56 lines
1.4 KiB
Matlab
56 lines
1.4 KiB
Matlab
%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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