Measurement matrix design for hyperspectral image compressive sensing

Compressive sensing (CS) allows to reconstruct sparse signals from a smaller number of measurements than the Nyquist-Shannon criterion. CS can be considered as a natural candidate hyperspectral imaging, as it has recently been proved to significantly reduce the sampling rate and shift the computation cost to the receiver side of system in the form of a reconstruction process. A random measurement is used in most existent papers on hyperspectral CS. In this paper, according to analyzing the mutual coherence between the measurement matrix and the representing matrix, a optimization measurement matrix based on gradient descent method is proposed to improve reconstruction quality of hyperspectral images. The proposed method is designed to optimize an initially random measurement matrix to a matrix that presents a smaller coherence than the initial one. Experimental results show that the proposed method exhibits its higher reconstruction quality compared to those of previous methods.