图像恢复

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维纳滤波—deconvwnr函数利用维纳滤波器来对图像模糊修复

function image_restoration_deconvwnr()    %Read image    I = im2double(imread('lena.tif'));    I=rgb2gray(I);    figure,subplot(2,3,1),imshow(I);    title('Original Image');    %Simulate a motion blur    LEN = 21;    THETA = 11;    PSF = fspecial('motion', LEN, THETA);    blurred = imfilter(I, PSF, 'conv', 'circular');    subplot(2,3,2),imshow(blurred);    title('Blurred Image');    %Restore the blurred image    wnr1 = deconvwnr(blurred, PSF, 0);    subplot(2,3,3),imshow(wnr1);    title('Restored Image');    %Simulate blur and noise    noise_mean = 0;    noise_var = 0.0001;    blurred_noisy = imnoise(blurred, 'gaussian', ...                            noise_mean, noise_var);    subplot(2,3,4),imshow(blurred_noisy)    title('Simulate Blur and Noise')    %Restore the blurred and noisy image:First attempt    wnr2 = deconvwnr(blurred_noisy, PSF, 0);    subplot(2,3,5);imshow(wnr2);title('Restoration of Blurred, Noisy Image Using NSR = 0')    %Restore the Blurred and Noisy Image: Second Attempt    signal_var = var(I(:));    wnr3 = deconvwnr(blurred_noisy, PSF, noise_var / signal_var);    subplot(2,3,6),imshow(wnr3)    title('Restoration of Blurred, Noisy Image Using Estimated NSR');end

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维纳滤波需要估计图像的信噪比(SNR)或者噪信比(NSR)，信号的功率谱使用图像的方差近似估计，噪声分布是已知的。从第一排中可以看出，若无噪声，此时维纳滤波相当于逆滤波，恢复运动模糊效果是极好的。从第二排可以看出噪信比估计的准确性对图像影响比较大的，二排中间效果几乎不可用。

逆滤波

function image_restoration_matlab()    % Display the original image.    I = im2double(imread('lena.tif'));    I=rgb2gray(I);    [hei,wid,~] = size(I);    subplot(2,3,1),imshow(I);    title('Original Image (courtesy of MIT)');    % Simulate a motion blur.    LEN = 21;    THETA = 11;    PSF = fspecial('motion', LEN, THETA);    blurred = imfilter(I, PSF, 'conv', 'circular');    subplot(2,3,2), imshow(blurred); title('Blurred Image');    % Inverse filter    If = fft2(blurred);    Pf = fft2(PSF,hei,wid);    deblurred = ifft2(If./Pf);    subplot(2,3,3), imshow(deblurred); title('Restore Image')    % Simulate additive noise.    noise_mean = 0;    noise_var = 0.0001;    blurred_noisy = imnoise(blurred, 'gaussian', ...                            noise_mean, noise_var);    subplot(2,3,4), imshow(blurred_noisy)    title('Simulate Blur and Noise')    % Try restoration assuming no noise.    If = fft2(blurred_noisy);    deblurred2 = ifft2(If./Pf);    subplot(2,3,5), imshow(deblurred2)    title('Restoration of Blurred Assuming No Noise');    % Try restoration with noise is known.    noisy = blurred_noisy - blurred;    Nf = fft2(noisy);    deblurred2 = ifft2(If./Pf - Nf./Pf);    subplot(2,3,6), imshow(deblurred2)    title('Restoration of Blurred with Noise Is Known')end

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逆滤波对噪声非常敏感，除非我们知道噪声的分布情况（事实上，这也很难知道），逆滤波几乎不可用，可以从二排中间看出，恢复图像效果极差。但若知道噪声分布，也是可以完全复原信息的。可以从二排最后一张图可以看出。

参考文献：
数字图像处理matlab版（左飞）
数字图像处理第三版（Gonzalez）
http://blog.csdn.net/zhoufan900428/article/details/38064125
http://blog.csdn.net/bluecol/article/details/47357717
http://blog.csdn.net/bluecol/article/details/46242355

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