Blind Recover Conditions for Images with Side Information

We consider the blind recovery problem such that images embedded with side information are given, and we want to obtain the side information under some prescribed constraints. In this case, the system equation becomes y = Ax + b where in addition to the unknown A and x, b also is an unknown quantity and but clearly not a noise component. We assume that several images with the same embedding side information are given, and the image processing to b is described as the perturbation of A. We formulate the optimization function to obtain A, b and x, under the constraint of some finite brightness levels i.e. finite alphabets.