Path: news.mathworks.com!not-for-mail
From: <HIDDEN>
Newsgroups: comp.soft-sys.matlab
Subject: HowTo deal with this transposition in inverse problem ie. image restoration
Date: Fri, 3 Apr 2009 07:22:02 +0000 (UTC)
Organization: The MathWorks, Inc.
Lines: 20
Message-ID: <gr4deq$1qh$1@fred.mathworks.com>
Reply-To: <HIDDEN>
NNTP-Posting-Host: webapp-05-blr.mathworks.com
Content-Type: text/plain; charset="ISO-8859-1"
Content-Transfer-Encoding: 8bit
X-Trace: fred.mathworks.com 1238743322 1873 172.30.248.35 (3 Apr 2009 07:22:02 GMT)
X-Complaints-To: news@mathworks.com
NNTP-Posting-Date: Fri, 3 Apr 2009 07:22:02 +0000 (UTC)
X-Newsreader: MATLAB Central Newsreader 1743417
Xref: news.mathworks.com comp.soft-sys.matlab:529954


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

For example, when minimizing || g &#8211; Hf ||^2 + &#955;||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+ &#955;Q^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