Noise Folding in Completely Perturbed Compressed Sensing

This paper first presents a new generally perturbed compressed sensing (cs) model y = (a + e) (x + u) + e,which incorporated a general nonzero perturbation e into sensing matrix a and a noise u into signal x simultaneously based on the standard cs model y = a x + e and 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 (r i p) 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 noise e,signal noise u,and perturbation e involved. © 2016 limin zhou et al.