Measurement matrix optimization based on incoherent unit norm tight frame

This paper considers the problem of measurement matrix optimization for compressed sensing (CS) in which the dictionary is assumed to be given, such that it leads to an effective sensing matrix. Due to important properties of equiangular tight frames (ETFs) to achieve Welch bound equality, the measurement matrix optimization based on ETF has received considerable attention and many algorithms have been proposed for this aim. These methods produce sensing matrix with low mutual coherence based on initializing the measurement matrix with random Gaussian ensembles. This paper, use incoherent unit norm tight frame (UNTF) as an important frame with the aim of low mutual coherence and proposes a new method to construction a measurement matrix of any dimension while measurement matrix initialized by partial Fourier matrix. Simulation results show that the obtained measurement matrix effectively reduces the mutual coherence of sensing matrix and has a fast convergence to Welch bound compared with other methods.