title: Accelerated perturbation-resilient block-iterative projection methods with application to image reconstruction.
abstract: We study the convergence of a class of accelerated perturbation-resilient block-iterative projection methods for solving systems of linear equations. We prove convergence to a fixed point of an operator even in the presence of summable perturbations of the iterates, irrespective of the consistency of the linear system. For a consistent system, the limit point is a solution of the system. In the inconsistent case, the symmetric version of our method converges to a weighted least squares solution. Perturbation resilience is utilized to approximate the minimum of a convex functional subject to the equations. A main contribution, as compared to previously published approaches to achieving similar aims, is a more than an order of magnitude speed-up, as demonstrated by applying the methods to problems of image reconstruction from projections. In addition, the accelerated algorithms are illustrated to be better, in a strict sense provided by the method of statistical hypothesis testing, than their unaccelerated versions for the task of detecting small tumors in the brain from X-ray CT projection data.
authors: Department of Mathematics, Iran University of Science and Technology, Narmak, Tehran, 16846-13114, Iran.
authors: T
authors: T
authors: Nikazad
authors: R
authors: R
authors: Davidi
authors: G T
authors: GT
authors: Herman
keywords: block-iterative algorithms; image reconstruction from projections; perturbation resilience; superiorization; total variation