A Generalized l₁ Greedy Algorithm for Image Reconstruction in CT

Authors

Jiehua Zhu, Georgia Southern UniversityFollow
Xiezhang Li, Georgia Southern UniversityFollow

Document Type

Article

Publication Date

1-15-2013

Publication Title

Applied Mathematics and Computations

DOI

10.1016/j.amc.2012.11.052

ISSN

0096-3003

Abstract

The sparse vector solutions for an underdetermined system of linear equations Ax=b have many applications in signal recovery and image reconstruction in tomography. Under certain conditions, the sparsest solution can be found by solving a constrained l₁ minimization problem: min||x||₁ subject toAx=b. Recently, the reweighted l₁ minimization and l₁ greedy algorithm have been introduced to improve the convergence of the l₁ minimization problem. As an extension, a generalized l₁ greedy algorithm for computerized tomography (CT) is proposed in this paper. It is implemented as a generalized total variation minimization for images with sparse gradients in CT. Numerical experiments are also given to illustrate the advantage of the new algorithm.

Recommended Citation

Zhu, Jiehua, Xiezhang Li. 2013. "A Generalized l₁ Greedy Algorithm for Image Reconstruction in CT." Applied Mathematics and Computations, 219 (10): 5487-5494. doi: 10.1016/j.amc.2012.11.052
https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/86