Error Analysis of Reweighted l₁ Greedy Algorithm for Noisy Reconstruction

Authors

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

Document Type

Article

Publication Date

10-1-2015

Publication Title

Journal of Computational and Applied Mathematics

DOI

10.1016/j.cam.2015.02.038

ISSN

0377-0427

Abstract

Sparse solutions for an underdetermined system of linear equations Φx=u can be found more accurately by l₁-minimization type algorithms, such as the reweighted l₁-minimization and l₁ greedy algorithms, than with analytical methods, in particular in the presence of noisy data. Recently, a generalized l₁ greedy algorithm was introduced and applied to signal and image recovery. Numerical experiments have demonstrated the convergence of the new algorithm and the superiority of the algorithm over the reweighted l₁-minimization and l₁ greedy algorithms although the convergence has not yet been proven theoretically. In this paper, we provide an error bound for the reweightedl₁ greedy algorithm, a type of the generalized l₁ greedy algorithm, in the noisy case and show its improvement over the reweighted l₁-minimization.

Recommended Citation

Zhu, Jiehua, Xiezhang Li, Fangjun Arroyo, Edward Arroyo. 2015. "Error Analysis of Reweighted l₁ Greedy Algorithm for Noisy Reconstruction." Journal of Computational and Applied Mathematics, 286: 93-101. doi: 10.1016/j.cam.2015.02.038
https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/351