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I want to implement Wiener filter. I have original image and image blurred with linear motion. The one thing I am lack of(to implement it) is Noise power spectrum.

I know that it is hard task. I've took a look on different papers:

I don't understand why it is that complicated to just find noise spectrum if I have original signal(image)?

If I take noise image minus original image, it will be my error image. And if I estimate variance of it, that will be my Noise variance(Noise Power)?

I totally confused and here is my question: " How to estimate Power spectrum of the noise of the blurred image if I have original image?"

Btw, I don't want get some matlab function which will do all of it, but rather algorithm or equation that I can implement.

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  • $\begingroup$ Oh, really! I'm sorry, I didn't know that you have this! Thank you! $\endgroup$
    – Mykola Servetnyk
    Commented Jan 7, 2015 at 1:15
  • $\begingroup$ No worries! :-) $\endgroup$
    – A. Donda
    Commented Jan 7, 2015 at 12:22
  • $\begingroup$ Could you review my answer? $\endgroup$
    – Royi
    Commented Jul 30, 2023 at 6:27

1 Answer 1

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Usually the model is something like:

$$ \boldsymbol{y} = \boldsymbol{H} \boldsymbol{x} + \boldsymbol{n} $$

Where $ \boldsymbol{y} $ is the output image, $ \boldsymbol{x} $ is the input image, $ \boldsymbol{H} $ is the operator (Blurring, Decimation, etc...) model and $ \boldsymbol{n} $ is the added noise.

Indeed it is easy to know the spectrum of $ \boldsymbol{n} $ if you have both $ \boldsymbol{y} $ and $ \boldsymbol{x} $ (And $ \boldsymbol{H} $).
Yet in practice, the model means we only have $ \boldsymbol{y} $ and some prior on $ \boldsymbol{H} $ and $ \boldsymbol{n} $.

Then the problem is not trivial at all.
It is called Inverse Problem.

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