Joint optimization methods for Gaussian random measurement matrix based on column coherence in compressed sensing

In compressed sensing, a measurement matrix phi having low coherence with sparse dictionary 41can achieve better signal reconstruction performance. To improve the signal reconstruction performance, this paper proposes two joint optimization algorithms for the Gaussian random measurement matrix to minimize the coherence between the measurement matrix phi and the sparse dictionary 41. First, a joint optimization algorithm is proposed that can simultaneously reduce the average mutual coherence mu g and the mutual coherence mu based on an alternating projection strategy. Then, to further decrease the coherence between phi and 41, an improved shrinkage method based on K-order cumulative coherence mu K is proposed. Furthermore, another joint optimization algorithm is proposed by fusing this improved shrinkage method, which can simultaneously decrease the average mutual coherence mu g and the K-order cumulative coherence mu K . Simulation results show that the two proposed joint optimization algorithms outperform existing algorithms in reducing coherence and improving reconstruction performance. (c) 2023 Published by Elsevier B.V.