Noise Folding in Completely Perturbed Compressed Sensing

This paper first presents a new generally perturbed compressed sensing (CS) modely=(A+E)(x+u)+e, which incorporated a general nonzero perturbationEinto sensing matrixAand a noiseuinto signalxsimultaneously based on the standard CS modely=Ax+eand is called noise folding in completely perturbed CS model. Our construction mainly will whiten the new proposed CS model and explore in restricted isometry property (RIP) and coherence of the new CS model under some conditions. Finally, we use OMP to give a numerical simulation which shows that our model is feasible although the recovered value of signal is not exact compared with original signal because of measurement noisee, signal noiseu, and perturbationEinvolved.