Question

Is there something like an anti-filter in image processing?

Say for instance, I am filtering an image using the following 13 tap symmetric filter:

{0, 0, 5, -6, -10, 37, 76, 37, -10, -6, 5, 0, 0} / 128

Each pixel is changed by this filtering process. My question is can we get back the original image by doing some mathematical operation on the filtered image.

Obviously such mathematical operations exists for trivial filters, like:

{1, 1} / 2

Can we generalize this to complex filters like the one I mentioned at the beginning?

Answer 1

Here is a pointer to one method of deconvolution – taking account of noise which in your case I guess you have due to rounding error – http://en.wikipedia.org/wiki/Wiener_deconvolution