图像复原实验

企业开发 2023-05-18 03:04:04 阅读次数: 0

一、 实验目的：

1.了解图像降质/复原处理的模型。
2.了解估计降质函数的基本原理。
3.掌握降质图像中常见噪声模型及参数估计方法、基本原理、实现步骤。
4.加深对几种常用的图像复原方法的理解。

二、实验原理：

对于线性移不变系统，在空域中图像降质过程通常建模为卷积形式，若已知点扩散函数和加性噪声，就很容易反解出原图像函数。由于在空域中直接复原存在大规模计算问题，所以复原一般通过对图像进行傅里叶变换后，在频域中进行图像复原。

(1) 无约束复原——维纳滤波(最小均方误差)
维纳滤波也称为最小二乘滤波，它是使原始图像与其恢复图像之间的均方误差最小的复原方法。对图像进行维纳滤波主要是为了消除图像中存在的噪声。

(2) 约束复原——平滑约束复原(约束最小平方滤波)
约束最小平方滤波是一种比较容易实现的线性复原方法，约束复原除要求了解关于降质系统的传递函数之外，还需要知道某些噪声的统计特性或噪声与图像的某些相关情况。

三、实验内容步骤（记录实验主要步骤，且在调试成功后，将结果截屏或拍照保存）

1.读入选择图像库中一幅灰度图像，对图像用motion（运动模糊）及disk（ 散焦模糊）类型进行模糊降质，显示模糊前后的图像。

lena = imread('lena.jpg');
lena_gray=rgb2gray(lena);

subplot(1,3,1);
imshow(lena_gray);
title('原始图像');

PSF = fspecial('motion',15,45);
h1 = fspecial('disk',40);
J1 = imfilter(lena_gray,PSF,'circular');
J2 = imfilter(lena_gray,h1,'circular');

subplot(1,3,2);
imshow(J1);
title('模糊运动图像');

subplot(1,3,3);
imshow(J2);
title('disk模糊图像');

在这里插入图片描述
2.生成大小为 的棋盘格式图像（自行查阅checkerboard函数的使用方法），对该图像进行模糊加噪，分别用点扩散函数、NSR、NCORR和ICORR为参数对降质图像进行恢复，显示并对比恢复结果。

%生成一个120×120的棋盘图像
chessboard=checkerboard(10,60,60);
PSF1=fspecial('motion',7,45);
GB1=imfilter(chessboard,PSF1,'circular');

subplot(2,3,1);
imshow(chessboard);
title('棋盘格式图像');


%对棋盘图像进行加噪
noise_mean=0;
noise_var=0.05;
GB1=imnoise(GB1,'gaussian',noise_mean,noise_var); 
subplot(2,3,2);
imshow(GB1);
title('模糊加噪图像');

% 使用点扩散函数恢复降质图像
frest1=deconvwnr(GB1,PSF1); 
subplot(2,3,3);
imshow(frest1);
title('点扩散函数恢复降质图像');


Sn=abs(fft2(GB1)).^2;
nA=sum(Sn(:))/numel(GB1); %噪声平均功率1
Sf=abs(fft2(chessboard)).^2; %图像功率谱1
fA=sum(Sf(:))/numel(chessboard); %图像平均功率1
R=nA/fA;%计算噪声和信号比例


% 使用NSR恢复降质图像
fr2=deconvwnr(GB1,PSF,R);%使用deconvwnr函数生成常数比率的维纳滤波图像
subplot(2,3,4);
imshow(fr2);
title('NSR恢复降质图像');


% 使用NCORR和ICORR恢复降质图像
NCORR=fftshift(real(ifft2(Sn))); 
ICORR=fftshift(real(ifft2(Sf))); 
fr3=deconvwnr(GB1,PSF,NCORR,ICORR); 

subplot(2,3,5);
imshow(fr3);
title('NCORR和ICORR恢复降质图像');

在这里插入图片描述
3.对内容1中降质图像采用维纳滤波（deconvwnr）和最小二乘方滤波（deconvreg）的方法复原，显示复原后的图像。

lena = imread('lena.jpg');
lena_gray=rgb2gray(lena);
subplot(2,2,1);
imshow(lena_gray);
title('原始图像');


LEN1=12;
THREN1=22;
PFS2=fspecial("motion",LEN1,THREN1);
fuzzy_lena=imfilter(lena_gray,PFS2,'circular'); %对图像进行模糊劣化
subplot(2,2,2);
imshow(fuzzy_lena);
title('模糊劣化图像');


deconvwnr_lena=deconvwnr(fuzzy_lena,PFS2);
subplot(2,2,3);
imshow(deconvwnr_lena);
title('采用维纳滤波复原图像');

least_squares_lena=deconvreg(fuzzy_lena,PFS2);
subplot(2,2,4);
imshow(least_squares_lena);
title('采用最小二乘法复原图像')

在这里插入图片描述
4.编写自适应中值滤波adpmedfilt(g, Smax)，分析自适应中值滤波的优点。中值滤波器受滤波窗口大小影响较大，用于消除噪声和保护图像细节，两者会存在冲突，而自适应中值滤波能根据预设好的条件，动态地改变中值滤波器的窗口尺寸，以同时兼顾去噪声作用和保护细节的效果。

%自适应中值滤波函数
function f = adpmedian (g, Smax) 
if (Smax <= 1) || (Smax/2 == round(Smax/2)) || (Smax ~= round(Smax)) 
    error ('SMAX必须是一个大于1的奇数整数.') 
end 

f = g; 
f(:) = 0;
alreadyProcessed = false (size(g)); 

for k = 3:2:Smax 
    zmin = ordfilt2(g, 1, ones(k, k),'symmetric');
    zmax = ordfilt2(g, k * k, ones(k, k), 'symmetric'); 
    zmed = medfilt2(g, [k k], 'symmetric'); 
    processUsingLevelB  = (zmed > zmin) & (zmax > zmed) &...
        ~alreadyProcessed;
    zB = (g > zmin) & (zmax > g); 
    outputZxy = processUsingLevelB & zB; 
    outputZmed = processUsingLevelB & ~zB; 
    f (outputZxy) = g(outputZxy); 
    f (outputZmed) = zmed(outputZmed); 
    alreadyProcessed = alreadyProcessed | processUsingLevelB; 
    if all (alreadyProcessed (:)) 
        break; 
    end 
end 

f (~alreadyProcessed) = zmed (~alreadyProcessed); 
end

lena = imread('lena.jpg');
lena_gray=rgb2gray(lena);
subplot(1,3,1);
imshow(lena_gray);
title('原始图像');

LEN1=50;
THREN1=100;
PFS2=fspecial("motion",LEN1,THREN1);
fuzzy_lena=imfilter(lena_gray,PFS2,'circular'); %对图像进行模糊劣化
median_filtering_lena=adpmedian(fuzzy_lena,15);

subplot(1,3,2);
imshow(fuzzy_lena);
title('劣化图像');

subplot(1,3,3);
imshow(median_filtering_lena);
title('中值滤波图像')

在这里插入图片描述
5.从图像库中读取三幅灰度图像，对每幅依次添加椒盐噪声、高斯噪声、均匀分布噪声，观察图像的变化。然后依次用均值滤波，中值滤波、自适应中值滤波和基于局部区域统计特征的自适应滤波方法（wiener2）对噪声图像进行处理，并比较处理后的结果。通过比较总结出自适应滤波的优势和适用的滤波场合。
自适应滤波的优势:不但能够滤除概率较大的椒盐噪声，而且能够更好的保
图像的细节，这是常规的中值滤波器做不到的。
适用的滤波场合: 在图像噪声密度不是很大的情况下。

%读取原始图像
wallpaper1=imread('wallpaper1.jpg');

%将图像转换为灰度图像
wallpaper1=rgb2gray(wallpaper1);

% 分别向wallpaperr1添加椒盐噪音、高斯噪声、均匀分布噪声
wallpaper1_salt_pepper=imnoise(wallpaper1,'salt & pepper',0.05);
wallpaper1_gauwallpaperian=imnoise(wallpaper1,'gaussian',0.05);
wallpaper1_speckle=imnoise(wallpaper1,'speckle',0.05);

% 对椒盐噪声图像依次用均值滤波，中值滤波、自适应中值滤波和二维自适应去噪滤波进行处理
wallpaper1_salt_pepper_mean_filtering=filter2(y11,wallpaper1_salt_pepper)/255;
wallpaper1_salt_pepper_median_filtering=medfilt2(wallpaper1_salt_pepper,[3,3]);
wallpaper1_salt_pepper_adaptive_median_filtering=adpmedian(wallpaper1_salt_pepper,15);
wallpaper1_salt_pepper_wiener2_filtering = wiener2(wallpaper1_salt_pepper,[5 5]);

% 对高斯噪声图像依次用均值滤波，中值滤波、自适应中值滤波和二维自适应去噪滤波进行处理
wallpaper1_gauwallpaperian_mean_filtering=filter2(y11,wallpaper1_salt_pepper)/255;
wallpaper1_gauwallpaperian_median_filtering=medfilt2(wallpaper1_salt_pepper,[3,3]);
wallpaper1_gauwallpaperian_adaptive_median_filtering=adpmedian(wallpaper1_salt_pepper,15);
wallpaper1_gauwallpaperian_wiener2_filtering = wiener2(wallpaper1_salt_pepper,[5 5]);

% 对均匀分布噪声图像依次用均值滤波，中值滤波、自适应中值滤波和二维自适应去噪滤波进行处理
wallpaper1_speckle_mean_filtering=filter2(y11,wallpaper1_salt_pepper)/255;
wallpaper1_speckle_median_filtering=medfilt2(wallpaper1_salt_pepper,[3,3]);
wallpaper1_speckle_adaptive_median_filtering=adpmedian(wallpaper1_salt_pepper,15);
wallpaper1_speckle_wiener2_filtering = wiener2(wallpaper1_salt_pepper,[5 5]);

subplot(5,3,1);imshow(wallpaper1_salt_pepper);title('添加椒盐噪音');
subplot(5,3,2);imshow(wallpaper1_gauwallpaperian);title('添加高斯噪声');
subplot(5,3,3);imshow(wallpaper1_speckle);title('添加均匀分布噪音');

subplot(5,3,4);imshow(wallpaper1_salt_pepper_mean_filtering);title('均值滤波');
subplot(5,3,5);imshow(wallpaper1_speckle_mean_filtering);title('均值滤波');
subplot(5,3,6);imshow(wallpaper1_salt_pepper_wiener2_filtering);title('均值滤波');

subplot(5,3,7);imshow(wallpaper1_salt_pepper_mean_filtering);title('中值滤波');
subplot(5,3,8);imshow(wallpaper1_speckle_mean_filtering);title('中值滤波');
subplot(5,3,9);imshow(wallpaper1_salt_pepper_wiener2_filtering);title('中值滤波');

subplot(5,3,10);imshow(wallpaper1_salt_pepper_mean_filtering);title('自适应中值滤波');
subplot(5,3,11);imshow(wallpaper1_speckle_mean_filtering);title('自适应中值滤波');
subplot(5,3,12);imshow(wallpaper1_salt_pepper_wiener2_filtering);title('自适应中值滤波');

subplot(5,3,13);imshow(wallpaper1_salt_pepper_mean_filtering);title('二维自适应去噪滤波');
subplot(5,3,14);imshow(wallpaper1_speckle_mean_filtering);title('二维自适应去噪滤波');
subplot(5,3,15);imshow(wallpaper1_salt_pepper_wiener2_filtering);title('二维自适应去噪滤波');

在这里插入图片描述

%读取原始图像
wallpaper2=imread('wallpaper2.jpg');

%将图像转换为灰度图像
wallpaper2=rgb2gray(wallpaper2);

% 分别向wallpaperr1添加椒盐噪音、高斯噪声、均匀分布噪声
wallpaper2_salt_pepper=imnoise(wallpaper2,'salt & pepper',0.05);
wallpaper2_gauwallpaperian=imnoise(wallpaper2,'gaussian',0.05);
wallpaper2_speckle=imnoise(wallpaper2,'speckle',0.05);

% 对椒盐噪声图像依次用均值滤波，中值滤波、自适应中值滤波和二维自适应去噪滤波进行处理
wallpaper2_salt_pepper_mean_filtering=filter2(y11,wallpaper2_salt_pepper)/255;
wallpaper2_salt_pepper_median_filtering=medfilt2(wallpaper2_salt_pepper,[3,3]);
wallpaper2_salt_pepper_adaptive_median_filtering=adpmedian(wallpaper2_salt_pepper,15);
wallpaper2_salt_pepper_wiener2_filtering = wiener2(wallpaper2_salt_pepper,[5 5]);

% 对高斯噪声图像依次用均值滤波，中值滤波、自适应中值滤波和二维自适应去噪滤波进行处理
wallpaper2_gauwallpaperian_mean_filtering=filter2(y11,wallpaper2_salt_pepper)/255;
wallpaper2_gauwallpaperian_median_filtering=medfilt2(wallpaper2_salt_pepper,[3,3]);
wallpaper2_gauwallpaperian_adaptive_median_filtering=adpmedian(wallpaper2_salt_pepper,15);
wallpaper2_gauwallpaperian_wiener2_filtering = wiener2(wallpaper2_salt_pepper,[5 5]);

% 对均匀分布噪声图像依次用均值滤波，中值滤波、自适应中值滤波和二维自适应去噪滤波进行处理
wallpaper2_speckle_mean_filtering=filter2(y11,wallpaper2_salt_pepper)/255;
wallpaper2_speckle_median_filtering=medfilt2(wallpaper2_salt_pepper,[3,3]);
wallpaper2_speckle_adaptive_median_filtering=adpmedian(wallpaper2_salt_pepper,15);
wallpaper2_speckle_wiener2_filtering = wiener2(wallpaper2_salt_pepper,[5 5]);

subplot(5,3,1);imshow(wallpaper2_salt_pepper);title('添加椒盐噪音');
subplot(5,3,2);imshow(wallpaper2_gauwallpaperian);title('添加高斯噪声');
subplot(5,3,3);imshow(wallpaper2_speckle);title('添加均匀分布噪音');

subplot(5,3,4);imshow(wallpaper2_salt_pepper_mean_filtering);title('均值滤波');
subplot(5,3,5);imshow(wallpaper2_speckle_mean_filtering);title('均值滤波');
subplot(5,3,6);imshow(wallpaper2_salt_pepper_wiener2_filtering);title('均值滤波');

subplot(5,3,7);imshow(wallpaper2_salt_pepper_mean_filtering);title('中值滤波');
subplot(5,3,8);imshow(wallpaper2_speckle_mean_filtering);title('中值滤波');
subplot(5,3,9);imshow(wallpaper2_salt_pepper_wiener2_filtering);title('中值滤波');

subplot(5,3,10);imshow(wallpaper2_salt_pepper_mean_filtering);title('自适应中值滤波');
subplot(5,3,11);imshow(wallpaper2_speckle_mean_filtering);title('自适应中值滤波');
subplot(5,3,12);imshow(wallpaper2_salt_pepper_wiener2_filtering);title('自适应中值滤波');

subplot(5,3,13);imshow(wallpaper2_salt_pepper_mean_filtering);title('二维自适应去噪滤波');
subplot(5,3,14);imshow(wallpaper2_speckle_mean_filtering);title('二维自适应去噪滤波');
subplot(5,3,15);imshow(wallpaper2_salt_pepper_wiener2_filtering);title('二维自适应去噪滤波');

在这里插入图片描述

%读取原始图像
wallpaper3=imread('wallpaper3.jpg');

%将图像转换为灰度图像
wallpaper3=rgb2gray(wallpaper3);

% 分别向wallpaperr1添加椒盐噪音、高斯噪声、均匀分布噪声
wallpaper3_salt_pepper=imnoise(wallpaper3,'salt & pepper',0.05);
wallpaper3_gauwallpaperian=imnoise(wallpaper3,'gaussian',0.05);
wallpaper3_speckle=imnoise(wallpaper3,'speckle',0.05);

% 对椒盐噪声图像依次用均值滤波，中值滤波、自适应中值滤波和二维自适应去噪滤波进行处理
wallpaper3_salt_pepper_mean_filtering=filter2(y11,wallpaper3_salt_pepper)/255;
wallpaper3_salt_pepper_median_filtering=medfilt2(wallpaper3_salt_pepper,[3,3]);
wallpaper3_salt_pepper_adaptive_median_filtering=adpmedian(wallpaper3_salt_pepper,15);
wallpaper3_salt_pepper_wiener2_filtering = wiener2(wallpaper3_salt_pepper,[5 5]);

% 对高斯噪声图像依次用均值滤波，中值滤波、自适应中值滤波和二维自适应去噪滤波进行处理
wallpaper3_gauwallpaperian_mean_filtering=filter2(y11,wallpaper3_salt_pepper)/255;
wallpaper3_gauwallpaperian_median_filtering=medfilt2(wallpaper3_salt_pepper,[3,3]);
wallpaper3_gauwallpaperian_adaptive_median_filtering=adpmedian(wallpaper3_salt_pepper,15);
wallpaper3_gauwallpaperian_wiener2_filtering = wiener2(wallpaper3_salt_pepper,[5 5]);

% 对均匀分布噪声图像依次用均值滤波，中值滤波、自适应中值滤波和二维自适应去噪滤波进行处理
wallpaper3_speckle_mean_filtering=filter2(y11,wallpaper3_salt_pepper)/255;
wallpaper3_speckle_median_filtering=medfilt2(wallpaper3_salt_pepper,[3,3]);
wallpaper3_speckle_adaptive_median_filtering=adpmedian(wallpaper3_salt_pepper,15);
wallpaper3_speckle_wiener2_filtering = wiener2(wallpaper3_salt_pepper,[5 5]);

subplot(5,3,1);imshow(wallpaper3_salt_pepper);title('添加椒盐噪音');
subplot(5,3,2);imshow(wallpaper3_gauwallpaperian);title('添加高斯噪声');
subplot(5,3,3);imshow(wallpaper3_speckle);title('添加均匀分布噪音');

subplot(5,3,4);imshow(wallpaper3_salt_pepper_mean_filtering);title('均值滤波');
subplot(5,3,5);imshow(wallpaper3_speckle_mean_filtering);title('均值滤波');
subplot(5,3,6);imshow(wallpaper3_salt_pepper_wiener2_filtering);title('均值滤波');

subplot(5,3,7);imshow(wallpaper3_salt_pepper_mean_filtering);title('中值滤波');
subplot(5,3,8);imshow(wallpaper3_speckle_mean_filtering);title('中值滤波');
subplot(5,3,9);imshow(wallpaper3_salt_pepper_wiener2_filtering);title('中值滤波');

subplot(5,3,10);imshow(wallpaper3_salt_pepper_mean_filtering);title('自适应中值滤波');
subplot(5,3,11);imshow(wallpaper3_speckle_mean_filtering);title('自适应中值滤波');
subplot(5,3,12);imshow(wallpaper3_salt_pepper_wiener2_filtering);title('自适应中值滤波');

subplot(5,3,13);imshow(wallpaper3_salt_pepper_mean_filtering);title('二维自适应去噪滤波');
subplot(5,3,14);imshow(wallpaper3_speckle_mean_filtering);title('二维自适应去噪滤波');
subplot(5,3,15);imshow(wallpaper3_salt_pepper_wiener2_filtering);title('二维自适应去噪滤波');

在这里插入图片描述

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