The Minimax Method of Design of Measurement Matrices for Compressed Sensing Based on Incoherence Criterion

Abstract

A design of measurement matrices of satisfying the incoherence criterion or Restricted Isometry Rroperty is among the core issues of compressed sensing theory. Whether there is an optimal determinate measurement matrix for some stable reconfiguration algorithms is one of the key problems which need to be solved urgently in compressed sensing. For the fixed orthonormal basis, the design of the determinate measurement matrix is investigated by using the incoherence criterion between the measurement matrix and the sparse basis. The minor the coherence is, the less the required measurement number in the process of compressed sampling is, the more information in the original signal will be contained, and the higher the probability of reconstruction is, therefore, the minimax method of satisfying optimal incoherence could be constructed for the design of measurement matrix. Finally, considering the discrete cosine basis as fixed orthonormal basis, compared with the coherence corresponding to the common measurement matrices, a numerical simulation example is presented to verify the effectiveness of the method.