[image denoising] image denoising based on MATLAB Gaussian + mean + median + bilateral filtering [including Matlab source code 1872]

One 、 gaussian + mean value + The median + Introduction of bilateral filtering image denoising

1 A brief introduction of digital image denoising technology
1.1 Research background and purpose
Image is the first perspective for human beings to understand the world , We can get more real information and intuitive results through images . But actually , In the process of generation and transmission, the signal will inevitably mix with some noise . therefore , When receiving an image signal , Eliminating or reducing noise has become an important method to obtain high-definition images . Before denoising the image , We need to model noisy images , Get the original information of noise . Because noise generation is inevitable , therefore , You can only choose to eliminate by corresponding methods , This is also the research significance of image noise elimination .

With the rapid development of computer application technology , The information that human contact is no longer a simple voice signal . More image signals , The more digital information , There will be more interference and noise . With the development of society , People's requirements for image quality of receiving external information sources are increasing , This also puts forward higher requirements for noise removal technology . With the deepening of people's research , A lot about image processing technology is improving , Image denoising technology is becoming more and more perfect .

Nowadays, image denoising has been a relatively visual research topic , Its scope is very wide , It is of great help to the military and medical fields . therefore , Further research on image denoising from the computer level has important practical significance .

1.2 Research status of digital image denoising technology
In reality, image signals inevitably have noise signals . therefore , The only way to eliminate noise is to filter the noise signal . According to the nature of image and noise , Scientists have proposed a variety of methods to remove noise . With the development of modern science and Technology , These methods are gradually applied to practice , There are commonly used adaptive median filtering methods based on the concept of fuzzy index 、 Average filtering method based on fuzzy weighting method, etc . Although these two methods are widely used , But there are also some disadvantages . for example , When multiple noises interfere with the image signal at the same time , The results of the above two methods are not ideal , Because it smoothes the details of the image while removing the noise , The details of the image become blurred , The quality of the image also declines .

Image and vision , It is the most direct means and method for human beings to obtain information , Although other human organs have the ability to receive information , however , In general , Vision always comes first . It is often intuitive for people to understand the world with the help of vision , We need to deal with the events we see . During the event processing , It mainly includes the basic stored procedure of image 、 The smoothing and noise filtering process of the original image , In this way, the image information we get can be more intuitive and efficient . because , The existence of image noise , It mainly affects the image recognition .

The process of image processing is a collection of integrated disciplines , Including signaling 、 mathematics 、 Computer science 、 Statistics and other disciplines , The comprehensive treatment of subjects is the process of algorithm complexity . We are in a complicated situation , They often summarize the corresponding laws of the noise studied . therefore , Analyze from a numerical point of view , Image noise generally includes Gaussian noise 、 White noise 、 Poisson noise and other noises with strong regularity , For some noise that does not conform to the law of change , It can be smoothed by filtering , Common filtering methods include median filtering 、 Gaussian filtering and so on . According to different noise types and image types , Before image analysis , The noise needs to be analyzed , And for different analysis requirements, different methods are used for noise reduction .

The noise signal distribution of Gaussian noise is mainly Gaussian distribution , This type of noise is a common system noise . For images , It is mainly the noise interference caused by the image medium propagation in the process of image formation , Such noise can be defined as a relatively strong quantization noise , It is the inevitable noise interference in the process of image formation .

The noise processing is completed in the frequency domain [11]. Fourier transform is commonly used to transform images from space to transform domain 、 Wavelet transform, etc . For noise treatment , Image information can be converted into numbers , In the process of signal processing , We need to convert the image digital signal into the frequency domain , Gaussian noise can be stripped out in the frequency domain , And through the corresponding filter , Deal with the noise , Then the processed signal is transformed by inverse transformation , Applied to the image domain , You get the output image .

2 Gaussian filtering algorithm and its implementation
On the whole , Gaussian filter is a kind of linear smoothing filter , It is very effective in dealing with systematic Gaussian noise , It mainly deals with the weighted average of the digital signal corresponding to the image . such as , The position result of any noise , Use the weighted average of the surrounding areas , The noise points can disappear in the surrounding weighted average results , In the process of concrete implementation , It mainly uses the weighted average function to weight the results , after , Overwrite the special value with the average value .

Noise removal process , In fact, it is the implementation process of the filter . Gaussian filter is to filter Gaussian noise , So we can get an image with good signal-to-noise ratio , The higher the SNR is , The more distortion free the result is . For an image , If the noise persists , It may cause poor noise transmission . The process of Gaussian filtering is to smooth the signal first . And then , Remove the noise accordingly . The purpose of Gaussian filter is to construct a filter , Carry out second-order filtration , And carry out the corresponding energy conversion process , In the frequency domain , Energy is a relatively direct manifestation . We often can not directly use the ideal filter to process the signal , Because it is very likely that the signal will ring . The advantage of Gaussian filter is that its system function is relatively reliable , It can effectively smooth the system noise , Avoid undesirable ringing .

A filter is a model , Through the model, the image data is transformed into energy , The noise belongs to the high frequency part , After smoothing by Gaussian filter, the influence of noise on image can be reduced .

3 Mean filtering
Mean filtering is also called linear filtering , The main method is neighborhood average method . The basic principle of linear filtering is to replace each pixel value in the original image with the mean value , The current pixel to be processed (x, y) , Select a template , The template is composed of several neighboring pixels , Find the mean value of all pixels in the template , Then assign the mean value to the current pixel (x, y) , As the gray level of the processed image at this point g (x, y) , namely g(x,y)=1M∑f∈sf(x,y), among , s As a template , M Is the total number of pixels in the template including the current pixel .

4 median filtering
Median filter is a kind of nonlinear signal processing technology which can effectively suppress noise based on sorting statistics theory . The basic principle of median filter is to replace the value of a point in a digital image or digital sequence with the median value of each point in a neighborhood of the point , Let the pixel with a large difference in the gray value of the surrounding pixels change to a value close to the surrounding pixel value , Thus, isolated noise points can be eliminated . The method is to take a two-dimensional sliding template of a certain structure , Sort the pixels in the template according to the size of the pixel value , Generate monotonous rise ( Or down ) Two-dimensional data sequence . The output of two-dimensional median filter is g (x, y) =Med{f (x-k, y-l) , (k, l) ∈W}, among , f (x, y) , g (x, y) They are the original image and the processed image .W It's a two-dimensional template , Usually it is 3×3, 5×5 Area , It can also be in different shapes , Like a thread , circular , cross , Torus, etc .

5 Bilateral filtering
Through the analysis and research of bilateral filtering , The author thinks , The algorithms of bilateral filtering and Gaussian filtering are different . Different from Gaussian filtering , Bilateral filtering is a nonlinear digital processing method for image signals , Bilateral filtering can cover Gaussian filtering algorithm , It also takes into account the dual effects of gray point value and burr removal . But for images , It is better to choose the combination of Gaussian filter and bilateral filter for denoising . Specifically speaking from the algorithm , Bilateral filtering is transformed from Gaussian filtering , Double convolution processing for Gaussian filtering function , Optimize the filter weight coefficient , The coefficients of the filter weights are multiplied by the convolution results in the frequency domain of the image , Thus, the effect of removing burr on the basis of removing gray is obtained , It gives full play to the advantages of Gaussian filtering noise , At the same time, the bilateral smoothing optimization effect is also obtained .

In theory , The result of bilateral filtering is better , The smoothness of the image is good , Practical . Let's explain the weight enhancement in the bilateral filtering process , Generally speaking, the weighting coefficients of bilateral filtering are a nonlinear combination of Gaussian filtering and convoluted result coefficients , It mainly uses the coefficient memory convolution calculation of spatial image approximation function and brightness approximation function . For the former , As the calculation step changes , The mathematical distance between the pixel point obtained from the image and the back center point will become smaller , If you increase the clarity of the image , Then the distance becomes smaller . in other words , The higher the pixel, the higher the image , During processing , The bilateral filter will be transformed into the corresponding low-pass filter , The edge of the image can be better protected . Generally speaking , The results of bilateral filtering are affected by 3 The influence of two parameters , They are the half width of the filter N、 Parameters δs and δr. For general bilateral filtering analysis , In the filtering process, the proximity factor and the brightness change factor are both violent . We are in the process of image processing , You can't just keep high-frequency or low-frequency signals , therefore , Use of bilateral filtering , It can protect the image processing with wide frequency domain , The realization of its effect is mainly accomplished by the function of bilateral filtering . In a bilateral filter , The output result of pixels will be generated . According to previous studies , Bilateral filtering has strong nonlinear processing ability 、 The local processing effect is good and the calculation process does not have the characteristics of iteration . However, the disadvantage of bilateral filtering is that it is easy to process the signal of its own image , This requires the cooperation of Gaussian filtering . In other words , If gray processing or other processing methods are not used in the early stage , Cover the rough edges , Then the effect of bilateral filtering may not be ideal , The mathematical model of bilateral filtering is given below .

Bilateral filter , The value of the output pixel depends on the weighted combination of the values of the neighboring pixels , The formula says :

Weight factor w(i,j,k,l) It depends on the domain

utilize Matlab Software bilateral filtering method on the graph 1 To deal with , Get the picture 3、 chart 4 Sum graph 5 The effect of , stay Matlab Build :function B = bfilter2(A,w,sigma) and function B =bfltGray(A,w,sigma_d,sigma_r) Function of .

Two 、 Partial source code

function B = bfilter2(A,w,sigma)
% Confirm that the input graphic exists and is valid 
% Verify that the input image exists and is valid.
if ~exist('A','var') || isempty(A)
   error('Input image A is undefined or invalid.');
end
if ~isfloat(A) || ~sum([1,3] == size(A,3)) || ...
      min(A(:)) < 0 || max(A(:)) > 1
   error(['Input image A must be a double precision ',...
          'matrix of size NxMx1 or NxMx3 on the closed ',...
          'interval [0,1].']);      
end

% Verify bilateral filter window size 
% Verify bilateral filter window size.
if ~exist('w','var') || isempty(w) || ...
      numel(w) ~= 1 || w < 1
   w = 5;
end
w = ceil(w);

% Verify the standard deviation of the bilateral filter 
% Verify bilateral filter standard deviations.
if ~exist('sigma','var') || isempty(sigma) || ...
      numel(sigma) ~= 2 || sigma(1) <= 0 || sigma(2) <= 0
   sigma = [3 0.1];
end

% Apply color or grayscale bilateral filtering 
% Apply either grayscale or color bilateral filtering.
if size(A,3) == 1
   B = bfltGray(A,w,sigma(1),sigma(2));
else
   B = bfltColor(A,w,sigma(1),sigma(2));
end

3、 ... and 、 Running results

Four 、matlab Edition and references

1 matlab edition
2014a

2 reference
[1] Cai Limei .MATLAB The image processing —— theory 、 Algorithm and example analysis [M]. tsinghua university press ,2020.
[2] Yang Dan , Zhao Haibin , Long Zhe .MATLAB Detailed explanation of image processing examples [M]. tsinghua university press ,2013.
[3] Zhou pin .MATLAB Image processing and graphical user interface design [M]. tsinghua university press ,2013.
[4] Liu Chenglong . Master MATLAB The image processing [M]. tsinghua university press ,2015.
[5] Hu Lei , Zhang Wei , Qin Qingyan . Application analysis of several image denoising algorithms [J]. information technology . 2007,(07)
[6] Pan Liangjing . Digital image denoising algorithm based on Gaussian filter and bilateral filter [J]. Journal of Shangqiu Vocational and technical college . 2020,19(01)

3 remarks
This part of the introduction is taken from the Internet , For reference only , If infringement , Contact deletion