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[求助]
为什么ROMP的仿真性能比OMP还弱啊？
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function [val,pos] = Regularize(product,Kin) %Regularize Summary of this function goes here % Detailed explanation goes here % product = A'*r_n;%传感矩阵A各列与残差的内积 % K为稀疏度 % pos为选出的各列序号 % val为选出的各列与残差的内积值 % Reference:Needell D，Vershynin R. Uniform uncertainty principle and % signal recovery via regularized orthogonal matching pursuit. % Foundations of Computational Mathematics, 2009,9(3): 317-334. productabs = abs(product);%取绝对值 [productdes,indexproductdes] = sort(productabs,'descend');%降序排列 for ii = length(productdes):-1:1 if productdes(ii)>1e-6%判断productdes中非零值个数 break; end end %Identify:Choose a set J of the K biggest coordinates if ii>=Kin J = indexproductdes(1:Kin);%集合J Jval = productdes(1:Kin);%集合J对应的序列值 K = Kin; else%or all of its nonzero coordinates,whichever is smaller J = indexproductdes(1:ii);%集合J Jval = productdes(1:ii);%集合J对应的序列值 K = ii; end %Regularize:Among all subsets J0∈J with comparable coordinates MaxE = -1;%循环过程中存储最大能量值 for kk = 1:K J0_tmp = zeros(1,K);iJ0 = 1; J0_tmp(iJ0) = J(kk);%以J(kk)为本次寻找J0的基准(最大值) Energy = Jval(kk)^2;%本次寻找J0的能量 for mm = kk+1:K if Jval(kk)<2*Jval(mm)%找到符合|u(i)|<=2|u(j)|的 iJ0 = iJ0 + 1;%J0自变量增1 J0_tmp(iJ0) = J(mm);%更新J0 Energy = Energy + Jval(mm)^2;%更新能量 else%不符合|u(i)|<=2|u(j)|的 break;%跳出本轮寻找，因为后面更小的值也不会符合要求 end end if Energy>MaxE%本次所得J0的能量大于前一组 J0 = J0_tmp(1:iJ0);%更新J0 MaxE = Energy;%更新MaxE，为下次循环做准备 end end pos = J0; val = productabs(J0); end %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% function [ theta ] = CS_ROMP( y,A,K ) %CS_ROMP Summary of this function goes here %Version: 1.0 written by jbb0523 @2015-04-24 % Detailed explanation goes here % y = Phi * x % x = Psi * theta % y = Phi*Psi * theta % 令 A = Phi*Psi, 则y=A*theta % 现在已知y和A，求theta % Reference:Needell D，Vershynin R．Signal recovery from incomplete and % inaccurate measurements via regularized orthogonal matching pursuit[J]． % IEEE Journal on Selected Topics in Signal Processing，2010，4(2)：310—316. [y_rows,y_columns] = size(y); if y_rows<y_columns y = y';%y should be a column vector end [M,N] = size(A);%传感矩阵A为M*N矩阵 theta = zeros(N,1);%用来存储恢复的theta(列向量) At = zeros(M,3*K);%用来迭代过程中存储A被选择的列 Pos_theta = zeros(1,2*K);%用来迭代过程中存储A被选择的列序号 Index = 0; r_n = y;%初始化残差(residual)为y %Repeat the following steps K times(or until |I|>=2K) for ii=1:K%迭代K次 product = A'*r_n;%传感矩阵A各列与残差的内积 %[val,pos] = max(abs(product));%找到最大内积绝对值，即与残差最相关的列 [~,pos] = Regularize(product,K);%按正则化规则选择原子 At(:,Index+1:Index+length(pos)) = A(:,pos);%存储这几列 Pos_theta(Index+1:Index+length(pos)) = pos;%存储这几列的序号 if Index+length(pos)<=M%At的行数大于列数，此为最小二乘的基础(列线性无关) Index = Index+length(pos);%更新Index，为下次循环做准备 else%At的列数大于行数，列必为线性相关的,At(:,1:Index)'*At(:,1:Index)将不可逆 break;%跳出for循环 end A(:,pos) = zeros(M,length(pos));%清零A的这几列(其实此行可以不要因为它们与残差正交) %y=At(:,1:Index)*theta，以下求theta的最小二乘解(Least Square) theta_ls = (At(:,1:Index)'*At(:,1:Index))^(-1)*At(:,1:Index)'*y;%最小二乘解 %At(:,1:Index)*theta_ls是y在At(:,1:Index)列空间上的正交投影 r_n = y - At(:,1:Index)*theta_ls;%更新残差 if norm(r_n)<1e-6%Repeat the steps until r=0 break;%跳出for循环 end if Index>=2*K%or until |I|>=2K break;%跳出for循环 end end theta(Pos_theta(1:Index))=theta_ls;%恢复出的theta end %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %压缩感知重构算法测试 clear all;close all;clc; M = 128;%观测值个数 N = 256;%信号x的长度 K = 12;%信号x的稀疏度 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 Psi = eye(N);%x本身是稀疏的，定义稀疏矩阵为单位阵x=Psi*theta Phi = randn(M,N);%测量矩阵为高斯矩阵 A = Phi * Psi;%传感矩阵 sigma = 0.5; e = sigma*randn(M,1); y = Phi * x + e;%得到观测向量y %% 恢复重构信号x tic theta = CS_ROMP(y,A,K); x_r = Psi * theta;% x=Psi * theta toc %% 绘图 figure; plot(x_r,'k.-');%绘出x的恢复信号 hold on; plot(x,'r');%绘出原信号x hold off; legend('Recovery','Original') fprintf('\n恢复残差：'); norm(x_r-x)%恢复残差 以上是ROMP的算法 function [ theta ] = CS_OMP( y,A,t ) %CS_OMP Summary of this function goes here %Version: 1.0 written by jbb0523 @2015-04-18 % Detailed explanation goes here % y = Phi * x % x = Psi * theta % y = Phi*Psi * theta % 令 A = Phi*Psi, 则y=A*theta % 现在已知y和A，求theta [y_rows,y_columns] = size(y); if y_rows<y_columns y = y';%y should be a column vector end [M,N] = size(A);%传感矩阵A为M*N矩阵 theta = zeros(N,1);%用来存储恢复的theta(列向量) At = zeros(M,t);%用来迭代过程中存储A被选择的列 Pos_theta = zeros(1,t);%用来迭代过程中存储A被选择的列序号 r_n = y;%初始化残差(residual)为y for ii=1:t%迭代t次，t为输入参数 product = A'*r_n;%传感矩阵A各列与残差的内积 [val,pos] = max(abs(product));%找到最大内积绝对值，即与残差最相关的列 At(:,ii) = A(:,pos);%存储这一列 Pos_theta(ii) = pos;%存储这一列的序号 A(:,pos) = zeros(M,1);%清零A的这一列，其实此行可以不要，因为它与残差正交 %y=At(:,1:ii)*theta，以下求theta的最小二乘解(Least Square) theta_ls = (At(:,1:ii)'*At(:,1:ii))^(-1)*At(:,1:ii)'*y;%最小二乘解 %At(:,1:ii)*theta_ls是y在At(:,1:ii)列空间上的正交投影 r_n = y - At(:,1:ii)*theta_ls;%更新残差 end theta(Pos_theta)=theta_ls;%恢复出的theta end %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %压缩感知重构算法测试 clear all;close all;clc; M = 128;%观测值个数 N = 256;%信号x的长度 K = 12;%信号x的稀疏度 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 Psi = eye(N);%x本身是稀疏的，定义稀疏矩阵为单位阵x=Psi*theta Phi = randn(M,N);%测量矩阵为高斯矩阵 A = Phi * Psi;%传感矩阵 sigma = 0.5; e = sigma*randn(M,1); y = Phi * x + e;%得到观测向量y %% 恢复重构信号x tic theta = CS_OMP(y,A,K); x_r = Psi * theta;% x=Psi * theta toc %% 绘图 figure; plot(x_r,'k.-');%绘出x的恢复信号 hold on; plot(x,'r');%绘出原信号x hold off; legend('Recovery','Original') fprintf('\n恢复残差：'); norm(x_r-x)%恢复残差 mse(x_r-x) 以上是OMP的算法 算法来自OMP和ROMP 唯一的改变是在观测值上加了噪声 |
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