A gradient-based alternating minimization approach for optimization of the measurement matrix in compressive sensing

被引:143
作者
Abolghasemi, Vahid [1 ]
Ferdowsi, Saideh [1 ]
Sanei, Saeid [1 ]
机构
[1] Univ Surrey, Fac Engn & Phys Sci, Guildford GU2 7XH, Surrey, England
关键词
Basis pursuit (BP); Compressive sensing (CS); Gradient descent; Orthogonal matching pursuit (OMP); Random Gaussian matrices; Sparse representation; SIGNAL RECOVERY; UNCERTAINTY PRINCIPLES; SPARSE REPRESENTATION; DICTIONARIES; REGRESSION; PROJECTION; FRAMES;
D O I
10.1016/j.sigpro.2011.10.012
中图分类号
TM [电工技术]; TN [电子技术、通信技术];
学科分类号
080906 [电磁信息功能材料与结构]; 082806 [农业信息与电气工程];
摘要
In this paper the problem of optimization of the measurement matrix in compressive (also called compressed) sensing framework is addressed. In compressed sensing a measurement matrix that has a small coherence with the sparsifying dictionary (or basis) is of interest. Random measurement matrices have been used so far since they present small coherence with almost any sparsifying dictionary. However, it has been recently shown that optimizing the measurement matrix toward decreasing the coherence is possible and can improve the performance. Based on this conclusion, we propose here an alternating minimization approach for this purpose which is a variant of Grassmannian frame design modified by a gradient-based technique. The objective is to optimize an initially random measurement matrix to a matrix which presents a smaller coherence than the initial one. We established several experiments to measure the performance of the proposed method and compare it with those of the existing approaches. The results are encouraging and indicate improved reconstruction quality, when utilizing the proposed method. (C) 2011 Elsevier B.V. All rights reserved.
引用
收藏
页码:999 / 1009
页数:11
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