I want to decompose an image $A$ using the Discrete Wavelet Transform and then find the singular values, $S$, such that $A=USV$. I will then do the same to another image such that $B=USV$. I will modify the values of $S_A$ using $S_B$.
For example, $A'_S = A_S+B_S$ and $A'_U=A_U$, $A'_V=A_V$.
I will then perform the Inverse Discrete Wavelet Transform on $A'$, a watermarked image which contains $B$.
I will then run the Discrete Wavelet Transform and SVD on $A'$ to get $A'=USV$. I can subtract $A'_S$ from $A_S$ to get $B_S$. However, to obtain the complete image $B$, how can I get $B_U$ and $B_V$?