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I am looking for methods to enhance noisy images, where:

  • some pixels in the image are very noise,
  • some other pixels do not contain so much noise.

My first thought is to build an adaptive Gaussian filter. This means that the Gaussian kernel will depend on the (estimated) noise status of the current pixel (large radius of the Gaussian kernel for noisy pixels and a smaller in the converse case).

Could you help me in calculating the kernel values?

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  • $\begingroup$ I't unclear when you mean noise and when you mean noisy. Can you edit your question and clarify? $\endgroup$
    – Phonon
    Commented May 19, 2014 at 5:38
  • $\begingroup$ @Phonon: My question is noise. For example gaussian noise $\endgroup$
    – John
    Commented May 19, 2014 at 6:05
  • $\begingroup$ @John, Are you still after this? $\endgroup$
    – Royi
    Commented Apr 12, 2022 at 13:41

2 Answers 2

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So if I understand your description correctly your data looks something like this:

enter image description here

In this case you could try using a robust Gaussian smoothing. This involves an extra weight term to discard 'outliers'. There are many possible ways to define the outliers using deviation from the local mean (over the kernel) greater than $\pm 3 \sigma$ is a common way. Unfortunately I can't seem to find any decent papers or articles describing the method in more detail.

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It's not clear in your case that Gaussian kernels will help you.

Since you have a noise shape that is closer to salt-and-pepper noise instead of additive white noise, you may want to try other algorithms (that are somehow linked to an $L_1$ best fit instead of a least squares solution):

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