Improved optimization algorithm for measurement matrix in compressed sensing

In compressed sensing theory, the measurement matrix optimization is a kind of approach of improving performance by decreasing the mutual coherence between the measurement matrix and sparse dictionary. This paper presents a measurement matrix optimization algorithm, which can decrease the global coherent coefficient and the maximum coherent coefficient at the same time. This algorithm is divided into two steps. First, average the eigenvalues of the Gram matrix to decrease the global coherent coefficient. Second, use threshold function to shrink the off-diagonal elements of the Gram matrix. Two steps are alternately performed until the measurement matrix which meets the requirement of the optimal solution is worked out. This algorithm ensures that the global coherent coefficient is reduced to the minimum while the maximum coherent coefficient is significant reduced. Experimental results show that this proposed algorithm is better than the existing algorithms in deceasing coherent coefficient and the success rate of reconstruction.