Van-Giang Nguyen

GPU-accelerated 3D Bayesian image reconstruction from Compton scattered data

This paper describes the development of fast Bayesian reconstruction methods for Compton cameras using commodity graphics hardware. For fast iterative reconstruction, not only is it important to increase the convergence rate, but also it is equally important to accelerate the computation of time-consuming and repeated operations, such as projection and backprojection. Since the size of the system matrix for a typical Compton camera is intractably large, it is impractical to use a conventional caching scheme that stores the pre-calculated elements of a system matrix and uses them for the calculation of projection and backprojection. In this paper we propose GPU (graphics processing unit)-accelerated methods that can rapidly perform conical projection and backprojection on the fly. Since the conventional ray-based backprojection method is inefficient for parallel computing on GPUs, we develop voxel-based conical backprojection methods using two different approximation schemes. In the first scheme, we approximate the intersecting chord length of the ray passing through a voxel by the perpendicular distance from the center to the ray. In the second scheme, each voxel is regarded as a dimensionless point rather than a cube so that the backprojection can be performed without the need for calculating intersecting chord lengths or their approximations. Our simulation studies show that the GPU-based method dramatically improves the computational speed with only minor loss of accuracy in reconstruction. With the development of high-resolution detectors, the difference in the reconstruction accuracy between the GPU-based method and the CPU-based method will eventually be negligible.

Incorporating Anatomical Side Information Into PET Reconstruction Using Nonlocal Regularization

With the introduction of combined positron emission tomography (PET)/computed tomography (CT) or PET/magnetic resonance imaging (MRI) scanners, there is an increasing emphasis on reconstructing PET images with the aid of the anatomical side information obtained from X-ray CT or MRI scanners. In this paper, we propose a new approach to incorporating prior anatomical information into PET reconstruction using the nonlocal regularization method. The nonlocal regularizer developed for this application is designed to selectively consider the anatomical information only when it is reliable. As our proposed nonlocal regularization method does not directly use anatomical edges or boundaries which are often used in conventional methods, it is not only free from additional processes to extract anatomical boundaries or segmented regions, but also more robust to the signal mismatch problem that is caused by the indirect relationship between the PET image and the anatomical image. We perform simulations with digital phantoms. According to our experimental results, compared to the conventional method based on the traditional local regularization method, our nonlocal regularization method performs well even with the imperfect prior anatomical information or in the presence of signal mismatch between the PET image and the anatomical image.

Three-dimensional edge-preserving regularization for Compton camera reconstruction

Compton imaging is often recognized as a potentially more valuable 3-D technique than conventional emission tomography. However, due to the inherent complexity of massive data set computations for the conical projection-backprojection operation, most reconstruction algorithms have been based on analytical methods rather than statistical methods. In this paper, we investigate a maximum a posteriori (MAP) approach to Compton camera reconstruction, which provides reconstructions with superior noise characteristics compared to analytical methods. In order to preserve edges that can occur occasionally in the underlying object, we use a convex-nonquadratic smoothing prior and apply to a row-action based regularized maximum likelihood method, which is provably convergent to a true MAP solution. Our preliminary results indicate that, although the statistical methods considered in this paper are not as fast as analytical methods, they have a great potential to improve quantitative accuracy in Compton imaging.

Image reconstruction from limited-view projections by convex nonquadratic spline regularization

We investigate performance of a convex nonquadratic (CNQ) spline regularization method applied to limited-angle tomography reconstruction. Since limited-angle data lack projections over a certain range of view angles, they produce poor reconstructions with streak artifacts and geometric distortions. To obtain a good solution, a feasible prior that can eliminate or reduce artifacts and distortions is necessary. The CNQ prior used in this paper is expressed as a linear combination of the first- and the second-order spatial derivatives and applied to a CNQ penalty function. To determine a solution efficiently, we use the fast globally convergent block sequential regularized expectation maximization algorithm. Our experimental results demonstrate that the hybrid CNQ spline prior outperforms conventional nonquadratic priors in eliminating limited-angle artifacts.

Anatomy-based PET image reconstruction using nonlocal regularization

We propose a new nonlocal regularization method for PET image reconstruction with the aid of high-resolution anatomical images. Unlike conventional reconstruction methods using prior anatomical information, our method using nonlocal regularization does not require additional processes to extract anatomical boundaries or segmented regions. The nonlocal regularization method applied to anatomy-based PET image reconstruction is expected to effectively reduce the error that often occurs due to signal mismatch between the PET image and the anatomical image. We also show that our method can be useful for enhancing the image resolution. To reconstruct the high-resolution image that represents the original underlying source distribution effectively sampled at a higher spatial sampling rate, we model the underlying PET image on a higher-resolution grid and perform our nonlocal regularization method with the aid of the side information obtained from high-resolution anatomical images. Our experimental results demonstrate that, compared to the conventional method based on local smoothing, our nonlocal regularization method enhances the resolution as well as the reconstruction accuracy even with the imperfect prior anatomical information or in the presence of signal mismatch between the PET image and the anatomical image.

Graphics processing unit-accelerated iterative tomographic reconstruction with strip-integral system model

Abstract. In tomographic reconstruction, the major factors that affect the performance of an algorithm are the computational efficiency and the reconstruction accuracy. The computational efficiency has recently been achieved by using graphics processing units (GPUs). However, efforts to improve the accuracy of modeling a projector-backprojector pair have been hindered by the need for approximations to maximize the efficiency of the GPU. The approximations used for modeling a projector-backprojector pair often cause artifacts in reconstruction which propagate through iterations and lower the accuracy of reconstruction. In addition to the approximations, the unmatched projector-backprojector pairs often used for GPU-accelerated methods also cause additional errors in iterative reconstruction. For reconstruction with relatively low resolution, the degradation due to these artifacts and errors becomes more significant as the number of iterations is increased. In this work, we develop GPU-accelerated methods for 2-D reconstruction without using any approximations for parallelizing the projection and backprojection operations. The methods of projection and backprojection we use in this work are the strip area-based method and the distance-driven method. Our proposed methods were successfully implemented on the GPU and resulted in high-performance computing in iterative reconstruction while retaining the reconstruction accuracy by providing a perfectly matched projector-backprojector pair.

Nonlocal-means approaches to anatomy-based PET image reconstruction

We propose nonlocal-means (NLM) approaches to incorporating prior anatomical information into PET image reconstruction. In our NLM approaches, adaptive smoothing is performed on the PET image by using the weights that reflect the self-similarity property of the underlying PET image with the aid of the additional information obtained from the anatomical image. Unlike conventional anatomy-based reconstruction methods, our methods using the anatomy-based NLM priors do not require additional processes to extract anatomical boundaries or segmented regions. In this work we apply the NLM algorithm to both the maximum a posteriori (MAP) and the minimum cross entropy (MXE) reconstruction methods. Our experimental results demonstrate that, compared to the conventional methods based on local smoothing, our methods based on the nonlocal means algorithm remarkably improve the reconstruction accuracy in terms of both percentage error and regional bias even with imperfect anatomical information or in the presence of signal mismatch between the PET image and the anatomical image.

GPU accelerated statistical image reconstruction for Compton cameras

We propose GPU (graphics processing unit) accelerated methods that can dramatically improve the computational performance of statistical image reconstruction algorithms for Compton cameras. Since the conventional ray-based backprojection method is inefficient for GPU, we develop a fully voxel-based backprojection method which can maximize the performance of GPU. In this method, the cone surface is sampled by the evenly distributed rays originated from the vertex of the cone. The intersecting chord length of the ray passing through a voxel is then approximated by the normal distance from the center of the voxel to the ray. Although this approximation can cause an error in backprojection, according to our simulation results, it does not noticeably affect the reconstruction. Our experimental phantom studies with the RAMLA (row-action maximum likelihood algorithm), which is a relaxed version of the OS-EM (ordered subsets expectation maximization) algorithm, indicate that the GPU-based method is roughly 50 times faster in computation time per iteration than the CPU-based method. According to our experimental results, for an acceptable 64×64×64 image reconstructed by RAMLA with 64 subsets and 8 iterations, the CPU-based method takes about 2.3 hours, whereas the GPU-based method takes only 2.7 minutes.

GPU-accelerated exact strip integrals for 2-D iterative reconstruction in emission tomography

The computational efficiency of iterative tomographic reconstruction has been dramatically improved by using GPUs (graphics processing units). However, the use of unmatched projector-backprojector pairs and the approximations for the efficiency of the GPU cause artifacts and errors in reconstruction. For PET or SPECT reconstruction with relatively low resolution, the degradation due to these artifacts and errors becomes more significant as the number of iterations is increased. In this work, we develop a GPU-accelerated method which does not use any approximation for parallelizing the projection and backprojection operations. The method of projection and backprojection we use in this work is based on the area weighted strip integral method which is known as one of the most accurate methods for 2-D reconstruction but has not been considered for acceleration by using the GPU. Our proposed method is guaranteed to retain the reconstruction accuracy by providing a perfectly matched projector-backprojector pair.

Rebinning-Based Deterministic Image Reconstruction Methods for Compton Camera

While Compton imaging is recognized as a valuable 3-D technique in nuclear medicine, reconstructing an image from Compton scattered data has been of a difficult problem due to its computational complexity. The most complex and time-consuming computation in Compton camera reconstruction is to perform the conical projection and backprojection operations. To alleviate the computational burden imposed by these operations, we investigate a rebinning method which can convert conical projections into parallel projections. The use of parallel projections allows to directly apply the existing deterministic reconstruction methods, which have been useful for conventional emission tomography, to Compton camera reconstruction. To convert conical projections into parallel projections, a cone surface is sampled with a number of lines. Each line is projected onto an imaginary plane that is mostly perpendicular to the line. The projection data rebinned in each imaginary plane can then be treated as the standard parallel projection data. To validate the rebinning method, we tested with the representative deterministic algorithms, such as the filtered backprojection method and the algebraic reconstruction technique. Our experimental results indicate that the rebinning method can be useful when the direct application of existing deterministic methods is needed for Compton camera reconstruction.