Finite projective spaces in deterministic construction of measurement matrices

Abstract

In this study, the authors concentrate on the designing of a deterministic measurement matrix. Unlike most of the studies, they employ the points on finite projective spaces rather than finite fields. These spaces provide more choices for the size of the proposed matrix. A new group of binary measurement matrices is presented through generalising DeVore's construction. For this purpose, homogenous polynomials over finite projective spaces are applied. To investigate the performance of the proposed matrix they provide an example on projective lines. It can be observed that the coherence of the result matrix is lower than DeVore's construction. The simulation results show that the proposed matrix outperforms the Gaussian matrix and DeVore's matrix in terms of noiseless and noisy signal recovery.