最有效的图像高斯噪声去噪方法是什么？

　　Today some new advancements from medical image processing. Our task was to implement bilateral filtering in matlab. First of all let me briefly explain our motivation: Image filtering is a very common task in gneral image processing. Often you want to smoothen your image, i.e. remove high image frequences, with e.g. a gaussian filter. Of course the smoothing works quite well, but as a side-effect your edges get blurred. To overcome this issue, we just do edge preserving filtering (what a brilliant idea ;-) ).

　　C. Tomasi and R. Manduchi introduced a first approach called Bilateral filtering in their paper: Bilateral filtering for gray and color images. In Proc. of the Sixth International Conference on Computer Vision, Bombay, India, January 1998. Let me cite the first lines of their abstract:

　　Bilateral filtering smooths images while preserving edges, by means of a nonlinear combination of nearby image values. The method is noniterative, local, and simple. It combines gray levels or colors based on both their geometric closeness and their photometric similarity, and prefers near values to distant values in both domain and range.

　　Matlab Code

　　So, this is exactly what we are going to do, and here goes the matlab code (you may also download it here):

　　function FA = bilateralfilter(A, size, std_c, std_s)
　　%BILATERALFILTER Filters a gray level image with a bilateral filter.
　　% FA = BILATERALFILTER(A, size, std_c, std_s) filters the
　　% gray level image A using a window of [size(1) size(2)] with a
　　% standard bilateral filter.
　　% Bilateral filtering smooths images while preserving edges in contrast.
　　% Therefor an adaptive filtering kernel for each image element in
　　% the convolution is created. The kernel is the product of a gaussian
　　% kernel (closeness function) and a gaussian weighted similarity function
　　% for pixel intensities. std_c and std_s are the standard derivations
　　% for closeness and similarity function.
　　%
　　% Reference
　　% ---------
　　% This implemtation is based on the original paper "Bilateral Filtering
　　% for Gray and Color Images" published by C. Tomasi and R. Manduchi
　　% (Proceedings of the 1998 IEEE International Conference on Computer Vision).
　　%
　　% (c) Christopher Rohkohl
　　% christopher@oneder.de
　　% http://www.oneder.de

　　% create gaussian closeness function
　　hs = (size-1)/2;
　　[x y] = meshgrid(-hs(2):hs(2),-hs(1):hs(1));
　　H_c = exp(-(x.*x + y.*y)/(2*std_c*std_c));

　　% perform filtering
　　FA = nlfilter(A, size, @simfunc, std_s, H_c);
　　end

　　% adaptive similarity function
　　function V = simfunc(B, std, H_c);
　　center = floor((size(B)+1)/2);
　　sim = reshape(exp(-(B(:) - repmat(B(center(1), center(2)), numel(B), 1)).^2
　　/ (2*std*std)), size(B));
　　ssum = sum(sim(:));
　　if (ssum ~= 0)
　　sim = sim ./ sum(sim(:));
　　end
　　V = sum(sum(sim.*B));
　　end
　　Example Results

　　Below is a fairly simple example, but the results look great :-)

　　filtered noise image comparison

　　The following code was used to create this example:

　　% create random noise image
　　im = rand(128);
　　im([40:80],[40:80]) = im([40:80],[40:80]) + 2.0;
　　im = ( im - min(min(im)) ) ./ ( max(max(im)) - min(min(im)) );
　　im(im(:) < 0) = 0;

　　% create bilateral filtered image
　　imbi = bilateralfilter(im, [7 7], 6, 0.2);

　　% create gaussian filtered image
　　imgauss = imfilter(im, fspecial("gaussian",[7 7], 6),"conv");

　　% display the results
　　figure();
　　subplot(1,3,1); imshow(im,[]); title("Original Image");
　　subplot(1,3,2); imshow(imbi,[]); title("Bilateral Filted Image");
　　subplot(1,3,3); imshow(imgauss,[]); title("Gaussian Filted Image");