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.

中文翻译：

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凸约束非线性单调方程共轭梯度法的修改及其在信号恢复和图像恢复中的应用


近年来，共轭梯度（CG）方法已广泛用于恢复压缩传感中的受损信号。本研究试图创建一种比最近现有的恢复中断信号方案更有效的 CG 方法。新创建的方法是对 Halilu 等人提出的方法的修改。 （2021）。因为作者在求解一般函数时，CG参数可能是未定义的。因此，为了达到预期的结果，提出了一种结合 Solodov 和 Svaiter (1999) 投影方案的新 CG 方法。此外，在温和条件下，该方法具有全局收敛性。用最新方法进行的数值实验表明了所提出方法的有效性。此外，所提出的方法有效地应用于解决信号恢复和图像恢复问题，比文献中的一些现有方法产生了更好的结果。