Measurement matrix optimization via mutual coherence minimization for compressively sensed signals reconstruction
type: Item
instance of: scholarly article
title: Measurement matrix optimization via mutual coherence minimization for compressively sensed signals reconstruction
zbMATH Open document ID: 1459.94051
DOI: 10.1155/2020/7979606
author: Ziran Wei
author: Jianlin Zhang
author: Zhiyong Xu
author: Yong Liu
published in: Mathematical Problems in Engineering
publication date: 2020-10-14T00:00:00Z
review text: Summary: For signals reconstruction based on compressive sensing, to reconstruct signals of higher accuracy with lower compression rates, it is required that there is a smaller mutual coherence between the measurement matrix and the sparsifying matrix. Mutual coherence between the measurement matrix and sparsifying matrix can be expressed indirectly by the property of the Gram matrix. On the basis of the Gram matrix, a new optimization algorithm of acquiring a measurement matrix has been proposed in this paper. Firstly, a new mathematical model is designed and a new method of initializing measurement matrix is adopted to optimize the measurement matrix. Then, the loss function of the new algorithm model is solved by the gradient projection-based method of Gram matrix approximating an identity matrix. Finally, the optimized measurement matrix is generated by minimizing mutual coherence between measurement matrix and sparsifying matrix. Compared with the conventional measurement matrices and the traditional optimization methods, the proposed new algorithm effectively improves the performance of optimized measurement matrices in reconstructing one-dimensional sparse signals and two-dimensional image signals that are not sparse. The superior performance of the proposed method in this paper has been fully tested and verified by a large number of experiments.
Mathematics Subject Classification ID: 94A12
Mathematics Subject Classification ID: 94A08
zbMATH DE Number: 7260978
describes a project that uses: PDCO
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2020/7979606
OpenAlex ID: W3090971136
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description: scientific article; zbMATH DE number 7260978