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

Abstract

In compressed sensing, a measurement matrix Φ having low coherence with sparse dictionary Ψ can 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 Φ and the sparse dictionary Ψ. First, a joint optimization algorithm is proposed that can simultaneously reduce the average mutual coherence μg and the mutual coherence μ based on an alternating projection strategy. Then, to further decrease the coherence between Φ and Ψ, an improved shrinkage method based on K-order cumulative coherence μK is proposed. Furthermore, another joint optimization algorithm is proposed by fusing this improved shrinkage method, which can simultaneously decrease the average mutual coherence μg and the K-order cumulative coherence μK. Simulation results show that the two proposed joint optimization algorithms outperform existing algorithms in reducing coherence and improving reconstruction performance.