This demonstration is a comparison of two methods to denoise an image:
Denoising with the Wiener filter
This is the classical way to reduce the additive noise in an image, it is also called a minimum meansquare estimator. The denoising is performed in the spatial domain using the following transfert function:
where:
In practical implementations, the noise N(u,v)^{2} is not available, so it is replaced by a constant K. If the noise is white with a variance of s^{2} and the mean is zero, a good estimation of K is K = s^{2}.
Denoising using a smoothing operator
An alternative to the Wiener filter is an algorithm using smoothing operators to denoise an image. The implementation corresponds to the following diagram:
The smoothing operator is the wellknown “Gaussian filter” with s that controls the strength of the smoothing. The threshold opertor is a “Soft thresholding” with a threshold parameter t that controls which low values are suppressed.
The method doesn’t require the knowledge of the noise or its estimation and it is possible to set the denoising with two parameters: s and t.
Example on Lena image 

Input Image
Lena image with additive noise (20). 


Output Image with the Wiener filter
SNR = 18.55 


Output image with the denoising using smooth operator
Sigma = 1.5 Threshold = 34 SNR= 21.61 
Source:
http://bigwww.epfl.ch/demo/denoise/desc.html
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