Spectral Conjugate Gradient Like Method for Signal Reconstruction

Abdulkarim Hassan Ibrahim, Kanikar Muangchoo, Auwal Bala Abubakar, Afeez Dewumi Adedokun, Hassan Mohammed

Abstract

This paper presents a derivative-free conjugate gradient algorithm for solving the $l_1$-regularization problem arising in compressive sensing. The search direction of the proposed method is bounded and satisfies the sufficient descent condition. Under some mild assumptions, the global convergence of the proposed algorithm is established. Numerical experiments in recovering sparse signal are performed to illustrate the efficiency of the algorithm compared with existing algorithms.