The Convergence of Block Cyclic Projection with Underrelaxation Parameters for Compressed Sensing Based Tomography

Authors

Fangjun Arroyo, Francis Marion UniversityFollow
Edward Arroyo, American Public University SystemFollow
Xiezhang Li, Georgia Southern UniversityFollow
Jiehua Zhu, Georgia Southern UniversityFollow

Document Type

Article

Publication Date

2014

Publication Title

Journal of X-Ray Science and Technology

DOI

10.3233/XST-140419

ISSN

1095-9114

Abstract

The block cyclic projection method in the compressed sensing framework (BCPCS) was introduced for image reconstruction in computed tomography and its convergence had been proven in the case of unity relaxation (λ=1). In this paper, we prove its convergence with underrelaxation parameters λ∈(0,1). As a result, the convergence of compressed sensing based block component averaging algorithm (BCAVCS) and block diagonally-relaxed orthogonal projection algorithm (BDROPCS) with underrelaxation parameters under a certain condition are derived. Experiments are given to illustrate the convergence behavior of these algorithms with selected parameters.

Recommended Citation

Arroyo, Fangjun, Edward Arroyo, Xiezhang Li, Jiehua Zhu. 2014. "The Convergence of Block Cyclic Projection with Underrelaxation Parameters for Compressed Sensing Based Tomography." Journal of X-Ray Science and Technology, 22 (2): 197-211. doi: 10.3233/XST-140419
https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/85