Principle of image nonlocal mean filtering

brief introduction

The principle of image nonlocal mean filtering makes use of the uncorrelated characteristics of noise . As shown in the figure below , In an image , There are many image blocks with the same pixels , And the noise is irrelevant , Of course, irrelevant assumptions are strong , It should be said that the correlation of noise is very weak , This assumption is also in line with certain practical application scenarios .

Principle analysis and derivation

We assume that the value of the noise free pixel block is f(x,y)f(x,y), Additive noise is n(x,y)n(x,y), Then the value of the pixel block after adding noise is g(x,y)=f(x,y)+n(x,y)g(x,y)=f(x,y)+n(x,y). We superimpose several similar pixel blocks and take the mean value to get g¯¯¯(x,y)=1K∑Ki=1gi(x,y)g¯(x,y)=1K∑i=1Kgi(x,y). It should be noted here that similarity is a vague concept , From a quantitative point of view, it is the distance between two similar blocks , This distance can be European distance, etc , For a rough explanation of the principle , The following derivation reinforces similar concepts . Apply the viewpoint of probability , We calculate the pixel block after averaging the superposition processing to get ,

Due to the similarity of pixel blocks , In the above formula, the first term of the formula on the right is reduced to f(x,y), The second term is due to the assumption that the mean value of noise is 0, therefore

In addition, due to the non correlation of noise , We can get g(x,y)g(x,y) The variance calculation formula of is

therefore , Finally, the derived variance is ：

among σf² The variance value of the pixel block without noise is 0.

thus it can be seen , Image denoising can be carried out by means of nonlocal mean .