Init

README.md

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+This project is used to host the code that reproduces [this academic paper](https://ieeexplore.ieee.org/document/9497742)
+
+Enviornment:
+
+- [MATLAB 2023a](https://ww2.mathworks.cn/products.html?s_tid=gn_ps)
+- [CVX: a Matlab-based convex modeling framework](http://cvxr.com/)
+- [Parallel Computing Toolbox](https://ww2.mathworks.cn/products/parallel-computing.html)
+
+Codes:
+
+- `can_recovery.m`: Determine if the signal can be recovered.
+- `get_recovery_prob.m`: Obtain the probability that the signal can be recovered under T experiments.
+- `main.m`: Main function entry.

can_recovery.m

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+function flg = can_recovery(n, s)
+    d = 100;
+    eps = 1e-5;
+    theta = randn(n, d);
+    y = theta * x;
+    
+    x = zeros(d, 1);
+    random_indices = randperm(d, s);
+    x(random_indices) = randn(s, 1);
+    x = sign(x);
+
+    cvx_begin
+        variable s1(d)
+        minimize(norm(s1, 1))
+        subject to
+            norm(y - theta * s1) <= eps
+    cvx_end
+
+    p = norm(x-s1, 2);
+    if p < eps
+        flg = 1;
+    else
+        flg = 0;
+    end
+end

get_recovery_prob.m

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+function x = get_recovery_prob(n, s, N)
+    x = 0;
+    for t = 1: N
+        x = x + can_recovery(n, s);
+    end
+    x = x / N;
+end

main.m

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+N = 100;
+M = 100;
+T = 50;
+
+prob = zeros(N, M);
+parfor n = 1: N
+    for s = 1: M
+        prob(n, s) = get_recovery_prob(n, s, T);
+    end
+end
+heatmap(prob)