An improved algorithm for basis pursuit problem and its applications

Tanay Saha, Shwetabh Srivastava, Swanand Khare, Predrag S. Stanimirović and Marko D. Petković

Applied Mathematics and Computation, 2019, vol. 355, issue C, 385-398

Abstract: We propose an algorithm for solving the basis pursuit problem minu∈Cn{∥u∥1:Au=f}. Our starting motivation is the algorithm for compressed sensing, proposed by Qiao, Li and Wu, which is based on linearized Bregman iteration with generalized inverse. Qiao, Li and Wu defined new algorithm for solving the basis pursuit problem in compressive sensing using a linearized Bregman iteration and the iterative formula of linear convergence for computing the matrix generalized inverse. In our proposed approach, we combine a partial application of the Newton’s second order iterative scheme for computing the generalized inverse with the Bregman iteration. Our scheme takes lesser computational time and gives more accurate results in most cases. The effectiveness of the proposed scheme is illustrated in two applications: signal recovery from noisy data and image deblurring.

Keywords: Generalized inverse; Linearized Bregman iteration; Compressive sensing; Sparse solution; Signal recovery; Image deblurring (search for similar items in EconPapers)
Date: 2019
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0096300319301833
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:355:y:2019:i:c:p:385-398

DOI: 10.1016/j.amc.2019.02.073

Access Statistics for this article

Applied Mathematics and Computation is currently edited by Theodore Simos

More articles in Applied Mathematics and Computation from Elsevier
Bibliographic data for series maintained by Catherine Liu ().