Accelerated Optimization Algorithms for Statistical 3D X-ray Computed Tomography Image Reconstruction.

Computed Tomography;Statistical Image Reconstruction;Optimization Algorithms;Iterative Algorithms;Ordered Subsets;Gradient Methods;Electrical Engineering;Engineering;Electrical Engineering: Systems

Kim, DonghwanHero Iii, Alfred O. ;

University of Michigan

关键词: Computed Tomography;    Statistical Image Reconstruction;    Optimization Algorithms;    Iterative Algorithms;    Ordered Subsets;    Gradient Methods;    Electrical Engineering;    Engineering;    Electrical Engineering: Systems;   

Others  :  https://deepblue.lib.umich.edu/bitstream/handle/2027.42/109007/kimdongh_1.pdf?sequence=1&isAllowed=y

瑞士|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

X-ray computed tomography (CT) has been widely celebrated for its ability to visualize patient anatomy, but increasing radiation exposure to patients is a concern. Statistical image reconstruction algorithms in X-ray CT can provide improved image quality for reduced dose levels in contrast to the conventional filtered back-projection (FBP) methods. However, the statistical approach requires substantial computation time. Therefore, this dissertation focuses on developing fast iterative algorithms for statistical reconstruction. Ordered subsets (OS) methods have been used widely in tomography problems, because they reduce the computational cost by using only a subset of the measurement data per iteration. They are already used in commercial PET and SPECT products. However, OS methods require too long a reconstruction time in X-ray CT to be used routinely for every clinical CT scan. In this dissertation, two main approaches are proposed for accelerating OS algorithms, one that uses new optimization transfer approaches and one that combines with momentum algorithms. The first, the separable quadratic surrogates (SQS) methods, one widely used optimization transfer method with OS methods, have been accelerated in three different ways. Among them, a nonuniform (NU) SQS method encouraging larger step sizes for the voxels that are expected to change more has highly accelerated OS methods. Second, combining OS methods and momentum approaches (OS-momentum) in a way that reuses previous updates with almost negligible increased computation resulted in a very fast convergence rate. This version focused on using widely celebrated Nesterov;;s momentum methods. OS-momentum algorithms sometimes encountered instability, so diminishing step size rule has been adapted for improving the stability while preserving the fast convergence rate. To further accelerate OS-momentum algorithms, this dissertation proposes novel momentum methods that are twice as fast yet have remarkably simple implementations comparable to Nesterov;;s methods. In addition to OS-type algorithms, one variant of the block coordinate descent (BCD) algorithm, called Axial BCD (ABCD), is investigated, which is specifically designed for 3D CT geometry. Simulated and real patient 3D CT scans are used to examine the acceleration of the proposed algorithms.