I am working on an encryption algorithm for images, and am stuck in the following factorization.
Let $A$ be a positive, invertible, non-sparse random matrix. Let $S$ be my image matrix that is scaled such that all entries are less than $1$. I multiply $A$ and $S$ to get $Y$ and then proceed with some algorithm. Finally, after after decryption, I get matrix $V$.
Given $Y$, how can I get my $S$? Or, how can i get as close as possible to $S$?
I have used non-negative factorization but that is not unique and it is not giving right results. Can somebody suggest some technique to approximate $S$ given $V$?