%0 Journal Article
%T 信号重构的优化算法及其在图片恢复中的应用<br>An Optimization Algorithm on Signal Reconstruction and Its Application in Image Restoration
%A 王尊阳
%A 郭超
%A 孙洪春
%J Advances in Applied Mathematics
%P 1732-1743
%@ 2324-8009
%D 2023
%I Hans Publishing
%R 10.12677/AAM.2023.124180
%X 本文进一步考虑信号重构与图像去躁问题的优化方法。 为此，提出了一种基于类似Armijo线搜索 的新型算法，详细证明了该算法的全局收敛性和O(1/k<sup>2</sup>)次线性收敛速率。 最后，通过稀疏信号恢 复和图像去躁的数值实验验证了所提算法的有效性和优越性。<br />
In this paper, we further consider an optimization method for solving the signal recon- struction and image denoising problem. To this end, a new algorithm with Armijo-like line search is proposed. Global convergence results of the new algorithm is established in detail. Furthermore, we also show that the method is sublinearly convergent rate of
O(1/k<sup>2</sup>). Finally, the efficiency of the proposed algorithm is illustrated through some
numerical examples on sparse signal recovery and image denoising.
%K 信号重建和图像去躁问题，算法，全局收敛，次线性收敛速度<br>The Signal Reconstruction and Image Denoising Problem
%K Algorithm
%K Global Convergence
%K Sublinearly Convergent Rate
%U http://www.hanspub.org/journal/PaperInformation.aspx?PaperID=64689