Sparse signal reconstruction in compressive sensing via derivative-free iterative method
Abstract
Finding sparse solutions to under-determined or ill-conditioned equations is a problem that usually arise in compressive sensing. In this article, a derivative-free iterative method is presented for recovering sparse signal in compressive sensing by approximating the solution to a convex constrained nonlinear equation. The proposed method is derived from the modified Polak-Ribiere-Polyak conjugate gradient method for unconstrained optimization. The global convergence is established under mild assumptions. Preliminary numerical results in recovering sparse signal are given to show that the proposed method is efficient.
Copyright © 2021 Abhiwat Kambheera, Sanusi Bala Abdullahi, Abdulkarim Hassan Ibrahim, Auwal Bala Abubakar. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Cite this article
A. Kambheera, S. B. Abdullahi, A. H. Ibrahim, A. B. Abubakar, Sparse signal reconstruction in compressive sensing via derivative-free iterative method, J. Math. Comput. Sci. 11 (2021), 6045–6060. https://doi.org/10.28919/jmcs/6157
BibTeX
@article{Kambheera2021,
author = {Kambheera, Abhiwat and Abdullahi, Sanusi Bala and Ibrahim, Abdulkarim Hassan and Abubakar, Auwal Bala},
title = {Sparse signal reconstruction in compressive sensing via derivative-free iterative method},
journal = {J. Math. Comput. Sci.},
volume = {11},
year = {2021},
pages = {6045--6060},
doi = {10.28919/jmcs/6157}
}