Convolution theorem. Fourier transform.

Hey ppl,

I have a question about convolution and Fourier transform. I have Final picture and initial picture. I know that the final picture results as convolution between the initial and something else, i.e. final picture=initial picture(*)X. All we know that F{final picture}=F{initial picture}F{X}=>F{X}=F{final picture}/F{initial picture}; then X=F{X}^(-1). Pretty easy but I got a blank picture after that manipulations. Take a look part of my code:

FFT_picture=fft2(picture); %?
FFT_hole=fft2(hole); %?
FFT_X=FFT_picture./FFT_hole;
X=ifft2(FFT_X);

what I do wrong?

I've attached two files. The first one is the initial picture and the second one is the final picture.

Thank you.

[Matt J]

I've attached two files. The first one is the initial picture and the second one is the final picture.

If you attach "picture" and "hole" in a .mat file instead, it will be easier for people to repeat your test.

Answer 1

[Matt J]

Your procedure won't work if FFT_hole has some pixels containing zero (or nearly zero). If that happens then your calculation of FFT_X will have a divide-by-zero situation and give NaNs and/or Infs in those pixels. Passing that through ifft2() will just yield junk.

You might want to look at deconvreg() instead.

[Dimani4]

No. It doesnt work. It gave me just a number. Secondly this function doesnt work with matrices, only with vectors. So I reshape it to vectors and added some numbers instead zeros. My pictures contain zeros. I wonder is any body didnt encounter with such a problem.

[Matt J]

You're using it wrong somehow. It's an Image Processing Toolbox function. It's specifically meant for image deconvolution. There is an example in its documentation.