Take an image $f$ with some characters on it (below, hjFu3). Let's apply a filter $h$ on it to obtain a second image $g$ where the text is not visible.

Is there a way to compute what kind of filter $h$ we have applied ? The aim being that this filter should be applied to decode a new blurred image that was blurred with the same filter $h$.

Some remarks :

- Let $\hat f=\text{fft}(f)$. I computed $\hat f$ and $\hat g$. Then $\hat h = \hat g / \hat f$ (pointwise) and then we can compute the $h$ by inverse fft. - I noticed that $g-f$ gives a image which is readable and I think I should exploit this fact because I can't explain why I should obtain a readable image.

I know that I should use a deconvolution algorithm. The point is I don't know the PSF function, so a blind algorithm could the solution. However I don't have any success using typical blind deconvolution algorithm of matlab.

I would like to know if we can compute the psf function given that we have the orignal and final image.

Data for the problem :

$f=$original image f

$\qquad \quad \large \downarrow PSF ?$

$g=$blurred image g

  • $\begingroup$ I don't that you can do it, in general. Let's consider a filter that averages all the values on the image, what would you do in that case? $\endgroup$ – nicoguaro Sep 20 at 19:01
  • $\begingroup$ I tried some some blind deconvolution algorithms without success $\endgroup$ – Smilia Sep 21 at 16:25
  • $\begingroup$ I agree with @nicoguaro that this seems unlikely to be solved without some assumptions or more data. If you had a lot of input-output image samples, you could perhaps find an operator to go from the output blurred image to the input one, but not sure if that's an option. $\endgroup$ – spektr Oct 4 at 5:31

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