Open AccessA Novel Optimization Method for Bipolar Chaotic Toeplitz Measurement Matrix in Compressed Sensing
Author(s) -
Rui Zhang,
Chen Meng,
Cheng Wang,
Qiang Wang
Publication year - 2021
Publication title -
journal of sensors
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.399
H-Index - 43
eISSN - 1687-7268
pISSN - 1687-725X
DOI - 10.1155/2021/4024737
Subject(s) - toeplitz matrix , chaotic , matrix (chemical analysis) , compressed sensing , algorithm , optimization problem , overhead (engineering) , sequence (biology) , computer science , mathematics , mathematical optimization , artificial intelligence , pure mathematics , materials science , biology , composite material , genetics , operating system
In this paper, a bipolar chaotic Toeplitz measurement matrix optimization algorithm for alternating optimization is presented. The construction of measurement matrices is one of the key techniques for compressive sensing from theory to engineering applications. Recent studies have shown that bipolar chaotic Toeplitz matrices, constructed by combining the intrinsic determinism of bipolar chaotic sequences with the advantages of Toeplitz matrices, have significant advantages over other measurement matrices in terms of memory overhead, computational complexity, and hard implementation. However, problems such as strong correlation and large interdependence coefficients between measurement matrices and sparse dictionaries may still exist in practical applications. To address this problem, we propose a new bipolar chaotic Toeplitz measurement matrix alternating optimization algorithm. Firstly, by introducing the structure matrix, the optimization problem of the measurement matrix is transformed into the optimization problem of the generating sequence, thus ensuring that the optimization process does not destroy the structural properties of the matrix; then, constraints are added to the values of the generating sequence during the optimization process, so that the optimized measurement matrix still maintains the bipolar properties. Finally, the effectiveness of the optimization algorithm in this paper is verified by simulation experiments. The experimental results show that the optimized bipolar chaotic Toeplitz measurement matrix can effectively reduce the reconstruction error and improve the reconstruction probability.