前向预测与回溯策略结合的重构算法(LABOMP)

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 = 500;%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 K = 20;%测量值集合 M_set = [60,70,80,90,100,110,120,130,140,150]; L = 5; Percentage = zeros(3,length(M_set));%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 P1 = 0; P2 = 0; P3 = 0; 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);%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 theta_lab = LABOMP_f(y,A,K,L); theta_la = LAOMP_f(y,A,K,L); theta = CS_OMP(y,A,K);%恢复重构信号theta x_r_lab = Psi * theta_lab;% x=Psi * theta x_r_la = Psi * theta_la;% x=Psi * theta x_r = Psi * theta;% x=Psi * theta if norm(x_r_lab-x)<1e-6%如果残差小于1e-6则认为恢复成功 P1 = P1 + 1; end if norm(x_r_la-x)<1e-6%如果残差小于1e-6则认为恢复成功 P2 = P2 + 1; end if norm(x_r-x)<1e-6%如果残差小于1e-6则认为恢复成功 P3 = P3 + 1; end end Percentage(1,mm) = (P1/CNT)*100;%计算labomp恢复概率 Percentage(2,mm) =(P2/CNT)*100;%计算laomp恢复概率 Percentage(3,mm) = (P3/CNT)*100;%计算omp恢复概率 end toc save KtoPercentage1000test %运行一次不容易，把变量全部存储下来 %绘图 S = ['-ks';'-ko';'-kd']; figure; for mm = 1:3 MM = 60:10:150; plot(MM,Percentage(mm,1:length(M_set)),S(mm,:));%绘出x的恢复信号 hold on; end hold off; xlim([58 152]); legend('LABOMP','LAOMP','OMP'); xlabel('观测数M'); ylabel('重构概率'); title('N = 256 K = 20情况下，观测数M不同对重构概率的影响');