A cooperative construction method for the measurement matrix and sensing dictionary used in compression sensing

A measurement matrix and sensing dictionary are the basic tools for signal compression sampling and reconstruction, respectively, which are important aspects in the field of compression sensing. Previous studies which have divided the measurement matrix and sensing dictionary into two separate processes did not make full use of their inherent intercorrelations. In case of which could be fully utilized, the mutual coherence of the atoms of measurement matrix and sensing dictionary can be further reduced under the premise of ensuring that the original signal information is stored, which could improve the accuracy of signal recovery. The present study attempted to reduce the mutual coherence between the sensing dictionary and measurement matrix by proposing the t-average mutual coherence coefficient as an evaluation index for the sensing dictionary. A mathematical model for co-constructing a measurement matrix and sensing dictionary is firstly proposed. Then, the measurement matrix and sensing dictionary cooperative construction(MSCA)algorithm is proposed to solve the model at a faster rate. The simulated results for sparse signal and binary image show that the proposed algorithm has faster computing speed and higher solution precision than the state-of-the-art construction algorithms.