quadratic Gibbs prior with beta selected according to the feasibility criterion. We conclude that fast ME approximation is possible using either RBI-MAP with the dynamic procedure or a feasibility-based stopping rule, and that such reconstructions may be particularly useful in applications where resolution is critical.

Scatter compensation in Tl-201 single photon emission computed tomography (SPECT) presents an interesting challenge because of the multiple emission energies and relatively large proportion of scattered photons. In this paper, we present a simulation study investigating reconstructed image noise levels arising from various implementations of iterative reconstruction-based scatter compensation (RBSC) in Tl-201 SPECT. A two-stage analysis was used to study single and multiple energy window implementations of reconstruction-based scatter compensation, and RBSC was compared to the upper limits on performance for other approaches to handling scatter. In the first stage, singular value decomposition of the system transfer matrix was used to analyze noise levels in a manner independent of the choice of reconstruction algorithm, providing results valid across a wide range of regularizations. In the second stage, the data were reconstructed using maximum-likelihood expectation-maximization, and the noise properties of the resultant images were analyzed. The best RBSC performance was obtained using multiple energy windows, one for each emission photopeak, and RBSC outperformed the upper limit on subtraction-based compensation methods. Implementing RBSC with the correct choice of energy window acquisition scheme is a promising method for performing scatter compensation for Tl-201 SPECT.

We investigate the effects of initial conditions in the iterative maximum-likelihood (ML) reconstruction of fan-beam transmission projection data with truncation. In an iterative ML reconstruction, the estimate of the transmission reconstructed image in the previous iteration is multiplied by some factors to obtain the current estimate. Normally, a flat initial condition (FIC) or an image with equal positive pixel values is used as initial condition for an ML reconstruction. Usage of FIC has also been perceived as a way of preventing any bias on the reconstruction which may have come from the initial condition. When projection data have truncation, we show that using an FIC in an ML iterative reconstruction can introduce a bias to the reconstruction inside the densely sampled region (DSR), whose projection data have no truncation at any angle. To reduce this bias, we propose to use the largest right singular vector (LRSV) of the system matrix as the initial condition, and demonstrate that the bias can be reduced with the LRSV. When data truncation is reduced, the LRSV approaches the FIC. This result does not contradict to the use of FIC when projection data are not truncated. We also demonstrate that the reconstructed transmission image using LRSV as initial condition provides a more accurate attenuation coefficient distribution than that using FIC. However, the improvement is mostly in the area outside the DSR.

The effects of several of Gibbs prior distributions in terms of noise characteristics, edge sharpness, and overall quantitative accuracy of the final estimates obtained from an iterative maximum a posteriori (MAP) procedure applied to data from a realistic chest phantom are demonstrated. The effects of the adjustable parameters built into the prior distribution on these properties are examined. It is found that these parameter values influence the noise and edge characteristics of the final estimate and can generate reconstructions closer to the actual solution than maximum likelihood (ML). In addition, it is found that the choice of the shape of the prior distribution affects the noise characteristics and edge sharpness in the final estimate.