Inverse convolution of image

Question

I have source and result image. I know, that some convolution matrix has been used on source to get result. Can this convolution matrix be computed ? Or at least not exact o

Answer 1

This is a classical problem of deconvolution. What you called a convolution matrix is usually called the "kernel". The convolution operation is often denoted with a star '*' (not to confuse with multiplication!). Using this notation

Result = Source * Kernel

The answers above using the FFT are correct, but you can't really use FFT based deconvolution in the presence of noise. The right way to do it is using Richardson-Lucy deconvolution (see https://en.wikipedia.org/wiki/Richardson%E2%80%93Lucy_deconvolution)

It is quite straightforward to implement. This answer also provides a sample Matlab implementation: Would Richardson–Lucy deconvolution work for recovering the latent kernel?