低相干高鲁棒性观测矩阵优化

doi:10.19665/j.issn1001-2400.2019.06.024

Abstract

Abstract:

An observation matrix optimization algorithm based on the tight frame and sparse representation error is proposed. First, the average mutual coherence of the sensing matrix is reduced by the Glam matrix which approximates the unit matrix and the constructed tight frame. Second, the sparse representation error as a regularization term is added to the conventional optimization model to improve the robustness of the observation matrix. Finally,the analytical method is applied to solve the observation matrix to ensure the convergence of the algorithm. Experimental results show that, compared with the contrast optimization matrix, the average mutual coherence of the proposed sensing matrix can be reduced by at least 0.03 with more robustness.

Key words: observation matrix, average mutual coherence, tight frame, sparse representation error

CLC Number:

TN911.7

ZHAO Hui,ZHANG Le,LIU Yingli,ZHANG Jing,ZHANG Tianqi. Optimization of the low coherence and high robustness observation matrix[J].Journal of Xidian University, 2019, 46(6): 171-178.

Figures/Tables 6

参数	原始投影矩阵	Elad优化矩阵	Li优化矩阵	Bai优化矩阵	文中优化矩阵
$‖ I L - G ‖ F 2$	5.669×10⁵	465	125	265	125
μ	0.76	0.64	0.58	0.88	0.91
μ_av	0.31	0.26	0.26	0.25	0.22

参数	原始投影矩阵	Elad优化矩阵	Li优化矩阵	Bai优化矩阵	文中优化矩阵
$‖ I L - G ‖ F 2$	7.389×10⁶	654	220	438	220
μ	0.54	0.37	0.33	0.72	0.83
μ_av	0.18	0.14	0.14	0.15	0.12

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Optimization of the low coherence and high robustness observation matrix

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