# How to solve this 2-D deconvolution $g*f=δ$?

$g*f=δ$, 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.

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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

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.