Compressed sensing and reconstruction with Semi-Hadamard matrices

Compressed sensing (CS) is a new signal acquisition technology which seeks to recover the signal using incomplete linear projections acquired by a projection matrix. Semi-Hadamard matrices and their simplifications are proposed as a kind of feasible projection matrix with binary structure in CS frame work. Basic definitions of semi-Hadamard and their simplifications are introduced. We present the mathematical results that the signal compressed sensing using binary or sparse binary matrices, including matrix presented in this paper, can be exactly recovered with high probability. Simulation results show that semi-Hadamard matrices perform equally well to the prominent Hadamard matrices and their simplifications can be regarded as a reliable operator in a computing resource limited environment.