Modification of a conjugate gradient approach for convex constrained nonlinear monotone equations with applications in signal recovery and image restoration

Conjugate gradient (CG )methods have received widespread use in recent years for recovering damaged signals in compressive sensing. This study attempts to create a CG method that is more effective than the recent existing scheme for recovering disrupted signals. The newly created method is a modification of the method proposed by Halilu et al. (2021). Because the authors' CG parameter can be undefined while solving general functions. As a result, to accomplish the desired result, a new CG method combined with the projection scheme of Solodov and Svaiter (1999) is presented. In addition, under mild conditions, the proposed method converges globally. Numerical experiments conducted with recent methods show the effectiveness of the proposed method. Furthermore, the proposed method is applied efficiently to address the signal recovery and image restoration problems, yielding a better result than some existing methods in the literature.