TY - JOUR
T1 - Derivative-Free MLSCD Conjugate Gradient Method for Sparse Signal and Image Reconstruction in Compressive Sensing
AU - Ibrahim, Abdulkarim Hassan
AU - Kumam, Poom
AU - Abubakar, Auwal Bala
AU - Abubakar, Jamilu
AU - Rilwan, Jewaidu
AU - Taddele, Guash Haile
N1 - Funding Information:
We are grateful to the anonymous referees and editor for their useful comments, which have made the paper clearer and more comprehensive than the earlier version. The first author was supported by the ”Petchra Pra Jom Klao Ph.D. Research Scholarship from King Mongkut’s University of Technology Thonburi” (Grant no. 16/2561). The authors also acknowledge the financial support provided by the Center of Excellence in Theoretical and Computational Science (TaCS-CoE), KMUTT. Moreover, this research project is supported by Thailand Science Research and Innovation (TSRI) Basic Research Fund: Fiscal year 2021 under project number 64A306000005. The first and the third author acknowledge with thanks, the Department of Mathematics and Applied Mathematics at the Sefako Makgatho Health Sciences University.
Publisher Copyright:
© 2022, University of Nis. All rights reserved.
PY - 2022
Y1 - 2022
N2 - Finding the sparse solution to under-determined or ill-condition equations is a fundamental problem encountered in most applications arising from a linear inverse problem, compressive sensing, machine learning and statistical inference. In this paper, inspired by the reformulation of the ℓ1-norm regularized minimization problem into a convex quadratic program problem by Xiao et al. (Nonlinear Anal Theory Methods Appl, 74(11), 3570-3577), we propose, analyze, and test a derivative-free conjugate gradient method to solve the ℓ1-norm problem arising from the reconstruction of sparse signal and image in compressive sensing. The method combines the MLSCD conjugate gradient method proposed for solving unconstrained minimization problem by Stanimirović et al. (J Optim Theory Appl, 178(3), 860-884) and a line search method. Under some mild assumptions, the global convergence of the proposed method is established using the backtracking line search. Computational experiments are carried out to reconstruct sparse signal and image in compressive sensing. The numerical results indicate that the proposed method is stable, accurate and robust.
AB - Finding the sparse solution to under-determined or ill-condition equations is a fundamental problem encountered in most applications arising from a linear inverse problem, compressive sensing, machine learning and statistical inference. In this paper, inspired by the reformulation of the ℓ1-norm regularized minimization problem into a convex quadratic program problem by Xiao et al. (Nonlinear Anal Theory Methods Appl, 74(11), 3570-3577), we propose, analyze, and test a derivative-free conjugate gradient method to solve the ℓ1-norm problem arising from the reconstruction of sparse signal and image in compressive sensing. The method combines the MLSCD conjugate gradient method proposed for solving unconstrained minimization problem by Stanimirović et al. (J Optim Theory Appl, 178(3), 860-884) and a line search method. Under some mild assumptions, the global convergence of the proposed method is established using the backtracking line search. Computational experiments are carried out to reconstruct sparse signal and image in compressive sensing. The numerical results indicate that the proposed method is stable, accurate and robust.
KW - Compressive sensing
KW - Conjugate gradient method
KW - Global convergence
KW - Nonlinear equations
KW - Projection method
UR - http://www.scopus.com/inward/record.url?scp=85140359437&partnerID=8YFLogxK
U2 - 10.2298/FIL2206011I
DO - 10.2298/FIL2206011I
M3 - Article
AN - SCOPUS:85140359437
SN - 0354-5180
VL - 36
SP - 2011
EP - 2024
JO - Filomat
JF - Filomat
IS - 6
ER -