CS的一些重构算法.zip_CS_ROMP_omp samp_samp_压缩感知

clear all;close all;clc; %% 参数配置初始化 CNT = 1000;%对于每组(K,M,N)，重复迭代次数 N = 256;%信号x的长度 Psi = eye(N);%x本身是稀疏的，定义稀疏矩阵为单位阵x=Psi*theta M_set = [128];%测量值集合 KIND = ['OMP ';'ROMP ';'StOMP ';'SP ';'CoSaMP ';... 'SAMP,s=1 ';'SAMP,s=5 ';'SAMP,s=10']; Percentage = zeros(N,length(M_set),size(KIND,1));%存储恢复成功概率 %% 主循环，遍历每组(K,M,N) tic for mm = 1:length(M_set) M = M_set(mm);%本次测量值个数 K_set = 10:5:70;%信号x的稀疏度K没必要全部遍历，每隔5测试一个就可以了 %存储此测量值M下不同K的恢复成功概率 PercentageM = zeros(size(KIND,1),length(K_set)); for kk = 1:length(K_set) K = K_set(kk);%本次信号x的稀疏度K P = zeros(1,size(KIND,1)); fprintf('M=%d,K=%d\n',M,K); for cnt = 1:CNT %每个观测值个数均运行CNT次 Index_K = randperm(N); x = zeros(N,1); x(Index_K(1:K)) = 5*randn(K,1);%x为K稀疏的，且位置是随机的 Phi = randn(M,N)/sqrt(M);%测量矩阵为高斯矩阵 A = Phi * Psi;%传感矩阵 y = Phi * x;%得到观测向量y %(1)OMP theta = CS_OMP(y,A,K);%恢复重构信号theta x_r = Psi * theta;% x=Psi * theta if norm(x_r-x)<1e-6%如果残差小于1e-6则认为恢复成功 P(1) = P(1) + 1; end %(2)ROMP theta = CS_ROMP(y,A,K);%恢复重构信号theta x_r = Psi * theta;% x=Psi * theta if norm(x_r-x)<1e-6%如果残差小于1e-6则认为恢复成功 P(2) = P(2) + 1; end %(3)StOMP theta = CS_StOMP(y,A);%恢复重构信号theta x_r = Psi * theta;% x=Psi * theta if norm(x_r-x)<1e-6%如果残差小于1e-6则认为恢复成功 P(3) = P(3) + 1; end %(4)SP theta = CS_SP(y,A,K);%恢复重构信号theta x_r = Psi * theta;% x=Psi * theta if norm(x_r-x)<1e-6%如果残差小于1e-6则认为恢复成功 P(4) = P(4) + 1; end %(5)CoSaMP theta = CS_CoSaMP(y,A,K);%恢复重构信号theta x_r = Psi * theta;% x=Psi * theta if norm(x_r-x)<1e-6%如果残差小于1e-6则认为恢复成功 P(5) = P(5) + 1; end %(6)SAMP,s=1 theta = CS_SAMP(y,A,1);%恢复重构信号theta x_r = Psi * theta;% x=Psi * theta if norm(x_r-x)<1e-6%如果残差小于1e-6则认为恢复成功 P(6) = P(6) + 1; end %(7)SAMP,s=5 theta = CS_SAMP(y,A,5);%恢复重构信号theta x_r = Psi * theta;% x=Psi * theta if norm(x_r-x)<1e-6%如果残差小于1e-6则认为恢复成功 P(7) = P(7) + 1; end %(8)SAMP,s=10 theta = CS_SAMP(y,A,10);%恢复重构信号theta x_r = Psi * theta;% x=Psi * theta if norm(x_r-x)<1e-6%如果残差小于1e-6则认为恢复成功 P(8) = P(8) + 1; end end for iii = 1:size(KIND,1) PercentageM(iii,kk) = P(iii)/CNT*100;%计算恢复概率 end end for jjj = 1:size(KIND,1) Percentage(1:length(K_set),mm,jjj) = PercentageM(jjj,:); end end toc save Sparsity_comparing_all %运行一次不容易，把变量全部存储下来 %% 绘图 S = ['-ks';'-ko';'-yd';'-gv';'-b*';'-r.';'-rx';'-r+']; figure; for mm = 1:length(M_set) M = M_set(mm); K_set = 10:5:70; L_Kset = length(K_set); for ii = 1:size(KIND,1) plot(K_set,Percentage(1:L_Kset,mm,ii),S(ii,:));%绘出x的恢复信号 hold on; end end hold off; xlim([10 70]); legend('OMP','ROMP','StOMP','SP','CoSaMP',... 'SAMP,s=1','SAMP,s=5','SAMP,s=10'); xlabel('Sparsity level K'); ylabel('The Probability of Exact Reconstruction'); title('Prob. of exact recovery vs. the signal sparsity K(M=128,N=256)(Gaussian)');