An Alternative Lagrange-Dual Based Algorithm for Sparse Signal Reconstruction

被引:34
作者
Wang, Yiju [1 ]
Zhou, Guanglu [2 ]
Caccetta, Louis [2 ]
Liu, Wanquan [3 ]
机构
[1] Qufu Normal Univ, Sch Operat Res & Management Sci, Rizhao 276800, Shandong, Peoples R China
[2] Curtin Univ Technol, Dept Math & Stat, Perth, WA, Australia
[3] Curtin Univ Technol, Dept Comp, Perth, WA, Australia
基金
澳大利亚研究理事会;
关键词
Dual program; gradient-type method; sparse signal reconstruction; strong duality theorem; MINIMAL L(1)-NORM SOLUTION; UNCERTAINTY PRINCIPLES; REPRESENTATION; RECOVERY;
D O I
10.1109/TSP.2010.2103066
中图分类号
TM [电工技术]; TN [电子技术、通信技术];
学科分类号
0808 ; 0809 ;
摘要
In this correspondence, we propose a new Lagrange-dual reformulation associated with an l(1)-norm minimization problem for sparse signal reconstruction. There are two main advantages of our proposed approach. First, the number of the variables in the reformulated optimization problem is much smaller than that in the original problem when the dimension of measurement vector is much less than the size of the original signals; Second, the new problem is smooth and convex, and hence it can be solved by many state of the art gradient-type algorithms efficiently. The efficiency and performance of the proposed algorithm are validated via theoretical analysis as well as some illustrative numerical examples.
引用
收藏
页码:1895 / 1901
页数:7
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