Update Expr3

Phase Transitions in FAR using CS/Expr3_can_recovery.m

@@ -1,39 +1,25 @@
 function flg = Expr3_can_recovery(Phi_far, N, M, n, s, eps)
-    Phi = zeros(n, N * M);
-    indices = randperm(N, n);
 
-    for i = 1:n
-        Phi(i, :) = Phi_far(indices(i), :);
-    end
-    d = M*N;
-    x = zeros(d, 1);
-    random_indices = randperm(d, s);
-    x(random_indices) = randn(s, 1);
-    x = sign(x);
+    % select random n cols
+    col_choose = randperm(N, n);
+    Phi = Phi_far(col_choose, :);
 
-    for i = 1:M * N
+    % generate sparse signal
+    sparse_signal = zeros(M, N);
+    block = randperm(N, s);
+    sparse_signal(:, block) = exp(1i * 2 * pi * rand(M, s));
 
-        if x(i) ~= 0
-            t = rand(1) * 2 * pi;
-            x(i) = cos(t) + 1j * sin(t);
-        end
-
-    end
-
-    y = Phi * x;
+    % generate y
+    y = Phi * sparse_signal(:);
 
     cvx_begin quiet
-        variable s1(d) complex
-        minimize(norm(s1, 1))
-        subject to
-        norm(y - Phi * s1) <= eps
+    variable x(M * N) complex
+    minimize(norm(x, 1))
+    subject to
+    Phi * x == y
     cvx_end
 
-    x = sign(real(x));
-    s1 = real(s1);
-    
-    p = norm(x - s1, 2);
-    disp(p);
+    p = norm(x - sparse_signal(:), 2);
 
     if p < eps
         flg = 1;