# Singular Value Decomposition

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 $B_V$?

Thanks!

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Your statement of the problem is not at all clear. But If you've just thrown away the $U$ and $V$ from the SVD of $B$, I see no way to get them back. – Robert Israel Nov 27 '11 at 6:12
As far as I can tell, they're thrown away. The papers I've been reading on this suggest you use U and V from the watermarked image. I was hoping someone familiar with the process could clarify. Also, if it helps, one of the papers I'm trying to follow is "Robust DWT-SVD Domain Image Watermarking: Embedding Data in All Frequencies" [Ganic, 2004]. Lastly, I'm only using the LL band to embed the watermark (not all 4 bands as Ganic suggests). – Daniel Gibbons Nov 27 '11 at 13:20
[Ganic, 2004]: google.com/… – Daniel Gibbons Nov 27 '11 at 13:21
Maybe this is more suited to dsp.stackexchange.com ? – tdc Jan 11 '12 at 12:48