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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.2011-11-27
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    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).2011-11-27
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    [Ganic, 2004]: http://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&ved=0CCIQFjAA&url=http%3A%2F%2Fwww.sci.brooklyn.cuny.edu%2F~eskicioglu%2Fpapers%2FACMworkshop2004.pdf&ei=VjnSTqG0L4mDtgeCh6ysDQ&usg=AFQjCNHOBcOsHGMnR0h7uoN0GoM89hk6zg&sig2=7ZxmILjHM_-yCxDbyW3BCA2011-11-27
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    Maybe this is more suited to http://dsp.stackexchange.com ?2012-01-11

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