Randomness, Coherence and Noise Robustness in Compressive Sensing

The theory of compressive sensing (CS) in contrast with well-known Nyquist sampling theorem was proposed. Sensing matrix and sparse matrix have key roles in perfect signal reconstruction by using either greedy algorithms like orthogonal matching pursuit (OMP) or -norm based methods. In this paper, different pairs as sensing and sparse matrices are evaluated in terms of randomness and coherence. Noiselet as a complex measurement matrix has low coherence with Haar wavelet, and so the recovered images by OMP in comparison with other measurement-sparse matrices are appropriate. But, because of complexity, it cannot be used for big size images. However, the pair structured random sensing matrix with values 0, 1 and Fourier sparse matrix which got the second rank in terms of coherence, approved to be a noise robust pair and showed a great potential to be used in CS.