title: Accelerated fast iterative shrinkage thresholding algorithms for sparsity-regularized cone-beam CT image reconstruction.
abstract: OBJECTIVE
  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.
authors.affiliation: Department of Biomedical Engineering, Washington University in St. Louis, St. Louis, Missouri 63130.
authors.forename: Qiaofeng
authors.initials: Q
authors.lastname: Xu
authors.affiliation: Department of Radiation Oncology, School of Medicine, Washington University in St. Louis, St. Louis, Missouri 63110.
authors.forename: Deshan
authors.initials: D
authors.lastname: Yang
authors.affiliation: Department of Radiation Oncology, The University of Texas Southwestern Medical Center, Dallas, Texas 75390.
authors.forename: Jun
authors.initials: J
authors.lastname: Tan
authors.affiliation: Department of Biomedical Engineering, Washington University in St. Louis, St. Louis, Missouri 63130.
authors.forename: Alex
authors.initials: A
authors.lastname: Sawatzky
authors.affiliation: Department of Biomedical Engineering, Washington University in St. Louis, St. Louis, Missouri 63130.
authors.forename: Mark A
authors.initials: MA
authors.lastname: Anastasio
mesh_terms: D000465:Algorithms; D054893:Cone-Beam Computed Tomography; D006258:Head and Neck Neoplasms / Q000000981:diagnostic imaging; D006801:Humans; D007091:Image Processing, Computer-Assisted / Q000379:methods*; D019047:Phantoms, Imaging; D013997:Time Factors; D058067:Wavelet Analysis