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An efficient algorithm for designing projection matrix in compressive sensing based on alternating optimization
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DOI：10.1016/j.sigpro.2015.12.015.png)
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Abstract
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This paper considers the problem of optimally designing the projection matrix Phi for a certain class of signals which can be sparsely represented by a specified dictionary Psi. The optimal projection matrix is proposed to minimize the distance between the Gram matrix of the equivalent dictionary Phi Psi and a set of relaxed Equiangular Tight Frames (ETFs). An efficient method is derived for the optimal projection matrix design with a given Gram matrix. In addition, an extension of projection matrix design is derived for the scenarios where the signals cannot be represented exactly sparse in a specified dictionary. Simulations with synthetic data and real images demonstrate that the obtained projection matrix significantly improves the signal recovery accuracy of a system and outperforms those obtained by the existing algorithms. (C) 2016 Elsevier B.V. All rights reserved.
Keywords:
Compressive sensing (CS)
Alternating optimization
Robust projection matrix
Mutual coherence
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