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.

In recent years., dictionary learning has attracted great interest in the field of sparse representation. To improve the sparse representation performance of signals., this paper proposes an incoherent dictionary learning algorithm based on the simulta-neous codeword optimization (SimCO) algorithm. The proposed algorithm is achieved by embedding a coherence penalty for the framework of the SimCO algorithm to avoid performance degradation caused by similar atoms appearing in the learned dictionary. Simulation results show that the proposed algorithm has a competitive sparse representation performance compared to existing algorithms.

The construction of measurement matrix is crucial to compressed sensing theory,its performance directly affects the efficiency of data sampling compression and the quality of signal reconstruction.In view of the fact that the performance of Toeplitz structure measurement matrix reconstruction is not high,we proposed a singular value decomposition-based construction method for Toeplitz structure measurement matrix.First,it decomposes the Toeplitz matrix by using singular value decomposition algorithm,then it enhances the independence of column vectors of the matrix by optimising its nonzero singular values,so as to improve the reconstruction performance.Simulation results showed that compared with the non-optimised Toeplitz structure measurement matrix and the frequently used Gauss random matrix,the signal reconstruction accuracy gained significant improvement when using the optimized Toeplitz structure measurement matrix to carry out compressed sensing on signals.