I have an image (that is a matrix), let's say of dimensions NxN. I then want to expand this matrix into M basis matrices (for the moment I'm still unsure how many M of these basis matrices I should assume) of the same dimensions NxN, that is analog to basis expansion of a vector into basis vectors. But as for the base matrices, I want them to be either only the translation (fixed scaling) or only the scaling (fixed translation) of a given mother basis matrix. Is such an expansion justifiable, or probably even feasible in the first place? I'm interested in searching for a set of basis matrices whose corresponding expansion coefficients form a sparse vector.