HowTo deal with this transposition in inverse problem ie. image restoration

timedcy Asayaku — Fri, 03 Apr 2009 07:22:02 -0400

How to deal with this transposition in inverse problem ie. image restoration

For example, when minimizing || g – Hf ||^2 + λ||Qf||^2 , where image matrix f & g are the true and observed value in column-lexically heaped vectors, H is block-toeplitz matrix of the convolution kernel.

Then the solution is f = H^Tg/(H^TH+ λQ^TQ) , here H^T means the conjugate transpose matrix of H.

In programming, we usually compute it in the Fourier domain.
My question is how to deal with H^T in convolution ie H & x. conv2(H,x) (here H, x is a image matrix)?

And what is the relation between (H^T x) and (H x) in frequency domain?

ifftn( conj(fftn(H)) .* fftn(x) )?
or conv2(rot90(H,2), x)

this problem confused me very long long time!

Can you help me ?

Sincerely timedcy
20090403

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HowTo deal with this transposition in inverse problem ie. image restoration