Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

$g*f=δ$, where $*$ refers to convolution, $δ$ is impulse, $f$ and $g$ is 2-D matrix, $f$ is given and sum of all the elements in $f$ equals $0$, $g$ is unknown. i want to find $g$.

i would appreciate it if you also can provide with matlab code

thanks in advance. this problem has bothered me for long.

share|cite|improve this question
I'd have guessed $\delta$ is the impulse, rather than the impulse response. Could that be what you meant? – Michael Hardy Apr 12 '12 at 4:53
yes, sorry for my mistake. I am new in image processing. – Jiapei Huang Apr 12 '12 at 5:27
up vote 0 down vote accepted

Assuming this is really convolution, on the transform side you get $\hat f \hat g = 1 $, however, when you represent convolution as a matrix the entries in every row are the same numbers rotated, so the fact that the sum of all the elts of f is $0$ means the sum over a row is $0$ which means $\hat f(0) = 0$ and this equation will not have any solutions.

share|cite|improve this answer

MATLAB has several image deconvolution (deblurring) commands; see the link for example code.

The next time you should post your image processing questions at

share|cite|improve this answer
thanks. very helpful info.. – Jiapei Huang Apr 15 '12 at 1:31

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.