Measurement Matrix Optimization via Mutual Coherence Minimization for Compressively Sensed Signals Reconstruction

Abstract

For signals reconstruction based on compressive sensing, to reconstruct signals of higher accuracy with lower compression rates, it is required that there is a smaller mutual coherence between the measurement matrix and the sparsifying matrix. Mutual coherence between the measurement matrix and sparsifying matrix can be expressed indirectly by the property of the Gram matrix. On the basis of the Gram matrix, a new optimization algorithm of acquiring a measurement matrix has been proposed in this paper. Firstly, a new mathematical model is designed and a new method of initializing measurement matrix is adopted to optimize the measurement matrix. Then, the loss function of the new algorithm model is solved by the gradient projection-based method of Gram matrix approximating an identity matrix. Finally, the optimized measurement matrix is generated by minimizing mutual coherence between measurement matrix and sparsifying matrix. Compared with the conventional measurement matrices and the traditional optimization methods, the proposed new algorithm effectively improves the performance of optimized measurement matrices in reconstructing one-dimensional sparse signals and two-dimensional image signals that are not sparse. The superior performance of the proposed method in this paper has been fully tested and verified by a large number of experiments.