【图像重构】基于OMP算法实现图像重构附matlab代码

为了提高可见光图像的识别和检测能力,提出基于OMP算法的可见光图像超分辨率重构方法.建立可见光图像的视觉信息采集模型,采用空间锚点邻域特征匹配方法进行的可见光图像超分辨特征分解,提取可见光图像边缘轮廓特征量,结合残差特征估计高分辨率图像特征融合和优化分割,建立可见光图像的超分辨率重建特征分布集,采用边缘信息空间区域融合方法进行可见光图像的像素信息融合和优化特征重组,提取可见光图像的模糊度特征分布集,结合OMP算法实现可见光图像超分辨率重构。

function Demo_CS_CoSaMP()

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% the DCT basis is selected as the sparse representation dictionary

% instead of seting the whole image as a vector, I process the image in the

% fashion of column-by-column, so as to reduce the complexity.

% Author: Chengfu Huo, roy@mail.ustc.edu.cn, http://home.ustc.edu.cn/~roy

% Reference: D. Deedell andJ. Tropp, “COSAMP: Iterative Signal Recovery from

% Incomplete and Inaccurate Samples,” 2008.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%------------ read in the image --------------

img=imread('lena.bmp'); % testing image

img=double(img);

[height,width]=size(img);

%------------ form the measurement matrix and base matrix ---------------

Phi=randn(floor(height/3),width); % only keep one third of the original data

Phi = Phi./repmat(sqrt(sum(Phi.^2,1)),[floor(height/3),1]); % normalize each column

mat_dct_1d=zeros(256,256); % building the DCT basis (corresponding to each column)

for k=0:1:255

dct_1d=cos([0:1:255]'*k*pi/256);

if k>0

dct_1d=dct_1d-mean(dct_1d);

end

mat_dct_1d(:,k+1)=dct_1d/norm(dct_1d);

end

%--------- projection ---------

img_cs_1d=Phi*img; % treat each column as a independent signal

%-------- recover using omp ------------

sparse_rec_1d=zeros(height,width);

Theta_1d=Phi*mat_dct_1d;

for i=1:width

column_rec=cs_cosamp(img_cs_1d(:,i),Theta_1d,height);

sparse_rec_1d(:,i)=column_rec'; % sparse representation

end

img_rec_1d=mat_dct_1d*sparse_rec_1d; % inverse transform

%------------ show the results --------------------

figure(1)

subplot(2,2,1),imagesc(img),title('original image')

subplot(2,2,2),imagesc(Phi),title('measurement mat')

subplot(2,2,3),imagesc(mat_dct_1d),title('1d dct mat')

psnr = 20*log10(255/sqrt(mean((img(:)-img_rec_1d(:)).^2)))

subplot(2,2,4),imagesc(img_rec_1d),title(strcat('1d rec img ',num2str(psnr),'dB'))

disp('over')

%************************************************************************%

function hat_x=cs_cosamp(y,T_Mat,m)

% y=T_Mat*x, T_Mat is n-by-m

% y - measurements

% T_Mat - combination of random matrix and sparse representation basis

% m - size of the original signal

% the sparsity is length(y)/4

n=length(y); % length of measurements

s=floor(n/4); % sparsity

r_n=y;

sig_pos_lt=[]; % significant pos for last time iteration

for times=1:s % number of iterations

product=abs(T_Mat'*r_n);

[val,pos]=sort(product,'descend');

sig_pos_cr=pos(1:2*s); % significant pos for curretn iteration

sig_pos=union(sig_pos_cr,sig_pos_lt);

Aug_t=T_Mat(:,sig_pos); % current selected entries of T_Mat

aug_x_cr=zeros(m,1);

aug_x_cr(sig_pos)=(Aug_t'*Aug_t)^(-1)*Aug_t'*y; % temp recovered x (sparse)

[val,pos]=sort(abs(aug_x_cr),'descend');

hat_x=zeros(1,m);

hat_x(pos(1:s))=aug_x_cr(pos(1:s));% recovered x with s sparsity

sig_pos_lt=pos(1:s); % refresh the significant positions

r_n=y-T_Mat*hat_x';

end

[1]陈宁, 阎琳, 邱岳恒. 基于OMP算法的图像重构研究与FPGA实现[J]. 计算机测量与控制, 2014, 22(9):3.