Generalized incoherence principle in compressed sensing

Compressed Sensing (CS) is a new framework for simultaneous sensing and compression, and how to analyze the stability of sensing matrix is one of the extremely important research domains in CS. Incoherence is an important principle for constructing the stable sensing matrix, but the principle is based on the assumption that row vectors of sensing matrix is a subset of the normalized orthobase. The assumption has limited the application of incoherence principle. In this paper, in order to conquer the limitation, we propose the generalized incoherence principle, which is only based on the assumption that row vectors of sensing matrix is a subset of the common base. Firstly, the definition of coherence is generalized, referred to generalized coherence. Secondly, the expression between compressive measure number and generalized coherence is constructed and proved. Finally, the Gaussian random matrix and Rademacher matrix with random ±1 entries are analyzed by generalized incoherence principle. Simulation results show that the Gaussian random matrix and Rademacher matrix are stable.