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De-noising

denoise_smoothing

This demonstration is a comparison of two methods to denoise an image:

  • the Wiener filter
  • a denoising using smooth operators:

Denoising with the Wiener filter

This is the classical way to reduce the additive noise in an image, it is also called a minimum mean-square estimator. The denoising is performed in the spatial domain using the following transfert function:

Wiener Filter Diagram

where:

  • F(u,v) : is the Fourier transform of the original image (uncorrupted image) with mf as mean
  • N(u,v) : is the Fourier transform of the additive noise with mn as mean

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 s2 and the mean is zero, a good estimation of K is K = s2.

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:

Wiener Filter Diagram

The smoothing operator is the well-known “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
Cells Original Border
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Input Image 

Lena image with additive noise (20).

Cells Original Border
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Output Image with the Wiener filter

SNR = 18.55

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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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