Methods of Sparse Measurement Matrix Optimization for Compressed Sensing

Abstract

In compressed sensing (CS), a sparse measurement matrix with few nonzero entries is more competitive than a dense matrix in reducing the number of multiplication units. Recent studies indicate that an optimized measurement matrix having low coherence with a specified dictionary can significantly improve the reconstruction performance. This paper considers the optimization problem of the sparse measurement matrix. The optimized sparse measurement matrix is formulated by minimizing the Frobenius norm of the difference between the Gram matrix of the sensing matrix and the target Gram matrix. First, the approach for updating the target Gram matrix is designed to reduce the maximal, average, and global coherence simultaneously. Then, an improved momentum gradient algorithm for updating the sparse measurement matrix is derived to accelerate convergence. On the basis of alternating minimization, two optimization algorithms are proposed. The experimental results show that the proposed algorithms outperform several state-of-the-art methods in terms of reconstruction performance.