If we convolve an image with a point spread function and from the resulting image to find the input image, can we use any stochastic approaches? I feel like we will not be able to. A single image seems to me a deterministic quantity and I cannot think of any way to approach this deconvolution problem in a stochastic way. However, I am not sure and I want to know if there is a way. Any help is appreciated

  • $\begingroup$ Any approach which takes into account the noise in the image is stochastic. $\endgroup$ – Royi Jan 17 at 19:38
  • $\begingroup$ I see, thank you so much @Royi ! $\endgroup$ – xhensa Jan 18 at 9:13
  • $\begingroup$ Would you accept this as an answer? $\endgroup$ – Royi Jan 18 at 9:22
  • $\begingroup$ Though I could not figure out how it would work in the real case, yes, I would accept it as an answer. But if you are asking for me to accept your comment as the approved answer, I would like to say that you have written it as a comment not an answer, hence I am not able to accept it as the answer $\endgroup$ – xhensa Jan 19 at 12:59
  • $\begingroup$ Hi, I added it as an answer. $\endgroup$ – Royi Jan 19 at 15:48

Any Deconvolution method which takes into account the noise in the image is basically a stochastic approach.

Usually, the model for Deconvolution is:

enter image description here

So having the noise in there makes it a problem with stochastic properties.

If by stochastic you meant sampling from the Posterior Distribution then you may have a look at Stochastic Image Denoising by Sampling from the Posterior Distribution (Though it is not about Deconvolution but on Denoising).

  • 1
    $\begingroup$ Thank you for the nice explanation! $\endgroup$ – xhensa Jan 19 at 15:53

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