[image denoising] image denoising based on partial differential equation (PDE) with matlab code

1 brief introduction

In engineering application , Image information is processed by digital image system 、 Storage and transmission, etc , Due to the inevitable noise interference , Make the original image information produce deviation and distortion , It brings inconvenience to the subsequent image processing , And then affect people's cognition of the visual characteristics of the image . therefore , In order to improve the quality of the image , Improve people's recognition of image visual characteristics , Effectively remove image noise , It is necessary to reduce the interference of noise to image information . In recent years , Based on partial differential equations ( partial differential equation,PDE) ​ Image de-noising method has been widely valued in the field of computer vision and image processing , Because it smoothes the noise while , The edge texture information of the image can be well preserved .

2 Part of the code

%---------------------------------------------%%                %clcclear all% I=imread('pentagram.bmp');%gray image% I=imread('lena1.bmp');% I=imread('cameraman.tif');I=double(I(25:125,70:170));I=imread('canal.gif');%gray noisy image% [I,map]=imread('ct_scan.bmp');I=ind2gray(I,map);% I=imread('haifa.bmp');%color imageI=double(I);[row,col,nchannel]=size(I);In=I;% Join in ( mean value =0, variance =sigma) Gaussian noise of ( Optional )sigma=15;if nchannel==1%gray image    In=I+sigma*randn(row,col);elseif nchannel==3%color image    In=I+sigma*randn(row,col,3);end​% Manually specify the gradient threshold (for smooth&directional diffusion)K=15;% use robust_statistic Automatic estimation of gradient threshold ( ginseng Sapiro P231)% K=autoK(In)% Draw the influence function curve % plot_edgestop(K);% Draw the level set curve % figure;contour(In);axis ij;% Diffusion denoising edgestop='pm1';method='cat';niter=50;% It=smooth_diffusion(In,edgestop,method,'is',niter,K,I);% It=directional_diffusion(In,'tky','av2','is',niter,K,I);% figure;contour(It);axis ij;% Draw the level set curve % It=TV_denoise(In,'is',niter,0,0,I);%without fedality termIt=TV_denoise(In,'is',1,1,sigma,I);%with fedality term% It=order4_diffusion(In,edgestop,'is',niter,K,I);figure;subplot(131);imshow(uint8(I)); title(' Original picture ')subplot(132);imshow(uint8(In)); title(' Noise map ')subplot(133);imshow(uint8(It)); title(' Denoising map ')% title(['SNR=',num2str(SNR(I,In))]);% Signal to noise ratio :​

3 Simulation results

4 reference

[1] Yangyingchun . Research on image denoising algorithm based on partial differential equation [D]. North China University , 2012.

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