【图像重建】基于matlab迭代步长自适应图像超分辨重建【含Matlab源码 048期】

一、获取代码方式

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二、迭代步长自适应简介

传统的超分辨重建算法往往采用梯度下降法进行求解，迭代时步长往往通过经验确定。而且不同的图像的最优步长往往不相同。步长过大会导致发散，步长过小会导致收敛缓慢。本算法基于对正则化超分辨重建算法实现的基础上，对步长的选取进行了优化，推导出了每次迭代时的最优步长大小，并将其自适应化，改进了超分辨算法的收敛性，从而能够在更短的时间内取得更加精确的重建结果。相关具体内容请参考对应的论文：Yingqian Wang, Jungang Yang, Chao Xiao, and Wei An, “Fast convergence strategy for multi-image superresolution via adaptive line search,” IEEE Access, vol. 6, no. 1, pp. 9129-9139.

三、部分源代码


clear all
clcfilename = 'Set';
files = dir(fullfile( filename,'*.bmp'));
file_num = 2;       % different number corresponds to defferent test images in 'Set'
reg_term = 1;       %regularization term: 1-BTV, 2-TikhonovImage =imread([filename,'\',files(file_num).name]);
SZ = size(size(Image));if (SZ(2)==2)       % turn grayscale image to RGB imagefor qw = 1:3IMAGE (:,:,qw) = Image;end
elseIMAGE = Image;
end%% Image Degradation
D = [1,1;-2,1;-1,-3;3,-2];                    % Shearing shift
Gau = fspecial( 'gaussian', [3 3], 1);   % Gaussian bluring kernel
spf = 2;                                              % sampling factor
sigma2 = 1;                                       % variation of noise
LR = ImDegrate(IMAGE,D,Gau,spf,sigma2); % image degradation function%% Turn RGB to YCbCr, and only SR the Y component
[~, ~, ~, M] = size(LR);
for w = 1:MLR(:,:,:,w) = rgb2ycbcr(uint8( squeeze(LR(:,:,:,w))));
endmaxiter = 10;  % maximum number of iterationy1(:,:,:) =  LR(:,:,1,:);
y2(:,:,:) =  LR(:,:,2,:);
y3(:,:,:) =  LR(:,:,3,:);HRitp1 =  imresize(y1(:,:,1), spf, 'bicubic');  % bicubic interpolation
HRitp1 = ImWarp(HRitp1, -D(1,1), -D(1,2));  % shift recoveringI1 = Wang_SR(HRitp1, y1, D, Gau, spf, maxiter, reg_term);   %Our proposed SR methodHRitp2 =  imresize(y2(:,:,1), spf, 'bicubic');
HRitp2 = ImWarp(HRitp2, -D(1,1), -D(1,2));
I2 = HRitp2;HRitp3 =  imresize(y3(:,:,1), spf, 'bicubic');
HRitp3 = ImWarp(HRitp3, -D(1,1), -D(1,2));
I3 = HRitp3;ImZ(:, :, 1) =  I1;
ImZ(:, :, 2) =  I2;
ImZ(:, :, 3) =  I3;ImZ = ycbcr2rgb(uint8( ImZ)); % Turn YCbCr to RGBfigure; imshow( uint8( ImZ ) ); title('Wang et al.');
figure; imshow( uint8( IMAGE ) ); title('groundtruth');%%  EvaluationIf = double(ImZ);   %output image
Is = double(IMAGE); %reference image
[row,col,~]=size(If); %RMSE
rmse=0;
for color = 1:3Ifc = If(:,:,color);  Isc = Is(:,:,color);SSE=sum(sum((Ifc-Isc).^2));rmsec=sqrt(SSE/(row*col));rmse = rmse+rmsec/3;
end
rmse%PSNR
psnr=0;
for color = 1:3Ifc = If(:,:,color);  Isc = Is(:,:,color);maxIs = max(max(Isc));minIs = min(min(Isc));PSNRc = 10*log10((row*col*(maxIs-minIs)^2)/sum(sum((Ifc-Isc).^2)));psnr = psnr+PSNRc/3;
end
psnr%SSIM
ssim=0;
for color = 1:3Ifc = uint8(If(:,:,color));  Isc = uint8(Is(:,:,color));ssimc = cal_ssim(Ifc, Isc, 0, 0);ssim = ssim + ssimc/3;
end
ssim
function ssim = cal_ssim( im1, im2, b_row, b_col)[h, w, ch] = size( im1 );
ssim = 0;
if (ch == 1)ssim = ssim_index ( im1(b_row+1:h-b_row, b_col+1:w-b_col), im2(b_row+1:h-b_row,b_col+1:w-b_col));
elsefor i = 1:chssim = ssim + ssim_index ( im1(b_row+1:h-b_row, b_col+1:w-b_col, i), im2(b_row+1:h-b_row,b_col+1:w-b_col, i));endssim = ssim/3;
end
returnfunction [mssim, ssim_map] = ssim_index(img1, img2, K, window, L)if (nargin < 2 || nargin > 5)mssim = -Inf;ssim_map = -Inf;return;
endif (size(img1) ~= size(img2))mssim = -Inf;ssim_map = -Inf;return;
end[M N] = size(img1);if (nargin == 2)if ((M < 11) || (N < 11))mssim = -Inf;ssim_map = -Inf;returnendwindow = fspecial('gaussian', 11, 1.5);  %K(1) = 0.01;                  % default settingsK(2) = 0.03;                 %L = 255;                                     %
endif (nargin == 3)if ((M < 11) || (N < 11))mssim = -Inf;ssim_map = -Inf;returnendwindow = fspecial('gaussian', 11, 1.5);L = 255;if (length(K) == 2)if (K(1) < 0 || K(2) < 0)mssim = -Inf;ssim_map = -Inf;return;endelsemssim = -Inf;ssim_map = -Inf;return;end
endif (nargin == 4)[H W] = size(window);if ((H*W) < 4 || (H > M) || (W > N))mssim = -Inf;ssim_map = -Inf;returnendL = 255;if (length(K) == 2)if (K(1) < 0 || K(2) < 0)mssim = -Inf;ssim_map = -Inf;return;endelsemssim = -Inf;ssim_map = -Inf;return;end
endif (nargin == 5)[H W] = size(window);if ((H*W) < 4 || (H > M) || (W > N))mssim = -Inf;ssim_map = -Inf;returnendif (length(K) == 2)if (K(1) < 0 || K(2) < 0)mssim = -Inf;ssim_map = -Inf;return;endelsemssim = -Inf;ssim_map = -Inf;return;end
endimg1 = double(img1);
img2 = double(img2);% automatic downsampling
f = max(1,round(min(M,N)/256));
%downsampling by f
%use a simple low-pass filter
if(f>1)lpf = ones(f,f);lpf = lpf/sum(lpf(:));img1 = imfilter(img1,lpf,'symmetric','same');img2 = imfilter(img2,lpf,'symmetric','same');img1 = img1(1:f:end,1:f:end);img2 = img2(1:f:end,1:f:end);
endC1 = (K(1)*L)^2;
C2 = (K(2)*L)^2;
window = window/sum(sum(window));mu1   = filter2(window, img1, 'valid');
mu2   = filter2(window, img2, 'valid');
mu1_sq = mu1.*mu1;
mu2_sq = mu2.*mu2;
mu1_mu2 = mu1.*mu2;
sigma1_sq = filter2(window, img1.*img1, 'valid') - mu1_sq;
sigma2_sq = filter2(window, img2.*img2, 'valid') - mu2_sq;
sigma12 = filter2(window, img1.*img2, 'valid') - mu1_mu2;if (C1 > 0 && C2 > 0)ssim_map = ((2*mu1_mu2 + C1).*(2*sigma12 + C2))./((mu1_sq + mu2_sq + C1).*(sigma1_sq + sigma2_sq + C2));
elsenumerator1 = 2*mu1_mu2 + C1;numerator2 = 2*sigma12 + C2;denominator1 = mu1_sq + mu2_sq + C1;denominator2 = sigma1_sq + sigma2_sq + C2;ssim_map = ones(size(mu1));index = (denominator1.*denominator2 > 0);ssim_map(index) = (numerator1(index).*numerator2(index))./(denominator1(index).*denominator2(index));index = (denominator1 ~= 0) & (denominator2 == 0);ssim_map(index) = numerator1(index)./denominator1(index);
endmssim = mean2(ssim_map);return

四、运行结果

五、matlab版本及参考文献

1 matlab版本
2014a

2 参考文献
[1] 蔡利梅.MATLAB图像处理——理论、算法与实例分析[M].清华大学出版社，2020.
[2]杨丹,赵海滨,龙哲.MATLAB图像处理实例详解[M].清华大学出版社，2013.
[3]周品.MATLAB图像处理与图形用户界面设计[M].清华大学出版社，2013.
[4]刘成龙.精通MATLAB图像处理[M].清华大学出版社，2015.