Accelerated fast iterative shrinkage thresholding algorithms for sparsity-regularized cone-beam CT image reconstruction

• Published in: Medical physics (Lancaster) Vol. 43; no. 4; pp. 1849 - 1872
• Main Authors: Xu, Qiaofeng, Yang, Deshan, Tan, Jun, Sawatzky, Alex, Anastasio, Mark A.
• Format: Journal Article
• Language: English
• Published: United States American Association of Physicists in Medicine 01.04.2016
• Subjects: 60 APPLIED LIFE SCIENCES; ALGORITHMS; ANIMAL TISSUES; Biological material, e.g. blood, urine; Haemocytometers; COMPARATIVE EVALUATIONS; computed tomographic image reconstruction; Computed tomography; Computer modeling; Computerised tomographs; computerised tomography; COMPUTERIZED SIMULATION; COMPUTERIZED TOMOGRAPHY; Cone beam computed tomography; DIAGNOSTIC IMAGING (IONIZING AND NON-IONIZING); Digital computing or data processing equipment or methods, specially adapted for specific applications; graphics processing units; Head and Neck Neoplasms - diagnostic imaging; Humans; Image data processing or generation, in general; Image guided radiation therapy; IMAGE PROCESSING; Image Processing, Computer-Assisted - methods; image reconstruction; ITERATIVE METHODS; medical image processing; Medical image quality; Medical image reconstruction; Medical X‐ray imaging; Phantoms, Imaging; Processor architectures; Processor configuration, e.g. pipelining; RADIATION PROTECTION AND DOSIMETRY; RADIOTHERAPY; sparsity‐regularized inverse problems; Three dimensional image processing; Time Factors; Wavelet Analysis; x‐ray cone‐beam computed tomography; sparsity-regularized inverse problems; computed tomographic image reconstruction; x-ray cone-beam computed tomography
• ISSN: 0094-2405; 2473-4209; 1522-8541; 2473-4209
• DOI: 10.1118/1.4942812

Purpose: The development of iterative image reconstruction algorithms for cone-beam computed tomography (CBCT) remains an active and important research area. Even with hardware acceleration, the overwhelming majority of the available 3D iterative algorithms that implement nonsmooth regularizers remain computationally burdensome and have not been translated for routine use in time-sensitive applications such as image-guided radiation therapy (IGRT). In this work, two variants of the fast iterative shrinkage thresholding algorithm (FISTA) are proposed and investigated for accelerated iterative image reconstruction in CBCT. Methods: Algorithm acceleration was achieved by replacing the original gradient-descent step in the FISTAs by a subproblem that is solved by use of the ordered subset simultaneous algebraic reconstruction technique (OS-SART). Due to the preconditioning matrix adopted in the OS-SART method, two new weighted proximal problems were introduced and corresponding fast gradient projection-type algorithms were developed for solving them. We also provided efficient numerical implementations of the proposed algorithms that exploit the massive data parallelism of multiple graphics processing units. Results: The improved rates of convergence of the proposed algorithms were quantified in computer-simulation studies and by use of clinical projection data corresponding to an IGRT study. The accelerated FISTAs were shown to possess dramatically improved convergence properties as compared to the standard FISTAs. For example, the number of iterations to achieve a specified reconstruction error could be reduced by an order of magnitude. Volumetric images reconstructed from clinical data were produced in under 4 min. Conclusions: The FISTA achieves a quadratic convergence rate and can therefore potentially reduce the number of iterations required to produce an image of a specified image quality as compared to first-order methods. We have proposed and investigated accelerated FISTAs for use with two nonsmooth penalty functions that will lead to further reductions in image reconstruction times while preserving image quality. Moreover, with the help of a mixed sparsity-regularization, better preservation of soft-tissue structures can be potentially obtained. The algorithms were systematically evaluated by use of computer-simulated and clinical data sets.