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From: "Bruno Luong" <b.luong@fogale.findmycountry>
Newsgroups: comp.soft-sys.matlab
Subject: Re: How to deal with this transposition in inverse problem ie. image
Date: Fri, 3 Apr 2009 07:02:03 +0000 (UTC)
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aheartthatlovesisalwaysyoung@gmail.com wrote in message <471e1973-38cd-4ba9-b081-d9a74c7b8d9c@w35g2000prg.googlegroups.com>...

> 
> My question is how to deal with H^T in convolution ie H & x. conv2
> (H,x) (here H, x is a image matrix)?

I believe H^T is convolution with the flipped kernel. Write down what is transpose operator. This relation might be useful to come back to the basic
     dot(H^T y , x) = (y , conv2(H,x)) for all images x

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

Multiplication of the flipped Fourier transform of the kernel, I believe. You have now all the idea to check by yourself.

Bruno