Compressed sensing and reconstruction with bernoulli matrices

Abstract

Compressed sensing seeks to recover a sparse or compressible signal from a small number of linear and non-adaptive measurements. While most of the studies so far focus on the prominent Gaussian random measurements, we investigate the performances of matrices with Bernoulli distribution. As extensions of symmetric signs ensemble, random binary ensemble and semi-Hadamard ensemble are proposed as sensing matrices with simplex structures. Based on some results of symmetric signs ensemble and the concept of compressed sensing matrices, we obtain a theoretical result that signal compressed sensing using random binary matrices can be exactly reconstructed with high probability. In reconstruction processes, the fast and low-consumed orthogonal matching pursuit is adopted. Numerical results show that such matrices perform equally well to the Gaussian matrices.