Noise Folding in Completely Perturbed Compressed Sensing

Figure 1

(a) Recover from . The error of the recovered signal value and original signal value is by the Euclidean norm which indicates that the recovered signal and original signal are almost the same. (b) Recover from . The error of the recovered signal value and the original signal value is 6.2258 by the Euclidean norm which means that the recovered signal and original signal are quite different. (c) Recover from . The error of the recovered signal value and the original signal value is by the Euclidean norm which indicates that the recovered signal is much different from the original signal. Compared with the change (error) between the recovery signal and the original signal in (a), the changes (errors) in (b) and (c) differ little. What is more, comparing the change between the recovery signal and the original signal of (c) with that of (b), the change of (c) is quite a little bigger because is involved in (c) but is not involved in (b).

(a)

(b)

(c)