The Convergence of Two Algorithms for Compressed Sensing Based Tomography

Xiezhang Li, Jiehua Zhu

Department of Mathematical Sciences, Georgia Southern University, Statesboro, USA.

DOI: 10.4236/act.2012.13007                

Abstract

The constrained total variation minimization has been developed successfully for image reconstruction in computed tomography. In this paper, the block component averaging and diagonally-relaxed orthogonal projection methods are proposed to incorporate with the total variation minimization in the compressed sensing framework. The convergence of the algorithms under a certain condition is derived. Examples are given to illustrate their convergence behavior and noise performance.

Keywords

Compressed Sensing; Image Reconstruction; Total Variation Minimization; Block Iterative Methods

Conflicts of Interest

The authors declare no conflicts of interest.

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