A hybrid conjugate gradient approach by combining FR and LS algorithms for solving compressive sensing problem

Rahpeymaii, Farzad; Rostami, Majid

doi:10.48301/kssa.2024.406037.2627

A hybrid conjugate gradient approach by combining FR and LS algorithms for solving compressive sensing problem

Document Type : Original Article

Authors

Farzad Rahpeymaii ¹

Majid Rostami ²

¹ Department of Mathematics , Technical and Vocational University (TVU), Tehran, Ira n,

² Department of Mathematics , Technical and Vocational University (TVU), Tehran, Ira n

10.48301/kssa.2024.406037.2627

Abstract

In this paper, we introduce a hybrid conjugate gradient method for solving monotonic nonlinear equations with convex constraints by combining FR and LS conjugate gradient methods. Conjugate gradient (CG) iterative methods have a simple structure and are low-memory algorithms. In these methods, no matrix is stored and only matrix multiplication by vector is done. If the generated iterations be out of the convex region, we move them to the convex region using the projection method. The new algorithm is a combination of a conjugate gradient method with strong convergence and another conjugate gradient method with high computational efficiency. Also, the generated directions by the hybrid conjugate gradient method are sufficient descent. We prove the global convergence of the new algorithm under some standard assumptions. The compressive sensing problem is formulated as a nonlinear equation with convex constraints. So, we use the hybrid method to solve the compressive sensing minimization problem and remove noise from images.

Keywords

Conjugate gradient method

Convex constraints

Projection method

Monotone equations

Compressive sensing

Subjects