In recent years there is a vast application of conjugate gradient methods to restore the disturbed signals in compressive sensing. This research aims at developing a scheme, which is more effective for restoring disturbed signals than the popular PCG method (Liu & Li, 2015). To realize the desired goal, a new conjugate gradient approach combined with the projection scheme of Solodov and Svaiter [Kluwer Academic Publishers, pp. 355-369(1998)] for solving monotone nonlinear equations with convex constraints is presented. The main idea employed in this algorithm is to approximate the Jacobian matrix via acceleration parameter in order to propose an effective conjugate gradient parameter. In addition, the step length is calculated using inexact line search technique. The proposed approach is proved to converge globally under some mild conditions . The numerical experiment, depicts the efficacy our method. Apart from generating search directions that are vital for global convergence, a significant contribution of the new method lies in its applications to solve the ${\ell }_1$-norm regularization problem in signal recovery. Experiments with the scheme and the effective PCG solver, existing in the previous literature, shows that the new method provides much better results.

近年来，共轭梯度法在压缩感测中恢复受干扰信号的广泛应用。这项研究旨在开发一种方案，该方案比常用的PCG方法更有效地恢复受干扰的信号（Liu＆Li，2015）。为了实现期望的目标，提出了一种新的共轭梯度法，结合了Solodov和Svaiter的投影方案[Kluwer Academic Publishers，第355-369（1998）]来求解具有凸约束的单调非线性方程。该算法采用的主要思想是通过加速度参数逼近雅可比矩阵，以提出有效的共轭梯度参数。另外，使用不精确的线搜索技术来计算步长。在一定温和条件下，所提出的方法被证明可以在全球范围内收敛。数值实验描述了我们方法的有效性。除了生成对于全球融合至关重要的搜索方向外，新方法的重要作用还在于其解决以下问题的应用：${\ell }_{\mathrm{1个}}$-信号恢复中的范数正则化问题。在以前的文献中对这种方案和有效的PCG求解器进行的实验表明，该新方法提供了更好的结果。