Measurement matrix optimization method based on matrix orthogonal similarity transformation

Abstract

Optimization of the measurement matrix is one of the important research aspects of compressive sensing theory. A measurement matrix optimization method is presented based on the orthogonal similarity transformation of the information operator’s Gram matrix. In terms of the fact that the information operator’s Gram matrix is a singular symmetric matrix, a simplified orthogonal similarity transformation is deduced, and thus the simplified diagonal matrix that is orthogonally similar to it is obtained. Then an approximation of the Gram matrix is obtained by letting all the nonzero diagonal entries of the simplified diagonal matrix equal their average value. Thus an optimized measurement matrix can be acquired according to its relationship with the information operator. Results of experiments show that the optimized measurement matrix compared to the random measurement matrix is less coherent with dictionaries. The relative signal recovery error also declines when the proposed measurement matrix is utilized.