Consider the Robust PCA problem for noisy data. If we move constraint to the objective function we have

argmin | |M - (L + S) |IF + AllIll * + XISll1 L,S50 100 150 100 250 300 50 100 150 200 250 300 350The smooth background: 50 100 150 200 250 300 50 100 150 200 250 300 350