Add lyh-非满秩相变
This commit is contained in:
Ksyer
@@ -0,0 +1,229 @@
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close all;
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clear all;
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clc;
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M = 4;
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N = 128;
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%block_sparsity = 1;
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tol = 1e-5;
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trial = 50;
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epi = 0.02;
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result = zeros(N,25);
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for col = 4:4:128
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for block_sparsity = 10:18
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success_count = 0;
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for loop = 1:trial
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FAR_model = zeros(N,M*N);
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%Cn = randperm(M)-1
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for n = 0 : N-1
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Cn = floor(rand()*M);
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for q = 0 : N-1
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for p = 0:M-1
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FAR_model(n+1,q*M+p+1) = exp(1i*2*pi*p/M*Cn+1i*2*pi*q/N*n*(1+Cn*epi));
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end
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end
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end
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col_choose = randperm(N,col);
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FAR_model = FAR_model(col_choose,:);
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sparse_signal = zeros(M,N);
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block = randperm(N,block_sparsity);
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sparse_signal(:,block) = exp(1i*2*pi*rand(M,block_sparsity));
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y = FAR_model * sparse_signal(:);
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cvx_begin
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variable x(M,N) complex
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norm21 = 0;
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for i = 1:N
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norm21 = norm21 + norm(x(:,i));
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end
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minimize(norm21)
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subject to
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FAR_model * x(:) == y
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cvx_end
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if norm(x(:)-sparse_signal(:))<tol
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success_count = success_count+1;
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end
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end
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result(col,block_sparsity) = success_count/trial;
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end
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end
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%save('FARblockepsilon2.mat');
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%%
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close all;
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clear all;
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clc;
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M = 4;
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N = 128;
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%block_sparsity = 1;
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tol = 1e-5;
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trial = 30;
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epi = 0.02;
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result = zeros(1,25);
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col = 128;
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Prob = [1/3,1/3,1/6,1/6];
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for block_sparsity = 4:18
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success_count = 0;
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for loop = 1:trial
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FAR_model = zeros(N,M*N);
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%Cn = randperm(M)-1
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for n = 0 : N-1
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Cn = randsrc(1,1,[[0,1,2,3];Prob]);
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for q = 0 : N-1
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for p = 0:M-1
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FAR_model(n+1,q*M+p+1) = exp(1i*2*pi*p/M*Cn+1i*2*pi*q/N*n*(1+Cn*epi));
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end
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end
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end
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%col_choose = randperm(N,col);
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%FAR_model = FAR_model(col_choose,:);
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sparse_signal = zeros(M,N);
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block = randperm(N,block_sparsity);
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sparse_signal(:,block) = exp(1i*2*pi*rand(M,block_sparsity));
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y = FAR_model * sparse_signal(:);
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cvx_begin
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variable x(M,N) complex
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norm21 = 0;
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for i = 1:N
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norm21 = norm21 + norm(x(:,i));
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end
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minimize(norm21)
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subject to
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FAR_model * x(:) == y
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cvx_end
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if norm(x(:)-sparse_signal(:))<tol
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success_count = success_count+1;
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end
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end
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result(block_sparsity) = success_count/trial;
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end
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%%
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clc;
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M = 4;
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N = 128;
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%block_sparsity = 1;
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tol = 1e-5;
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trial = 30;
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epi = 0.02;
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result2 = zeros(2,25);
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col = 128;
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Prob = [1/3,1/3,1/6,1/6];
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for block_sparsity = 4:18
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success_count = 0;
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success_count2 = 0;
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for loop = 1:trial
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FAR_model = zeros(N,M*N);
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%Cn = randperm(M)-1
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for n = 0 : N-1
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Cn = randsrc(1,1,[[0,1,2,3];Prob]);
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for q = 0 : N-1
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for p = 0:M-1
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FAR_model(n+1,q*M+p+1) = exp(1i*2*pi*p/M*Cn+1i*2*pi*q/N*n*(1+Cn*epi));
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end
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end
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end
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%col_choose = randperm(N,col);
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%FAR_model = FAR_model(col_choose,:);
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sparse_signal = zeros(M,N);
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block = randperm(N,block_sparsity);
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sparse_signal(:,block) = exp(1i*2*pi*rand(M,block_sparsity));
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y = FAR_model * sparse_signal(:);
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cvx_begin
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variable x(M,N) complex
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norm21 = 0;
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for i = 1:N
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norm21 = norm21 + norm(FAR_model(:,M*i-3:M*i)*x(:,i));
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end
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minimize(norm21)
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subject to
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FAR_model * x(:) == y
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cvx_end
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err1 = 0;
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for i =1:N
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err1 = err1 + norm(FAR_model(:,M*i-3:M*i)*(x(:,i)-sparse_signal(:,i)));
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end
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if err1<tol
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success_count2 = success_count2 +1;
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end
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if norm(x(:)-sparse_signal(:))<tol
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success_count = success_count+1;
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end
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end
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result2(1,block_sparsity) = success_count/trial;
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result2(2,block_sparsity) = success_count2/trial;
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end
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%%
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close all;
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clear all;
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clc;
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M = 4;
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N = 64;
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%block_sparsity = 1;
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tol = 1e-5;
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trial = 50;
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epi = 0.02;
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%result = zeros(N,25);
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%for col = 4:4:128
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col = 64;
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block_sparsity = 6;
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err = 0.1;
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sigma = 0.5*sqrt(block_sparsity);
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FAR_model = zeros(N,M*N);
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%Cn = randperm(M)-1
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for n = 0 : N-1
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Cn = floor(rand()*M);
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for q = 0 : N-1
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for p = 0:M-1
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FAR_model(n+1,q*M+p+1) = exp(1i*2*pi*p/M*Cn-1i*2*pi*q/N*n*(1+Cn*epi));
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end
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end
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end
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%col_choose = randperm(N,col);
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%FAR_model = FAR_model(col_choose,:);
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sparse_signal = zeros(M,N);
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block = randperm(N,block_sparsity);
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sparse_signal(:,block) = exp(1i*2*pi*rand(M,block_sparsity));
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y = FAR_model * sparse_signal(:) + sigma*(randn(N,1)) + 1i*sigma*(randn(N,1));
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cvx_begin
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variable x(M,N) complex
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norm21 = 0;
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for i = 1:N
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norm21 = norm21 + norm(x(:,i));
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end
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minimize(norm21)
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subject to
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norm(FAR_model * x(:) - y)<err
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cvx_end
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x_block_norm = zeros(N,1);
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x_norm = zeros(N,1);
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for i = [1:N]
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x_block_norm(i) = norm(FAR_model(:,M*i-3:M*i)*x(:,i));
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x_norm(i) = norm(FAR_model(:,M*i-3:M*i)*sparse_signal(:,i));
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end
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hold on
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plot(x_block_norm,'--o');
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plot(x_norm,'-.s');
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lgh = legend("Estimated","Ground Truth", ...
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"MF");
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set(lgh,'interpreter','latex','FontName','Times New Roman')
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%set(gcf,'interpreter','latex','FontName','Times New Roman')
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xlabel("\fontname{Times New Roman}Velocity Cell Index");
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ylabel("\fontname{Times New Roman}Test Statistics \it{T_i}");
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xlim([0 75]);
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%end
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@@ -0,0 +1,80 @@
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N = 32;
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M =4;
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R =2;
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epi = 0.02;
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noise = [0.1,0.1^(0.5)];
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%contri1 = zeros(M,N);
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%contri2 = zeros(M,N);
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con1 = zeros(20,2);
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con2 = zeros(20,2);
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re1 = zeros(20,2);
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re2 = zeros(20,2);
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for noise_k = 1:2
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for k = 1:20
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for loop = 1:50
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FAR_model = zeros(N,M*N);
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order = randperm(M)-1;
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for n = 0 : N-1
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Cn = order(ceil(rand()*R));
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for q = 0 : N-1
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for p = 0:M-1
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FAR_model(n+1,q*M+p+1) = exp(1i*2*pi*p/M*Cn+1i*2*pi*q/N*n*(1+Cn*epi));
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end
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end
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end
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x = zeros(M,N);
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col = randperm(N,k);
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x(:,col) = randn(M,k) + 1i*randn(M,k);
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y = FAR_model * x(:) + (randn(N,1)+1i*randn(N,1))*noise(noise_k);
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cvx_begin
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variable x_e(M,N) complex
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norm21 = 0;
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for i = 1:N
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norm21 = norm21 + norm(FAR_model(:,(i-1)*M+1:i*M)*x_e(:,i));
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end
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minimize(norm21)
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subject to
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norm(FAR_model*x_e(:) - y) <= sqrt(N)*noise(noise_k);
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cvx_end
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contri2 = zeros(N,1);
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re_err = zeros(N,1);
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for i = 1:N
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if ismember(i,col)
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re_err = re_err+FAR_model(:,(i-1)*M+1:i*M)*(x_e(:,i));
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end
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contri2(i) = norm(FAR_model(:,(i-1)*M+1:i*M)*(x_e(:,i)));
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end
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re1(k,noise_k) = re1(k,noise_k) +norm(FAR_model*x(:)-re_err)/norm(FAR_model*x(:));
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con1(k,noise_k) = con1(k,noise_k) + 1-sum(contri2(col))/sum(contri2);
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cvx_begin
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variable x_e(M,N) complex
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norm21 = 0;
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for i = 1:N
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norm21 = norm21 + norm(x_e(:,i));
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end
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minimize(norm21)
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subject to
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norm(FAR_model*x_e(:) - y) <= sqrt(N)*noise(noise_k);
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cvx_end
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re_err = zeros(N,1);
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contri2 = zeros(N,1);
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for i = 1:N
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if ismember(i,col)
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re_err = re_err+FAR_model(:,(i-1)*M+1:i*M)*(x_e(:,i));
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end
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contri2(i) = norm(FAR_model(:,(i-1)*M+1:i*M)*(x_e(:,i)));
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end
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re2(k,noise_k) = re2(k,noise_k) +norm(FAR_model*x(:)-re_err)/norm(FAR_model*x(:));
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con2(k,noise_k) = con2(k,noise_k) + 1-sum(contri2(col))/sum(contri2);
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end
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end
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end
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save("FAR_noise_0206.mat")
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File diff suppressed because it is too large
Load Diff
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File diff suppressed because it is too large
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File diff suppressed because it is too large
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File diff suppressed because it is too large
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File diff suppressed because it is too large
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File diff suppressed because it is too large
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File diff suppressed because it is too large
Load Diff
File diff suppressed because it is too large
Load Diff
File diff suppressed because it is too large
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File diff suppressed because it is too large
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File diff suppressed because it is too large
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File diff suppressed because it is too large
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File diff suppressed because it is too large
Load Diff
@@ -0,0 +1,53 @@
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%初值设定
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N = 64; %最大行数
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D = 32; %块数
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m = 4; %块的列数
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d = 2; %块内rank/维度
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result = zeros(N,D); %保留结果
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%按行数循环
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for n = 1:N
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A = zeros(n,m*D);
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B = zeros(n,d*D);
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%按稀疏度循环
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for k = 1:D
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%50次重复实验
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for j = 1:50
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re_err = 0;
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for i = 0:D-1
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%生成高斯基集
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set = randn(n,d);
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%生成随机的模为1的向量，与基集相乘得到块不满秩的高斯矩阵
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theta = rand(1,4)*2*pi;
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tmp = [sin(theta);cos(theta)];
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A(:,m*i+1:m*i+m) = set*tmp;
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B(:,d*i+1:d*i+d) = set;
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end
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x = zeros(m,D);
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col = randperm(D,k);
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x(:,col) = randn(m,k);
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y = A * x(:);
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%凸优化利用l21范数求解基集下的恢复问题
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cvx_begin
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variable x_e(d,D)
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norm21 = 0;
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for i = 1:D
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norm21 = norm21 + norm(x_e(:,i));
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end
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minimize(norm21)
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subject to
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B*x_e(:) == y
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cvx_end
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for i = 1:D
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re_err = re_err+norm(B(:,(i-1)*d+1:i*d)*x_e(:,i)-A(:,(i-1)*m+1:i*m)*x(:,i));
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end
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if re_err<10e-4
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result(n,k) = result(n,k)+1;
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end
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end
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end
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end
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save('gaussD32m2d2base.mat');
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@@ -0,0 +1,55 @@
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%初值设定
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N = 64; %最大行数
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D = 32; %块数
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m = 4; %块的列数
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d = 2; %块内rank/维度
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result = zeros(N,D); %保留结果
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%按行数循环
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for n = 1:N
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A = zeros(n,m*D);
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B = zeros(n,d*D);
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%按稀疏度循环
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for k = 1:D
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%50次重复实验
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for j = 1:50
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re_err = 0;
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for i = 0:D-1
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%生成高斯基集
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set = randn(n,d);
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%生成随机的模为1的向量，与基集相乘得到块不满秩的高斯矩阵
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theta = rand(1,4)*2*pi;
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tmp = [sin(theta);cos(theta)];
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A(:,m*i+1:m*i+m) = set*tmp;
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%随机挑选块列向量作为降维后矩阵
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q = randperm(m,d);
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B(:,d*i+1:d*i+d) = A(:,m*i+q);
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end
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%生成稀疏块信号
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x = zeros(m,D);
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col = randperm(D,k);
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x(:,col) = randn(m,k);
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y = A * x(:);
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%凸优化利用特殊l21范数求解降维后的恢复问题
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cvx_begin
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variable x_e(d,D)
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norm21 = 0;
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for i = 1:D
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norm21 = norm21 + norm(B(:,(i-1)*d+1:i*d)*x_e(:,i));
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end
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minimize(norm21)
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subject to
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B*x_e(:) == y
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cvx_end
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%得到重建效果
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for i = 1:D
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re_err = re_err+norm(B(:,(i-1)*d+1:i*d)*x_e(:,i)-A(:,(i-1)*m+1:i*m)*x(:,i));
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end
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if re_err<10e-4
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result(n,k) = result(n,k)+1;
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end
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end
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end
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end
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save('gaussD32m2d2randalter.mat');
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@@ -0,0 +1,53 @@
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%初值设定
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N = 64; %最大行数
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D = 32; %块数
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m = 4; %块的列数
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d = 2; %块内rank/维度
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result = zeros(N,D); %保留结果
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%按行数循环
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for n = 1:N
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A = zeros(n,m*D);
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B = zeros(n,d*D);
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%按稀疏度循环
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for k = 1:D
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%50次重复实验
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for j = 1:50
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re_err = 0;
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for i = 0:D-1
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%生成高斯基集
|
||||
set = randn(n,d);
|
||||
%生成随机的模为1的向量，与基集相乘得到块不满秩的高斯矩阵
|
||||
theta = rand(1,4)*2*pi;
|
||||
tmp = [sin(theta);cos(theta)];
|
||||
A(:,m*i+1:m*i+m) = set*tmp;
|
||||
q = randperm(m,d);
|
||||
B(:,d*i+1:d*i+d) = A(:,m*i+q);
|
||||
end
|
||||
%随机挑选块列向量作为降维后矩阵
|
||||
x = zeros(m,D);
|
||||
col = randperm(D,k);
|
||||
x(:,col) = randn(m,k);
|
||||
y = A * x(:);
|
||||
%凸优化利用l21范数求解降维后的恢复问题
|
||||
cvx_begin
|
||||
variable x_e(d,D)
|
||||
norm21 = 0;
|
||||
for i = 1:D
|
||||
norm21 = norm21 + norm(x_e(:,i));
|
||||
end
|
||||
minimize(norm21)
|
||||
subject to
|
||||
B*x_e(:) == y
|
||||
cvx_end
|
||||
|
||||
%得到重建效果
|
||||
for i = 1:D
|
||||
re_err = re_err+norm(B(:,(i-1)*d+1:i*d)*x_e(:,i)-A(:,(i-1)*m+1:i*m)*x(:,i));
|
||||
end
|
||||
if re_err<10e-4
|
||||
result(n,k) = result(n,k)+1;
|
||||
end
|
||||
end
|
||||
end
|
||||
end
|
||||
save('gaussD32m2d2rand.mat');
|
||||
@@ -0,0 +1,52 @@
|
||||
%初值设定
|
||||
N = 64; %最大行数
|
||||
D = 32; %块数
|
||||
m = 4; %块的列数
|
||||
d = 2; %块内rank/维度
|
||||
result = zeros(N,D); %保留结果
|
||||
%按行数循环
|
||||
for n = 1:N
|
||||
A = zeros(n,m*D);
|
||||
B = zeros(n,d*D);
|
||||
%按稀疏度循环
|
||||
for k = 1:D
|
||||
%50次重复实验
|
||||
for j = 1:50
|
||||
re_err = 0;
|
||||
for i = 0:D-1
|
||||
%生成高斯基集
|
||||
set = randn(n,d);
|
||||
|
||||
|
||||
%生成随机的模为1的向量，与基集相乘得到块不满秩的高斯矩阵
|
||||
theta = rand(1,4)*2*pi;
|
||||
temp = [sin(theta);cos(theta)];
|
||||
A(:,m*i+1:m*i+m) = set*temp;
|
||||
end
|
||||
x = zeros(m,D);
|
||||
col = randperm(D,k);
|
||||
x(:,col) = randn(m,k);
|
||||
y = A * x(:);
|
||||
|
||||
%凸优化利用特殊l21范数求解恢复问题
|
||||
cvx_begin
|
||||
variable x_e(m,D)
|
||||
norm21 = 0;
|
||||
for i = 1:D
|
||||
norm21 = norm21 + norm(A(:,(i-1)*m+1:i*m)*x_e(:,i));
|
||||
end
|
||||
minimize(norm21)
|
||||
subject to
|
||||
A*x_e(:) == y
|
||||
cvx_end
|
||||
|
||||
for i = 1:D
|
||||
re_err = re_err+norm(A(:,(i-1)*m+1:i*m)*(x_e(:,i)-x(:,i)));
|
||||
end
|
||||
if re_err<10e-4
|
||||
result(n,k) = result(n,k)+1;
|
||||
end
|
||||
end
|
||||
end
|
||||
end
|
||||
save('gaussD32m4d2alter.mat');
|
||||
@@ -0,0 +1,51 @@
|
||||
%初值设定
|
||||
N = 64; %最大行数
|
||||
D = 32; %块数
|
||||
m = 4; %块的列数
|
||||
d = 2; %块内rank/维度
|
||||
result = zeros(N,D); %保留结果
|
||||
%按行数循环
|
||||
for n = 1:N
|
||||
A = zeros(n,m*D);
|
||||
B = zeros(n,d*D);
|
||||
%按稀疏度循环
|
||||
for k = 1:D
|
||||
%50次重复实验
|
||||
for j = 1:50
|
||||
re_err = 0;
|
||||
for i = 0:D-1
|
||||
%生成高斯基集
|
||||
set = randn(n,d);
|
||||
%生成随机的模为1的向量，与基集相乘得到块不满秩的高斯矩阵
|
||||
theta = rand(1,4)*2*pi;
|
||||
temp = [sin(theta);cos(theta)];
|
||||
A(:,m*i+1:m*i+m) = set*temp;
|
||||
end
|
||||
x = zeros(m,D);
|
||||
col = randperm(D,k);
|
||||
x(:,col) = randn(m,k);
|
||||
y = A * x(:);
|
||||
%凸优化利用l21范数求解恢复问题
|
||||
cvx_begin
|
||||
variable x_e(m,D)
|
||||
norm21 = 0;
|
||||
for i = 1:D
|
||||
norm21 = norm21 + norm(x_e(:,i));
|
||||
end
|
||||
minimize(norm21)
|
||||
subject to
|
||||
A*x_e(:) == y
|
||||
cvx_end
|
||||
|
||||
|
||||
%得到重建效果
|
||||
for i = 1:D
|
||||
re_err = re_err+norm(A(:,(i-1)*m+1:i*m)*(x_e(:,i)-x(:,i)));
|
||||
end
|
||||
if re_err<10e-4
|
||||
result(n,k) = result(n,k)+1;
|
||||
end
|
||||
end
|
||||
end
|
||||
end
|
||||
save('gaussD32m4d2class.mat');
|
||||
@@ -0,0 +1,24 @@
|
||||
N = 40; %行数
|
||||
D = 32; %块数
|
||||
m = 4; %块的列数
|
||||
d = 2; %块内rank/维度
|
||||
resulta = zeros(5000,1);
|
||||
resultb = zeros(5000,1);
|
||||
%resulta = zeros(5,20,50); %保留结果
|
||||
%resultb = zeros(5,20,50);
|
||||
%按行数循环
|
||||
A = zeros(N,m*D);
|
||||
B = zeros(N,d*D);
|
||||
%按稀疏度循环
|
||||
n = N;
|
||||
parfor i = 0:199
|
||||
t = floor(i/1000) + 1;
|
||||
k = floor(mod(i,1000)/50)+1;
|
||||
j = mod(i,50)+1;
|
||||
[a,b] = test(t,k,j);
|
||||
resulta(i+1) = a;
|
||||
resultb(i+1) = b;
|
||||
end
|
||||
resulta = reshape(resulta,5,20,50);
|
||||
resultb = reshape(resultb,5,20,50);
|
||||
save('gaussnoise.mat');
|
||||
File diff suppressed because it is too large
Load Diff
File diff suppressed because it is too large
Load Diff
File diff suppressed because it is too large
Load Diff
File diff suppressed because it is too large
Load Diff
File diff suppressed because it is too large
Load Diff
File diff suppressed because it is too large
Load Diff
File diff suppressed because it is too large
Load Diff
File diff suppressed because it is too large
Load Diff
File diff suppressed because it is too large
Load Diff
@@ -0,0 +1,48 @@
|
||||
load("result1.mat");
|
||||
%ambient_dim = 100;
|
||||
%sparsities = 1:100;
|
||||
d = 32;%¿é¸öÊý
|
||||
m = 2;%¿éÄÚÔªËØÊý
|
||||
l1recovery = zeros(100,1);
|
||||
for i = 1:32
|
||||
l1recovery(i) = theoretic(m,i,d);
|
||||
end
|
||||
m = 1:32;
|
||||
n = 1:64;
|
||||
figure;
|
||||
contourf( m, n, result, 20, 'LineColor', 'none' );
|
||||
hold on
|
||||
cbar = colorbar;
|
||||
myplot2 = plot( n, l1recovery, 'Color', 'w', 'Linewidth', 3 );
|
||||
mylegend2 = legend(myplot2, ' Theory', 'Location', 'SouthEast' );
|
||||
mylegend2.Box = 'off';
|
||||
mylegend2.TextColor = [1,1,1];
|
||||
mylegend2.FontSize = 12;
|
||||
|
||||
figure
|
||||
plot(con1(:,1)/400,'*-')
|
||||
xlabel("\fontname{Times New Roman} Block Sparsity \it K");
|
||||
ylabel("\fontname{Times New Roman} Block Contribution Error");
|
||||
savefig("contri_noise001.fig");
|
||||
saveas(gca,"contri_noise001.eps");
|
||||
|
||||
figure
|
||||
plot(con1(:,2)/400,'*-')
|
||||
xlabel("\fontname{Times New Roman} Block Sparsity \it K");
|
||||
ylabel("\fontname{Times New Roman} Block Contribution Error");
|
||||
savefig("contri_noise01.fig");
|
||||
saveas(gca,"contri_noise01.eps");
|
||||
|
||||
figure
|
||||
plot(re1(:,1)/400,'*-')
|
||||
xlabel("\fontname{Times New Roman} Block Sparsity \it K");
|
||||
ylabel("\fontname{Times New Roman} Reconstruction Error");
|
||||
savefig("re_noise001.fig");
|
||||
saveas(gca,"re_noise001.eps");
|
||||
|
||||
figure
|
||||
plot(re1(:,2)/400,'*-')
|
||||
xlabel("\fontname{Times New Roman} Block Sparsity \it K");
|
||||
ylabel("\fontname{Times New Roman} Reconstruction Error");
|
||||
savefig("re_noise01.fig");
|
||||
saveas(gca,"re_noise01.eps");
|
||||
File diff suppressed because it is too large
Load Diff
File diff suppressed because it is too large
Load Diff
File diff suppressed because it is too large
Load Diff
File diff suppressed because it is too large
Load Diff
File diff suppressed because it is too large
Load Diff
File diff suppressed because it is too large
Load Diff
File diff suppressed because it is too large
Load Diff
File diff suppressed because it is too large
Load Diff
File diff suppressed because it is too large
Load Diff
File diff suppressed because it is too large
Load Diff
File diff suppressed because it is too large
Load Diff
File diff suppressed because it is too large
Load Diff
File diff suppressed because it is too large
Load Diff
File diff suppressed because it is too large
Load Diff
@@ -0,0 +1,228 @@
|
||||
%function[out1,out2,out3,out4,out5,out6] = test(t,k,~)
|
||||
|
||||
%sigma = [0,0.01, 0.5, 1, 1.5, 2];
|
||||
n = 40;
|
||||
d = 2;
|
||||
D = 32;
|
||||
m = 4;
|
||||
%t = 1;
|
||||
k = 13;
|
||||
|
||||
err = zeros(20,1);
|
||||
|
||||
A = zeros(n,D*m);
|
||||
contri1 = zeros(n,D);
|
||||
contri2 = zeros(n,D);
|
||||
for i = 0:32-1
|
||||
%生成高斯基集
|
||||
set = randn(n,d);
|
||||
%生成随机的模为1的向量，与基集相乘得到块不满秩的高斯矩阵
|
||||
theta = rand(1,4)*2*pi;
|
||||
temp = [sin(theta);cos(theta)];
|
||||
A(:,m*i+1:m*i+m) = set*temp*(i+1);
|
||||
end
|
||||
x = zeros(m,D);
|
||||
col = randperm(D,k);
|
||||
x(:,col) = randn(m,k);
|
||||
y = A * x(:);
|
||||
|
||||
weight = diag(rand(D*m,1)*30);
|
||||
%A2 = zeros(n,D*m);
|
||||
%for i= 0:31
|
||||
% A2(:,m*i+1:m*i+m) = A(:,m*i+1:m*i+m) * weight(i+1);
|
||||
%end
|
||||
A2 = A*weight;
|
||||
|
||||
%凸优化利用特殊l21范数求解恢复问题
|
||||
cvx_begin
|
||||
variable x_e(m,D)
|
||||
norm21 = 0;
|
||||
for i = 1:D
|
||||
norm21 = norm21 + norm(A(:,(i-1)*m+1:i*m)*x_e(:,i));
|
||||
end
|
||||
minimize(norm21)
|
||||
subject to
|
||||
A*x_e(:) == y;
|
||||
cvx_end
|
||||
re_err = 0;
|
||||
for i = 1:D
|
||||
re_err = re_err+norm(A(:,(i-1)*m+1:i*m)*(x_e(:,i)-x(:,i)));
|
||||
contri1(:,i) = A(:,(i-1)*m+1:i*m)*(x_e(:,i));
|
||||
end
|
||||
out1 = re_err;
|
||||
x3 = x_e;
|
||||
|
||||
|
||||
|
||||
cvx_begin
|
||||
variable x_e(m,D)
|
||||
norm21 = 0;
|
||||
for i = 1:D
|
||||
norm21 = norm21 + norm(A2(:,(i-1)*m+1:i*m)*x_e(:,i));
|
||||
end
|
||||
minimize(norm21)
|
||||
subject to
|
||||
A2*x_e(:) == y;
|
||||
cvx_end
|
||||
re_err = 0;
|
||||
for i = 1:D
|
||||
re_err = re_err+norm(A2(:,(i-1)*m+1:i*m)*(x_e(:,i)-inv(weight((i-1)*m+1:i*m,(i-1)*m+1:i*m))*x(:,i)));
|
||||
contri2(:,i) = A2(:,(i-1)*m+1:i*m)*(x_e(:,i));
|
||||
end
|
||||
out2 = re_err;
|
||||
%err(iter) =norm(contri1-contri2,'fro');
|
||||
|
||||
|
||||
a1 = 0;
|
||||
a2 = 0;
|
||||
for i = 1:32
|
||||
a1 = a1 +norm(contri1(:,i));
|
||||
a2 = a2 +norm(contri1(:,i));
|
||||
end
|
||||
|
||||
|
||||
% cvx_begin
|
||||
% variable x_e(m,D)
|
||||
% norm21 = 0;
|
||||
% for i = 1:D
|
||||
% norm21 = norm21 + norm(A2(:,(i-1)*m+1:i*m)*x_e(:,i));
|
||||
% end
|
||||
% minimize(norm21)
|
||||
% subject to
|
||||
% A2*x_e(:) == y;
|
||||
% cvx_end
|
||||
% re_err = 0;
|
||||
% for i = 1:D
|
||||
% re_err = re_err+norm(A2(:,(i-1)*m+1:i*m)*(x_e(:,i)-inv(weight((i-1)*m+1:i*m,(i-1)*m+1:i*m))*x(:,i)));
|
||||
% contri2(:,i) = A2(:,(i-1)*m+1:i*m)*(x_e(:,i));
|
||||
% end
|
||||
% out2 = re_err;
|
||||
%%
|
||||
n = 40;
|
||||
d = 2;
|
||||
D = 32;
|
||||
m = 4;
|
||||
%t = 1;
|
||||
k = 4;
|
||||
A = zeros(n,D*m);
|
||||
contri1 = zeros(n,D);
|
||||
contri2 = zeros(n,D);
|
||||
for i = 0:32-1
|
||||
%生成高斯基集
|
||||
set = randn(n,d);
|
||||
%生成随机的模为1的向量，与基集相乘得到块不满秩的高斯矩阵
|
||||
theta = rand(1,4)*2*pi;
|
||||
temp = [sin(theta);cos(theta)];
|
||||
A(:,m*i+1:m*i+m) = set*temp*(i+1);
|
||||
end
|
||||
x = zeros(m,D);
|
||||
col = randperm(D,k);
|
||||
x(:,col) = randn(m,k);
|
||||
y = A * x(:);
|
||||
|
||||
A2 = A * diag(randn(D*m,1)*30);
|
||||
|
||||
%凸优化利用特殊l21范数求解恢复问题
|
||||
cvx_begin
|
||||
variable x_e(m,D)
|
||||
norm21 = 0;
|
||||
for i = 1:D
|
||||
norm21 = norm21 + norm(x_e(:,i));
|
||||
end
|
||||
minimize(norm21)
|
||||
subject to
|
||||
A*x_e(:) == y;
|
||||
cvx_end
|
||||
re_err = 0;
|
||||
for i = 1:D
|
||||
re_err = re_err+norm(A(:,(i-1)*m+1:i*m)*(x_e(:,i)-x(:,i)));
|
||||
contri1(:,i) = A(:,(i-1)*m+1:i*m)*(x_e(:,i));
|
||||
end
|
||||
out1 = re_err;
|
||||
|
||||
|
||||
|
||||
cvx_begin
|
||||
variable x_e(m,D)
|
||||
norm21 = 0;
|
||||
for i = 1:D
|
||||
norm21 = norm21 + norm(x_e(:,i));
|
||||
end
|
||||
minimize(norm21)
|
||||
subject to
|
||||
A2*x_e(:) == y;
|
||||
cvx_end
|
||||
re_err = 0;
|
||||
for i = 1:D
|
||||
re_err = re_err+norm(A2(:,(i-1)*m+1:i*m)*(x_e(:,i)-inv(weight((i-1)*m+1:i*m,(i-1)*m+1:i*m))*x(:,i)));
|
||||
contri2(:,i) = A2(:,(i-1)*m+1:i*m)*(x_e(:,i));
|
||||
end
|
||||
out2 = re_err;
|
||||
%%
|
||||
n = 40;
|
||||
d = 2;
|
||||
D = 32;
|
||||
m = 4;
|
||||
%t = 1;
|
||||
k = 6;
|
||||
A = zeros(n,D*m);
|
||||
noise = 0.01;
|
||||
contri1 = zeros(n,D);
|
||||
contri2 = zeros(n,D);
|
||||
for i = 0:32-1
|
||||
%生成高斯基集
|
||||
set = randn(n,d);
|
||||
%生成随机的模为1的向量，与基集相乘得到块不满秩的高斯矩阵
|
||||
theta = rand(1,4)*2*pi;
|
||||
temp = [sin(theta);cos(theta)];
|
||||
A(:,m*i+1:m*i+m) = set*temp*(i+1);
|
||||
end
|
||||
x = zeros(m,D);
|
||||
col = randperm(D,k);
|
||||
x(:,col) = randn(m,k);
|
||||
y = A * x(:) + randn(n,1)*noise;
|
||||
|
||||
weight = diag(rand(D*m,1)*30);
|
||||
%A2 = zeros(n,D*m);
|
||||
%for i= 0:31
|
||||
% A2(:,m*i+1:m*i+m) = A(:,m*i+1:m*i+m) * weight(i+1);
|
||||
%end
|
||||
A2 = A*weight;
|
||||
|
||||
%凸优化利用特殊l21范数求解恢复问题
|
||||
cvx_begin
|
||||
variable x_e(m,D)
|
||||
norm21 = 0;
|
||||
for i = 1:D
|
||||
norm21 = norm21 + norm(A(:,(i-1)*m+1:i*m)*x_e(:,i));
|
||||
end
|
||||
minimize(norm21)
|
||||
subject to
|
||||
norm(A*x_e(:) - y) <= sqrt(40)*0.01;
|
||||
cvx_end
|
||||
re_err = 0;
|
||||
for i = 1:D
|
||||
re_err = re_err+norm(A(:,(i-1)*m+1:i*m)*(x_e(:,i)-x(:,i)));
|
||||
contri1(:,i) = A(:,(i-1)*m+1:i*m)*(x_e(:,i));
|
||||
end
|
||||
out1 = re_err;
|
||||
|
||||
|
||||
|
||||
cvx_begin
|
||||
variable x_e(m,D)
|
||||
norm21 = 0;
|
||||
for i = 1:D
|
||||
norm21 = norm21 + norm(A2(:,(i-1)*m+1:i*m)*x_e(:,i));
|
||||
end
|
||||
minimize(norm21)
|
||||
subject to
|
||||
norm(A2*x_e(:) - y) <= sqrt(40)*0.01;
|
||||
cvx_end
|
||||
re_err = 0;
|
||||
for i = 1:D
|
||||
re_err = re_err+norm(A2(:,(i-1)*m+1:i*m)*(x_e(:,i)-inv(weight((i-1)*m+1:i*m,(i-1)*m+1:i*m))*x(:,i)));
|
||||
contri2(:,i) = A2(:,(i-1)*m+1:i*m)*(x_e(:,i));
|
||||
end
|
||||
out2 = re_err;
|
||||
|
||||
@@ -0,0 +1,7 @@
|
||||
function n = theoretic(m,s,d)
|
||||
syms t;
|
||||
syms u;
|
||||
f = s*(m+t^2)+(d-s)*int((u-t)^2*u^(m-1)*exp(-u^2/2)/(2^(m/2-1)*gamma(m/2)),u,t,inf);
|
||||
g = diff(f,t);
|
||||
t1 = solve(g);
|
||||
n = s*(m+t1^2)+(d-s)*int((u-t1)^2*u^(m-1)*exp(-u^2/2)/(2^(m/2-1)*gamma(m/2)),u,t1,inf);
|
||||
@@ -0,0 +1,147 @@
|
||||
|
||||
len = 256;
|
||||
w = 0.05;
|
||||
m = [0:len-1];
|
||||
n = m;
|
||||
B = m - n';
|
||||
B = (sin(2*pi*w*B)./(pi*B));
|
||||
for i = 1:len
|
||||
B(i,i) = 2*w;
|
||||
end
|
||||
t = [0:0.1:25.5];
|
||||
r = 1/sqrt(2*pi*1)*exp(-t.^2/2*1);
|
||||
gau = toeplitz(r);
|
||||
|
||||
|
||||
|
||||
|
||||
%%
|
||||
len = 64;
|
||||
w = 0.2;
|
||||
m = [0:len-1];
|
||||
n = m;
|
||||
B = m - n';
|
||||
B_new = sin(2*pi*w*B)./(pi*B);
|
||||
for i = 1:len
|
||||
B_new(i,i) = 2*w;
|
||||
end
|
||||
|
||||
cor = 0.236;
|
||||
|
||||
final = zeros(len^2,len^2);
|
||||
for j = 1:len
|
||||
for k = 1:len
|
||||
tmp = sin(2*pi*w*(cor*B+(j-k)))./(pi*(cor*B+(j-k)));
|
||||
tmp(cor*B+(j-k) == 0) = 2*w;
|
||||
final((j-1)*len+1:j*len,(k-1)*len+1:k*len) = tmp.*B_new;
|
||||
end
|
||||
end
|
||||
|
||||
[a,b] = eig(final);
|
||||
plot(diag(b));
|
||||
c = diag(b);
|
||||
M = c'*c;
|
||||
plot(sort(M(:)));
|
||||
|
||||
|
||||
|
||||
%%
|
||||
|
||||
K = kron(B,B);
|
||||
|
||||
[a,b] = eig(B);
|
||||
plot(diag(b));
|
||||
c = diag(b);
|
||||
M = c*c';
|
||||
plot(sort(M(:)));
|
||||
|
||||
|
||||
f = zeros(1,1200);
|
||||
f(1:120) = randn(120,1);
|
||||
f(1081:1200) = randn(120,1);
|
||||
t = ifft(f);
|
||||
t = t(1:64);
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
%B = B + diag(exp(1i*2*pi*0.3*[0:len-1]))*B*diag(exp(1i*2*pi*0.3*[0:len-1]))';
|
||||
|
||||
[a,b] = eig(B);
|
||||
% plot(sort(abs(diag(b))))
|
||||
|
||||
D = B(1:8,:);
|
||||
E = B(1:2:16,:);
|
||||
[U2,S2,V2] = svd(D);
|
||||
[U3,S3,V3] = svd(E);
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
%sel = (1:2:1023);
|
||||
o = randn(1024,1024);
|
||||
%o = orth(o);
|
||||
sel = randperm(1024,512);
|
||||
% C = o(sel,:)*b;
|
||||
% D = B(sel,:);
|
||||
% E = o(sel,randperm(1024,204));
|
||||
D = B(1:512,:);
|
||||
C = B(sel,:);
|
||||
E = B(1:2:1023,:);
|
||||
[U,S,V] = svd(C);
|
||||
[U2,S2,V2] = svd(D);
|
||||
[U3,S3,V3] = svd(E);
|
||||
s = diag(S);
|
||||
s2 = diag(S2);
|
||||
s3 = diag(S3);
|
||||
figure;
|
||||
subplot(1,4,1);
|
||||
plot(s);
|
||||
subplot(1,4,2);
|
||||
plot(s2);
|
||||
subplot(1,4,3);
|
||||
plot(s3);
|
||||
q = sum(s);
|
||||
subplot(1,4,4);
|
||||
plot(flipud(abs(diag(b))));
|
||||
|
||||
|
||||
%t1 = squeeze(resulta(:,:,1));
|
||||
%t2 = squeeze(resultb(:,:,1));
|
||||
% t1 = squeeze(resulta(:,:,2));
|
||||
% t2 = squeeze(resultb(:,:,2));
|
||||
% figure;
|
||||
|
||||
result_cona = reshape(result_cona,200,20,2);
|
||||
result_conb = reshape(result_conb,200,20,2);
|
||||
for i = 1:2
|
||||
t1 = squeeze(result_cona(:,:,i)+t3(:,:,i))/2;
|
||||
t2 = squeeze(result_conb(:,:,i)+t4(:,:,i))/2;
|
||||
figure
|
||||
hold on
|
||||
plot(mean(t1),'-r.');
|
||||
plot(mean(t2),'-bo');
|
||||
h = legend("$P_{\ell_{2,1}}'$","$P_{\ell_{2,1}}$","Location","Southeast","Fontsize",15);
|
||||
set(h,'Interpreter','latex');
|
||||
xlabel("\fontname{Times New Roman} Block Sparsity \it s_B");
|
||||
ylabel("\fontname{Times New Roman} Block Contribution Error");
|
||||
end
|
||||
|
||||
|
||||
xlabel("\fontname{Times New Roman} Block Sparsity \it K");
|
||||
ylabel("\fontname{Times New Roman} Block Contribution Error");
|
||||
|
||||
|
||||
t3 = result_cona;
|
||||
t4 = result_conb;
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
Binary file not shown.
Reference in New Issue
Block a user