Measured Projection Data Research Articles

Optimizing Parameters for Enhanced Iterative Image Reconstruction Using Extended Power Divergence

In this paper, we propose a method for optimizing the parameter values in iterative reconstruction algorithms that include adjustable parameters in order to optimize the reconstruction performance. Specifically, we focus on the power divergence-based expectation-maximization algorithm, which includes two power indices as adjustable parameters. Through numerical and physical experiments, we demonstrate that optimizing the evaluation function based on the extended power-divergence and weighted extended power-divergence measures yields high-quality image reconstruction. Notably, the optimal parameter values derived from the proposed method produce reconstruction results comparable to those obtained using the true image, even when using distance functions based on differences between forward projection data and measured projection data, as verified by numerical experiments. These results suggest that the proposed method effectively improves reconstruction quality without the need for machine-learning techniques in parameter selection. Our findings also indicate that this approach is useful for enhancing the performance of iterative reconstruction algorithms, especially in medical imaging, where high-accuracy reconstruction under noisy conditions is required.

Iterative reconstruction for limited-angle CT using implicit neural representation

Objective. Limited-angle computed tomography (CT) presents a challenge due to its ill-posed nature. In such scenarios, analytical reconstruction methods often exhibit severe artifacts. To tackle this inverse problem, several supervised deep learning-based approaches have been proposed. However, they are constrained by limitations such as generalization issue and the difficulty of acquiring a large amount of paired CT images. Approach. In this work, we propose an iterative neural reconstruction framework designed for limited-angle CT. By leveraging a coordinate-based neural representation, we formulate tomographic reconstruction as a convex optimization problem involving a deep neural network. We then employ differentiable projection layer to optimize this network by minimizing the discrepancy between the predicted and measured projection data. In addition, we introduce a prior-based weight initialization method to ensure the network starts optimization with an informed initial guess. This strategic initialization significantly improves the quality of iterative reconstruction by stabilizing the divergent behavior in ill-posed neural fields. Our method operates in a self-supervised manner, thereby eliminating the need for extensive data. Main results. The proposed method outperforms other iterative and learning-based methods. Experimental results on XCAT and Mayo Clinic datasets demonstrate the effectiveness of our approach in restoring anatomical features as well as structures. This finding was substantiated by visual inspections and quantitative evaluations using NRMSE, PSNR, and SSIM. Moreover, we conduct a comprehensive investigation into the divergent behavior of iterative neural reconstruction, thus revealing its suboptimal convergence when starting from scratch. In contrast, our method consistently produced accurate images by incorporating an initial estimate as informed initialization. Significance. This work showcases the feasibility to reconstruct high-fidelity CT images from limited-angle x-ray projections. The proposed methodology introduces a novel data-free approach to enhance medical imaging, holding promise across various clinical applications.

Evaluation of low-dose computed tomography reconstruction using spatial-radon domain total generalized variation regularization

The x-ray radiation dose in computed tomography (CT) examination has been a major concern for patients. Lowing the tube current and exposure time in data acquisition is a straightforward and cost-effective strategy to reduce the x-ray radiation dose. However, this will inevitably increase the noise fluctuations in measured projection data, and the corresponding CT image quality will be severely degraded if noise suppression is not performed during image reconstruction. To reconstruct high-quality low-dose CT image, we present a spatial-radon domain total generalized variation (SRDTGV) regularization for statistical iterative reconstruction based on penalized weighted least-squares (PWLS) principle, which is called PWLS-SRDTGV for simplicity. The presented PWLS-SRDTGV model can simultaneously reconstruct high-quality CT image in space domain and its corresponding projection in radon domain. An efficient split Bregman algorithm was applied to minimize the cost function of the proposed reconstruction model. Qualitative and quantitative studies were performed to evaluate the effectiveness of the PWLS-SRDTGV image reconstruction algorithm using a digital 3D XCAT phantom and an anthropomorphic torso phantom. The experimental results demonstrate that PWLS-SRDTGV algorithm achieves notable gains in noise reduction, streak artifact suppression, and edge preservation compared with competing reconstruction approaches.

A high-resolution cone beam computed tomography (HRCBCT) reconstruction framework for CBCT-guided online adaptive therapy.

Kilo-voltage cone-beam computed tomography (CBCT) is a prevalent modality used for adaptive radiotherapy (ART) due to its compatibility with linear accelerators and ability to provide online imaging. However, the widely-used Feldkamp-Davis-Kress (FDK) reconstruction algorithm has several limitations, including potential streak aliasing artifacts and elevated noise levels. Iterative reconstruction (IR) techniques, such as total variation (TV) minimization, dictionary-based methods, and prior information-based methods, have emerged as viable solutions to address these limitations and improve the quality and applicability of CBCT in ART. One of the primary challenges in IR-based techniques is finding the right balance between minimizing image noise and preserving image resolution. To overcome this challenge, we have developed a new reconstruction technique called high-resolution CBCT (HRCBCT) that specifically focuses on improving image resolution while reducing noise levels. The HRCBCT reconstruction technique builds upon the conventional IR approach, incorporating three components: the data fidelity term, the resolution preservation term, and the regularization term. The data fidelity term ensures alignment between reconstructed values and measured projection data, while the resolution preservation term exploits the high resolution of the initial Feldkamp-Davis-Kress (FDK) algorithm. The regularization term mitigates noise during the IR process. To enhance convergence and resolution at each iterative stage, we applied Iterative Filtered Backprojection (IFBP) to the data fidelity minimization process. We evaluated the performance of the proposed HRCBCT algorithm using data from two physical phantoms and one head and neck patient. The HRCBCT algorithm outperformed all four different algorithms; FDK, Iterative Filtered Back Projection (IFBP), Compressed Sensing based Iterative Reconstruction (CSIR), and Prior Image Constrained Compressed Sensing (PICCS) methods in terms of resolution and noise reduction for all data sets. Line profiles across three line pairs of resolution revealed that the HRCBCT algorithm delivered the highest distinguishable line pairs compared to the other algorithms. Similarly, the Modulation Transfer Function (MTF) measurements, obtained from the tungsten wire insert on the CatPhan 600 physical phantom, showed a significant improvement with HRCBCT over traditional algorithms. The proposed HRCBCT algorithm offers a promising solution for enhancing CBCT image quality in adaptive radiotherapy settings. By addressing the challenges inherent in traditional IR methods, the algorithm delivers high-definition CBCT images with improved resolution and reduced noise throughout each iterative step. Implementing the HR CBCT algorithm could significantly impact the accuracy of treatment planning during online adaptive therapy.

A feasibility study on deep-neural-network-based dose-neutral dual-energy digital breast tomosynthesis.

Diagnostic performance based on x-ray breast imaging is subject to breast density. Although digital breast tomosynthesis (DBT) is reported to outperform conventional mammography in denser breasts, mass detection and malignancy characterization are often considered challenging yet. As an improved diagnostic solution to the dense breast cases, we propose a dual-energy DBT imaging technique that enables breast compositional imaging at comparable scanning time and patient dose compared to the conventional single-energy DBT. The proposed dual-energy DBT acquires projection data by alternating two different energy spectra. Then, we synthesize unmeasured projection data using a deep neural network that exploits the measured projection data and adjacent projection data obtained under the other x-ray energy spectrum. For material decomposition, we estimate partial path lengths of an x-ray through water, lipid, and protein from the measured and the synthesized projection data with the object thickness information. After material decomposition in the projection domain, we reconstruct material-selective DBT images. The deep neural network is trained with the numerical breast phantoms. A pork meat phantom is scanned with a prototype dual-energy DBT system to demonstrate the feasibility of the proposed imaging method. The developed deep neural network successfully synthesized missing projections. Material-selective images reconstructed from the synthesized data present comparable compositional contrast of the cancerous masses compared with those from the fully measured data. The proposed dual-energy DBT scheme is expected to substantially contribute to enhancing mass malignancy detection accuracy particularly in dense breasts.

Neural network regularization in the problem of few-view computed tomography

The computed tomography allows to reconstruct the inner morphological structure of an object without physical destructing. The accuracy of digital image reconstruction directly depends on the measurement conditions of tomographic projections, in particular, on the number of recorded projections. In medicine, to reduce the dose of the patient load there try to reduce the number of measured projections. However, in a few-view computed tomography, when we have a small number of projections, using standard reconstruction algorithms leads to the reconstructed images degradation. The main feature of our approach for few-view tomography is that algebraic reconstruction is being finalized by a neural network with keeping measured projection data because the additive result is in zero space of the forward projection operator. The final reconstruction presents the sum of the additive calculated with the neural network and the algebraic reconstruction. First is an element of zero space of the forward projection operator. The second is an element of orthogonal addition to the zero space. Last is the result of applying the algebraic reconstruction method to a few-angle sinogram. The dependency model between elements of zero space of forward projection operator and algebraic reconstruction is built with neural networks. It demonstrated that realization of the suggested approach allows achieving better reconstruction accuracy and better computation time than state-of-the-art approaches on test data from the Low Dose CT Challenge dataset without increasing reprojection error.

Low-dose computed tomography reconstruction regularized by structural group sparsity joined with gradient prior

Low-dose computed tomography (LdCT) imaging can greatly reduce the radiation dose imposed to patient, however it leads to the low signal-to-noise ratio (SNR) measured projection data. Using conventional analytical reconstruction method (e.g., filtered back-projection method), the reconstruction results usually suffer from serious noise in LdCT. To obtain high-quality CT images, iterative reconstruction method combined with prior knowledge of the object is of great importance. In this work, both structural group sparsity and gradient prior sparsity are jointed as a novel regularization constraint in the proposed CT reconstruction model. To solve the optimization-based CT reconstruction problem, original problem was transformed into a series of sub-problems based on alternating direction method of multipliers framework. The merit of the proposed joint regularization method is that global and local sparsity are both utilized. To valid the performance of proposed reconstruction algorithm, we did simulated experiments with different noise levels and real data studies. The qualitative and quantitative analyses show that the proposed reconstruction algorithm has better performance than other iterative reconstruction algorithms. What's more, compared to the existing iterative reconstruction methods, the proposed reconstruction algorithm can well reconstructed important structure features and effectively suppress the noise and artifacts.

Automated FDK-Filter Selection for Cone-Beam CT in Research Environments

Users of X-ray (micro-)CT in research environments often study many different types of objects, with many different research questions. For each new scan, the settings of the scan (number of angles, dose, cone angle) are chosen by the user, often based on how much time is available, the dose sensitivity of the sample, and geometrical characteristics of the particular CT-scanner that is used. The FDK algorithm is the most common reconstruction method used for circular cone-beam data. Its filter is typically chosen based on characteristics of the object, the scan parameters, and task-specific metrics. This imposes a problem for case-by-case research use, as selecting an optimal filter requires manual and subjective user choices as well as considerable expertise. In this article we present a computationally efficient and automated method to compute an FDK-filter for a given measured projection dataset that is optimal with respect to an objectively defined quality criterion that is based on the difference between the measured projection data and the computed projections of the reconstructed volume. We show that for a variety of objects, scan settings (number of angles and noise levels), and tasks (porosity quantification, threshold-based segmentation), the FDK-filters computed by our approach yield accurate results in terms of several different metrics that are comparable to filters manually selected for the experiments.

A Direct Method for Reconstructing Dynamic SPECT Images

The goal in dynamic SPECT studies is to estimate the time-activity functions describing the tracer activity changes in the observed tissue. Dynamic studies can be created as a series of static projection images recorded in several subsequent time frames. By applying a static reconstruction algorithm for each images independently and fitting the parameters of a kinetic model to the activity on the reconstructed images we can estimate the function of the tracer activity changes. However, due to the limited data collection time images in dynamic studies often suffer from poor statistics influencing the accuracy of the kinetic function estimation. According to previous studies improved function reconstruction can be achieved by applying reconstruction algorithms that estimate kinetic parameters directly from the measured projection data. In this study our previously developed Monte Carlo based maximum likelihood expectation maximization (ML-EM) SPECT reconstruction method - originally verified for static SPECT studies - is extended for dynamic studies. An iterative dynamic reconstruction algorithm is developed that estimates directly the temporal function of the tracer activity in the image voxels in each iterations and uses the static ML-EM iteration afterwards. The method of sieves has been applied for regularization of the estimated kinetic parameters. The estimation accuracy of the suggested dynamic reconstruction algorithm was evaluated in a mathematical phantom study with different time functions.

Iterative reconstruction for sparse-view x-ray CT using alpha-divergence constrained total generalized variation minimization.

Accurate statistical model of the measured projection data is essential for computed tomography (CT) image reconstruction. The transmission data can be described by a compound Poisson distribution upon an electronic noise background. However, such a statistical distribution is numerically intractable for image reconstruction. Although the sinogram data is easily manipulated, it lacks a statistical description for image reconstruction. To address this problem, we present an alpha-divergence constrained total generalized variation (AD-TGV) method for sparse-view x-ray CT image reconstruction. The AD-TGV method is formulated as an optimization problem, which balances the alpha-divergence (AD) fidelity and total generalized variation (TGV) regularization in one framework. The alpha-divergence is used to measure the discrepancy between the measured and estimated projection data. The TGV regularization can effectively eliminate the staircase and patchy artifacts which is often observed in total variation (TV) regularization. A modified proximal forward-backward splitting algorithm was proposed to minimize the associated objective function. Qualitative and quantitative evaluations were carried out on both phantom and patient data. Compared with the original TV-based method, the evaluations clearly demonstrate that the AD-TGV method achieves higher accuracy and lower noise, while preserving structural details. The experimental results show that the presented AD-TGV method can achieve more gains over the AD-TV method in preserving structural details and suppressing image noise and undesired patchy artifacts. The authors can draw the conclusion that the presented AD-TGV method is potential for radiation dose reduction by lowering the milliampere-seconds (mAs) and/or reducing the number of projection views.

The derivative-free Fourier shell identity for photoacoustics.

In X-ray tomography, the Fourier slice theorem provides a relationship between the Fourier components of the object being imaged and the measured projection data. The Fourier slice theorem is the basis for X-ray Fourier-based tomographic inversion techniques. A similar relationship, referred to as the ‘Fourier shell identity’ has been previously derived for photoacoustic applications. However, this identity relates the pressure wavefield data function and its normal derivative measured on an arbitrary enclosing aperture to the three-dimensional Fourier transform of the enclosed object evaluated on a sphere. Since the normal derivative of pressure is not normally measured, the applicability of the formulation is limited in this form. In this paper, alternative derivations of the Fourier shell identity in 1D, 2D polar and 3D spherical polar coordinates are presented. The presented formulations do not require the normal derivative of pressure, thereby lending the formulas directly adaptable for Fourier based absorber reconstructions.

Sparse-View CT Image Recovery Using Two-Step Iterative Shrinkage-Thresholding Algorithm

We investigate an image recovery method for sparse-view computed tomography (CT) using an iterative shrinkage algorithm based on a second-order approach. The two-step iterative shrinkage-thresholding (TwIST) algorithm including a total variation regularization technique is elucidated to be more robust than other first-order methods; it enables a perfect restoration of an original image even if given only a few projection views of a parallel-beam geometry. We find that the incoherency of a projection system matrix in CT geometry sufficiently satisfies the exact reconstruction principle even when the matrix itself has a large condition number. Image reconstruction from fan-beam CT can be well carried out, but the retrieval performance is very low when compared to a parallel-beam geometry. This is considered to be due to the matrix complexity of the projection geometry. We also evaluate the image retrieval performance of the TwIST algorithm using measured projection data.

Investigation of imaging properties for submillimeter rectangular pinholes.

Recently, a multipinhole collimator with inserts that have both rectangular apertures and rectangular fields of view (FOVs) has been proposed for SPECT imaging since it can tile the projection onto the detector efficiently and the FOVs in transverse and axial directions become separable. The purpose of this study is to investigate the image properties of rectangular-aperture pinholes with submillimeter apertures sizes. In this work, the authors have conducted sensitivity and FOV experiments for 18 replicates of a prototype insert fabricated in platinum/iridium (Pt/Ir) alloy with submillimeter square-apertures. A sin(q)θ fit to the experimental sensitivity has been performed for these inserts. For the FOV measurement, the authors have proposed a new formula to calculate the projection intensity of a flood image on the detector, taking into account the penumbra effect. By fitting this formula to the measured projection data, the authors obtained the acceptance angles. The mean (standard deviation) of fitted sensitivity exponents q and effective edge lengths we were, respectively, 10.8 (1.8) and 0.38 mm (0.02 mm), which were close to the values, 7.84 and 0.396 mm, obtained from Monte Carlo calculations using the parameters of the designed inserts. For the FOV measurement, the mean (standard deviation) of the transverse and axial acceptances were 35.0° (1.2°) and 30.5° (1.6°), which are in good agreement with the designed values (34.3° and 29.9°). These results showed that the physical properties of the fabricated inserts with submillimeter aperture size matched our design well.

Basis Functions in Image Reconstruction From Projections: A Tutorial Introduction

The series expansion approaches to image reconstruction from projections assume that the object to be reconstructed can be represented as a linear combination of fixed basis functions and the task of the reconstruction algorithm is to estimate the coefficients in such a linear combination based on the measured projection data. It is demonstrated that using spherically symmetric basis functions (blobs), instead of ones based on the more traditional pixels, yields superior reconstructions of medically relevant objects. The demonstration uses simulated computerized tomography projection data of head cross-sections and the series expansion method ART for the reconstruction. In addition to showing the results of one anecdotal example, the relative efficacy of using pixel and blob basis functions in image reconstruction from projections is also evaluated using a statistical hypothesis testing based task oriented comparison methodology. The superiority of the efficacy of blob basis functions over that of pixel basis function is found to be statistically significant.

Compressed-sensing (CS)-based digital breast tomosynthesis (DBT) reconstruction for low-dose, accurate 3D breast X-ray imaging

In practical applications of three-dimensional (3D) tomographic techniques, such as digital breast tomosynthesis (DBT), computed tomography (CT), etc., there are often challenges for accurate image reconstruction from incomplete data. In DBT, in particular, the limited-angle and few-view projection data are theoretically insufficient for exact reconstruction; thus, the use of common filtered-backprojection (FBP) algorithms leads to severe image artifacts, such as the loss of the average image value and edge sharpening. One possible approach to alleviate these artifacts may employ iterative statistical methods because they potentially yield reconstructed images that are in better accordance with the measured projection data. In this work, as another promising approach, we investigated potential applications to low-dose, accurate DBT imaging with a state-of-the-art reconstruction scheme based on compressed-sensing (CS) theory. We implemented an efficient CS-based DBT algorithm and performed systematic simulation works to investigate the imaging characteristics. We successfully obtained DBT images of substantially very high accuracy by using the algorithm and expect it to be applicable to developing the next-generation 3D breast X-ray imaging system.

GPU-accelerated Monte Carlo based scatter correction in brain PET/MR.

To develop and evaluate a fast and accurate Monte Carlo simulation (MCS) based scatter correction for PET/MR imaging, based on Geant4 using graphical processing units (GPUs). The GPU implementation by Bert et al. [1] including the photon tracking within a voxelized volume was extended with the modeling of the detection process in the Siemens MR-BrainPET. Using NVIDIA’s CUDA photon pairs undergo several kernel functions in parallel, from their generation according to the activity distribution up to their detection in the scanner. Subsequently, coincidences are sorted and stored in list-mode. The new GPU implementation (GeForce GTX690) was validated by comparison with Gate v6.2 on a single CPU (Intel Core i7, 3.4GHz), showing a speedup factor of 135. The use of multiple GPUs can further increase this acceleration. For Compton scatter correction the reconstructed emission image, the patient MR-derived attenuation map and a CT-derived attenuation template of the MR coils are used as input for the simulation. The resulting simulated projection data are scaled to the normalized measured projection data. Thus, the often unstable fit to the distribution tails, necessary for single scatter simulation (SSS)[2], is circumvented. The scaled simulated scatter distribution is then incorporated in the reconstruction. The proposed scatter correction methodology was evaluated and compared to the SSS approach using sphere phantom measurements. Finally, the effect on patient data was investigated. Phantom results suggest an improved contrast with our new MC-based scatter correction, especially for measurements including the MR coils, where the contrast recovery was improved by 10-14%. First patient images also show improved grey/white matter contrast. Table 1 Comparison of recovery coefficients after scatter correction based on MCS and SSS. MC-based scatter correction shows improved recovery coefficients for the hot spheres. Figure 1 Assessment of image quality according to NEMA NU 2-2007. Images show the phantom with a hot spheres/background ratio of 8:1 measured with MR head coils inside the BrainPET scanner. Figure 2 Comparison of reconstructed FDG images using the scatter estimate provided by the vendor’s SSS (left) and our MCS method (right). Images were reconstructed using the vendor provided 3D OP-OSEM algorithm with 2 subsets and 32 iterations. The new GPU-accelerated MCS allows for fast and accurate estimation of scattered coincidences in PET studies using the Siemens MR-BrainPET with a major speed-up compared to standard MCS and superior image quality compared with the standard correction based on SSS.

Neutron Tomography of a Fuel Cell: Statistical Learning Implementation of a Penalized Likelihood Method

At the NIST Neutron Imaging Facility, we collect neutron projection data for both the dry and wet states of a Proton-Exchange-Membrane (PEM) fuel cell. Transmitted thermal neutrons captured in a scintillator doped with lithium-6 produce scintillation light that is detected by an amorphous silicon detector. Based on joint analysis of the dry and wet state projection data, we reconstruct a residual neutron attenuation image with a Penalized Likelihood method with an edge-preserving Huber penalty function that has two parameters that control how well jumps in the reconstruction are preserved and how well noisy fluctuations are smoothed out. The choice of these parameters greatly influences the resulting reconstruction. We present a data-driven method that objectively selects these parameters, and study its performance for both simulated and experimental data. Before reconstruction, we transform the projection data so that the variance-to-mean ratio is approximately one. For both simulated and measured projection data, the Penalized Likelihood method reconstruction is visually sharper than a reconstruction yielded by a standard Filtered Back Projection method. In an idealized simulation experiment, we demonstrate that the cross validation procedure selects regularization parameters that yield a reconstruction that is nearly optimal according to a root-mean-square prediction error criterion.

Evaluation of robustness of maximum likelihood cone-beam CT reconstruction with total variation regularization

The objective of this paper is to evaluate an iterative maximum likelihood (ML) cone-beam computed tomography (CBCT) reconstruction with total variation (TV) regularization with respect to the robustness of the algorithm due to data inconsistencies. Three different and (for clinical application) typical classes of errors are considered for simulated phantom and measured projection data: quantum noise, defect detector pixels and projection matrix errors. To quantify those errors we apply error measures like mean square error, signal-to-noise ratio, contrast-to-noise ratio and streak indicator. These measures are derived from linear signal theory and generalized and applied for nonlinear signal reconstruction. For quality check, we focus on resolution and CT-number linearity based on a Catphan phantom. All comparisons are made versus the clinical standard, the filtered backprojection algorithm (FBP). In our results, we confirm and substantially extend previous results on iterative reconstruction such as massive undersampling of the number of projections. Errors of projection matrix parameters of up to 1° projection angle deviations are still in the tolerance level. Single defect pixels exhibit ring artifacts for each method. However using defect pixel compensation, allows up to 40% of defect pixels for passing the standard clinical quality check. Further, the iterative algorithm is extraordinarily robust in the low photon regime (down to 0.05 mAs) when compared to FPB, allowing for extremely low-dose image acquisitions, a substantial issue when considering daily CBCT imaging for position correction in radiotherapy. We conclude that the ML method studied herein is robust under clinical quality assurance conditions. Consequently, low-dose regime imaging, especially for daily patient localization in radiation therapy is possible without change of the current hardware of the imaging system.

Development and evaluation of an improved quantitative 90Y bremsstrahlung SPECT method

Yttrium-90 ((90)Y) is one of the most commonly used radionuclides in targeted radionuclide therapy (TRT). Since it decays with essentially no gamma photon emissions, surrogate radionuclides (e.g., (111)In) or imaging agents (e.g., (99m)Tc MAA) are typically used for treatment planning. It would, however, be useful to image (90)Y directly in order to confirm that the distributions measured with these other radionuclides or agents are the same as for the (90)Y labeled agents. As a result, there has been a great deal of interest in quantitative imaging of (90)Y bremsstrahlung photons using single photon emission computed tomography (SPECT) imaging. The continuous and broad energy distribution of bremsstrahlung photons, however, imposes substantial challenges on accurate quantification of the activity distribution. The aim of this work was to develop and evaluate an improved quantitative (90)Y bremsstrahlung SPECT reconstruction method appropriate for these imaging applications. Accurate modeling of image degrading factors such as object attenuation and scatter and the collimator-detector response is essential to obtain quantitatively accurate images. All of the image degrading factors are energy dependent. Thus, the authors separated the modeling of the bremsstrahlung photons into multiple categories and energy ranges. To improve the accuracy, the authors used a bremsstrahlung energy spectrum previously estimated from experimental measurements and incorporated a model of the distance between (90)Y decay location and bremsstrahlung emission location into the SIMIND code used to generate the response functions and kernels used in the model. This improved Monte Carlo bremsstrahlung simulation was validated by comparison to experimentally measured projection data of a (90)Y line source. The authors validated the accuracy of the forward projection model for photons in the various categories and energy ranges using the validated Monte Carlo (MC) simulation method. The forward projection model was incorporated into an iterative ordered subsets-expectation maximization (OS-EM) reconstruction code to allow for quantitative SPECT reconstruction. The resulting code was validated using both a physical phantom experiment with spherical objects in a warm background and a realistic anatomical phantom simulation. In the physical phantom study, the authors evaluated the method in terms of quantitative accuracy of activity estimates in the spheres; in the simulation study, the authors evaluated the accuracy and precision of activity estimates from various organs and compared them to results from a previously proposed method. The authors demonstrated excellent agreement between the experimental measurement and Monte Carlo simulation. In the XCAT phantom simulation, the proposed method achieved much better accuracy in the modeling (error in photon counts was -1.1 %) compared to a previously proposed method (errors were more than 20 %); the quantitative accuracy of activity estimates was excellent for all organs (errors were from -1.6 % to 11.9 %) and comparable to previously published results for (131)I using the same collimator. The proposed (90)Y bremsstrahlung SPECT reconstruction method provided very accurate estimates of organ activities, with accuracies approaching those previously observed for (131)I. The method may be useful in verifying organ doses for targeted radionuclide therapy using (90)Y.

Blockwise conjugate gradient methods for image reconstruction in volumetric CT

Cone beam computed tomography (CBCT) enables volumetric image reconstruction from 2D projection data and plays an important role in image guided radiation therapy (IGRT). Filtered back projection is still the most frequently used algorithm in applications. The algorithm discretizes the scanning process (forward projection) into a system of linear equations, which must then be solved to recover images from measured projection data. The conjugate gradients (CG) algorithm and its variants can be used to solve (possibly regularized) linear systems of equations Ax=b and linear least squares problems minx∥b−Ax∥2, especially when the matrix A is very large and sparse. Their applications can be found in a general CT context, but in tomography problems (e.g. CBCT reconstruction) they have not widely been used. Hence, CBCT reconstruction using the CG-type algorithm LSQR was implemented and studied in this paper. In CBCT reconstruction, the main computational challenge is that the matrix A usually is very large, and storing it in full requires an amount of memory well beyond the reach of commodity computers. Because of these memory capacity constraints, only a small fraction of the weighting matrix A is typically used, leading to a poor reconstruction. In this paper, to overcome this difficulty, the matrix A is partitioned and stored blockwise, and blockwise matrix-vector multiplications are implemented within LSQR. This implementation allows us to use the full weighting matrix A for CBCT reconstruction without further enhancing computer standards. Tikhonov regularization can also be implemented in this fashion, and can produce significant improvement in the reconstructed images.