维纳滤波器是一种自适应的滤波器，在数字信号处理中有着广泛的应用。ispforfun会在从今天开始定期给大家带来维纳滤波器在图像处理中应用。本节讲诉维纳滤波器在图像去噪中的简单应用。
让我们从Matlab中的函数wiener2开始。Matlab的help中对wiener2的说明如下：
wiener2估计图像中每个像素的局部均值和局部方差，
其中，是图像A中每个像素的NXM邻域。维纳滤波器的去噪原理如下：
其中是噪声的方差，如果没有给出来，那么会根据图像的局部方差进行估计。
ispforfun根据这段原理，编写了如下的matlab代码，共享给大家。
function J = wiener_image_denoising_filter(I, Win, noise_var)% J = wiener_image_denoising_filter(I, w)% -----------------------------------------% by: ispforfun% I is the input image. Single channel image.% Win is the window size for filtering.[img_height, img_width] = size(I);half_win_size = floor(Win/2.0);[X, Y] = meshgrid(1:img_width, 1:img_height);[dX, dY] = meshgrid(-half_win_size(2):half_win_size(2), -half_win_size(1):half_win_size(1));dX = reshape(dX, [1 1 Win(1) Win(2)]);dY = reshape(dY, [1 1 Win(1) Win(2)]);X = repmat(X, [1 1 Win(1) Win(2)]) + repmat(dX, [img_height img_width 1 1]);Y = repmat(Y, [1 1 Win(1) Win(2)]) + repmat(dY, [img_height img_width 1 1]);X(X<1) = 2 - X(X<1);X(X>img_width) = 2*img_width - X(X>img_width);Y(Y<1) = 2 - Y(Y<1);Y(Y>img_height) = 2*img_height - Y(Y>img_height);patch = @(f)f(Y + (X-1)*img_height);P = patch(I);img_mean = local_image_mean(P);img_var = local_image_var(P, img_mean, Win);if nargin < 3estimated_noise_var = sum(sum(img_var))/(img_height * img_width);elseestimated_noise_var = noise_var;endgain = (estimated_noise_var == 0.0).*zeros(img_height, img_width) + ...(estimated_noise_var ~= 0.0).*((img_var - estimated_noise_var)./img_var);J = img_mean + gain.*(double(I) - img_mean);J = min(max(J, 0), 255);J = uint8(J);%gain = (img_var - estimated_noise_var)./img_var;function img_mean = local_image_mean(P)% img_mean = local_image_mean(P)local_img_sum = sum(sum(double(P), 4), 3);sum_size = size(P,3)*size(P,4);img_mean = local_img_sum/sum_size;function img_var = local_image_var(P, img_mean, Win)% img_var = local_img_var(P, img_mean)diff_img_patch = double(P) - repmat(img_mean, [1 1 Win(1) Win(2)]);diff_img_patch_pow2 = diff_img_patch.^2;local_diff_img_sum = sum(sum(double(diff_img_patch_pow2), 4), 3);img_var = local_diff_img_sum/(Win(1)*Win(2) - 1);
实验如下，富含噪声的图像如下：
去噪后的图像如下：
