在matlab中使用高斯滤波器进行图像去模糊，没有加性噪声 [英] Image deblurring using gaussian filter in matlab without additive noise

问题描述

我必须使用逆滤镜来消除此图像中的模糊

I have to use an inverse filter to remove the blurring from this image

。

不幸的是，我必须弄清楚用于获取的成像
系统的传递函数 H 这些更清晰的图像，应该是高斯图像。因此，我应该通过在逆滤波器中尝试不同的高斯宽度并判断哪些结果图像看起来最佳来确定高斯的近似宽度。

Unfortunately, I have to figure out the transfer function H of the imaging system used to get these sharper images, It should be Gaussian. So, I should determine the approximate width of the Gaussian by trying different Gaussian widths in an inverse filter and judging which resulting images look the "best".

最佳结果将是最佳的 - 即边缘看起来很清晰但不会有明显的响铃。

The best result will be optimally sharp – i.e., edges will look sharp but will not have visible ringing.

我试过使用3种方法：

1. 我用 N 创建了一个传递函数维度（奇数，为简单起见），通过创建 N 维度的网格，然后将高斯函数应用于此网格。之后，我们为此传递函数添加零，以便获得与原始图像相同的大小。但是，在将滤镜应用于原始图像后，我只看到了噪声（太多的伪像）。


2. 通过创建与原始图像大小相同的网格，我创建了尺寸与原始图像一样高的传递函数。如果 sigma 太小，则 PSF FFT 幅度很大。否则会变瘦。如果 sigma 很小，那么图像会更加模糊，但如果我们设置一个非常高的 sigma 值，那么我们得到相同的图像（根本不是更好）。


3. 我使用了 fspecial 函数，玩的尺寸为 sigma 和 h 。但是我仍然没有比原始模糊图像更清晰。

1. I created a transfer function with N dimensions (odd number, for simplicity), by creating a grid of N dimensions, and then applying the Gaussian function to this grid. After that, we add zeroes to this transfer function in order to get the same size as the original image. However, after applying the filter to the original image, I just see noise (too many artifacts).
2. I created the transfer function with size as high as the original image, by creating a grid of the same size as the original image. If sigma is too small, then the PSF FFT magnitude is wide. Otherwise it gets thinner. If sigma is small, then the image is even more blurred, but if we set a very high sigma value then we get the same image (not better at all).
3. I used the fspecial function, playing with sizes of sigma and h. But still I do not get anything sharper than the original blurred image.

有任何想法吗？

以下是用于创建转移的代码方法1中的函数：

Here is the code used for creating the transfer function in Approach 1:

%Create Gaussian Filter
function h = transfer_function(N, sigma, I) %N is the dimension of the kernel
%create a 2D-grid that is the same size as the Gaussian filter matrix
grid = -floor(N/2) : floor(N/2);
[x, y] = meshgrid(grid, grid);
arg = -(x.*x + y.*y)/(2*sigma*sigma);
h = exp(arg); %gaussian 2D-function
kernel = h/sum(h(:)); %Normalize so that total weight equals 1

[rows,cols] = size(I);
add_zeros_w = (rows - N)/2;
add_zeros_h = (cols - N)/2;

h = padarray(kernel,[add_zeros_w  add_zeros_h],0,'both'); % h = kernel_final_matrix

end 

这是每种方法的代码：

I = imread('lena_blur.jpg');
I1 = rgb2gray(I);
figure(1),
I1 = double(I1);
%---------------Approach 1
% N = 5; %Dimension Assume is an odd number
% sigma = 20; %The bigger number, the thinner the PSF in FREQ
% H = transfer_function(N, sigma, I1);
%I1=I1(2:end,2:end); %To simplify operations
imagesc(I1); colormap('gray'); title('Original Blurred Image')

I_fft = fftshift(fft2(I1)); %Shift the image in Fourier domain to let its DC part in the center of the image



% %FILTER-----------Approach 2---------------
% N = 5; %Dimension Assume is an odd number
% sigma = 20; %The bigger number, the thinner the PSF in FREQ
% 
% 
% [x,y] = meshgrid(-size(I,2)/2:size(I,2)/2-1, -size(I,1)/2:size(I,1)/2-1);
% H = exp(-(x.^2+y.^2)*sigma/2);
% %// Normalize so that total area (sum of all weights) is 1
% H = H /sum(H(:));
% 
% %Avoid zero freqs
% for i = 1:size(I,2) %Cols
%     for j = 1:size(I,1) %Rows
%         if (H(i,j) == 0)
%             H(i,j) = 1e-8;
%         end
%     end
% end
% 
% [rows columns z] = size(I);
% G_filter_fft = fft2(H,rows,columns);
%FILTER---------------------------------


%Filter--------- Aproach 3------------
N = 21; %Dimension Assume is an odd number
sigma = 1.25; %The bigger number, the thinner the PSF in FREQ

H = fspecial('gaussian',N,sigma)
[rows columns z] = size(I);
G_filter_fft = fft2(H,rows,columns);

%Filter--------- Aproach 3------------



%DISPLAY FFT PSF MAGNITUDE
figure(2),
imshow(fftshift(abs(G_filter_fft)),[]); title('FFT PSF magnitude 2D');


% Yest = Y_blurred/Gaussian_Filter
I_restoration_fft = I_fft./G_filter_fft;
I_restoration = (ifft2(I_restoration_fft));
I_restoration = abs(I_restoration);




I_fft = abs(I_fft);

% Display of Frequency domain (To compare with the slides) 
figure(3),
subplot(1,3,1); 
imagesc(I_fft);colormap('gray');title('|DFT Blurred Image|')
subplot(1,3,2)
imshow(log(fftshift(abs(G_filter_fft))+1),[]) ;title('| Log DFT Point Spread Function + 1|');
subplot(1,3,3)
imagesc(abs(I_restoration_fft));colormap('gray'); title('|DFT Deblurred|')
% imshow(log(I_restoration+1),[])

%Display PSF FFT in 3D
figure(4)
hf_abs = abs(G_filter_fft);
%270x270
surf([-134:135]/135,[-134:135]/135,fftshift(hf_abs));
% surf([-134:134]/134,[-134:134]/134,fftshift(hf_abs));
shading interp, camlight, colormap jet
xlabel('PSF FFT magnitude')

%Display Result (it should be the de-blurred image)
figure(5),
%imshow(fftshift(I_restoration));
imagesc(I_restoration);colormap('gray'); title('Deblurred Image')

%Pseudo Inverse restoration
% cam_pinv = real(ifft2((abs(G_filter_fft) > 0.1).*I_fft./G_filter_fft));
% imshow(fftshift(cam_pinv));
% xlabel('pseudo-inverse restoration')

推荐答案

可能的解决方案是 deconvwr 。我将首先从未失真的lena图像开始显示其性能。所以，我确切地知道高斯模糊功能。请注意，将 estimated_nsr 设置为零会因量化噪声而完全破坏性能。

A possible solution is deconvwr. I will first show its performance starting from an undistorted lena image. So, I know exactly the gaussian blurring function. Note that setting estimated_nsr to zero will destroy the performance completely due to quantisation noise.

 I_ori = imread('lenaTest3.jpg'); % Download an original undistorted lena file
 N = 19;
 sigma = 5;
 H = fspecial('gaussian',N,sigma) 
 estimated_nsr = 0.05;

 I = imfilter(I_ori, H)

 wnr3 = deconvwnr(I, H, estimated_nsr); 
 figure
 subplot(1, 4, 1);
 imshow(I_ori) 
 subplot(1, 4, 2);
 imshow(I) 
 subplot(1, 4, 3);
 imshow(wnr3) 
 title('Restoration of Blurred, Noisy Image Using Estimated NSR'); 
 subplot(1, 4, 4);
 imshow(H, []);

我通过反复试验找到的最佳参数。

The best parameters I found for your problem by trial and error.

 N = 19; 
 sigma = 2; 
 H = fspecial('gaussian',N,sigma) 
 estimated_nsr = 0.05;

编辑：准确计算使用的模糊滤镜

EDIT: calculating exactly the used blurring filter

如果您下载未失真的lena（ I_original_fft ），您可以按如下方式计算使用的模糊过滤器：

If you download an undistorted lena (I_original_fft), you can calculate the used blurring filter as follows:

G_filter_fft = I_fft./I_original_fft

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