Iteratively weighted thresholding homotopy method for the sparse solution of underdetermined linear equations  

作　　者：Wenxing Zhu Zilin Huang Jianli Chen Zheng Peng 

机构地区：[1]Center for Discrete Mathematics and Theoretical Computer Science,Fuzhou University,Fuzhou 350116,China

出　　处：《Science China Mathematics》2021年第3期639-664,共26页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant Nos.61672005 and 11571074)。

摘　　要：Recently, iteratively reweighted methods have attracted much interest in compressed sensing, outperforming their unweighted counterparts in most cases. In these methods, decision variables and weights are optimized alternatingly, or decision variables are optimized under heuristically chosen weights. In this paper,we present a novel weighted l1-norm minimization problem for the sparsest solution of underdetermined linear equations. We propose an iteratively weighted thresholding method for this problem, wherein decision variables and weights are optimized simultaneously. Furthermore, we prove that the iteration process will converge eventually. Using the homotopy technique, we enhance the performance of the iteratively weighted thresholding method. Finally, extensive computational experiments show that our method performs better in terms of both running time and recovery accuracy compared with some state-of-the-art methods.

关 键 词：sparse optimization weighted thresholding method homotopy method 

分 类 号：O241.6[理学—计算数学]