An Optimization Algorithm for Observation Matrix in Compressive Sensing

The observation matrix plays a key role in Compressive Sensing. Aiming to reduce the correlation between the observation matrix and the sparse base and then to improve the quality of the reconstruction, an optimal algorithm for observation matrix with the premise of a known sparse base was presented in this paper, the Frobenius norm of the difference between the Gram matrix and the matrix which was approximately close to Equiangular Tight Frame(ETF) was considered to be the objective function, then the optimization solution was conducted from the objective function to get the theoretical expression of the optimal Gram matrix, finally the iterative optimization was adopted to reduce the mutual coherence between the observation matrix and the sparse base, then the proposed optimal Gram matrix processed by the threshold function would be the ETF in the next iteration. It was shown in the simulation results that with the acceptable amount of computation, the reconstruction performance is better with the observation matrix produced in the proposed algorithm, especially when the signal’s sparsity is high or the number of observations is few the reconstruction performance is much more better.