# Estimate Image power spectrum of the noise

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.

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

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