Algorithm 2 Generating measurement matrices using 2D hyperchaotic map.

Input: Parameters of the hyperchaotic system $a,b$; initial values of the system state $x_0,y_0$; number of rows of the image matrix: N; compressed sensing parameter: $subrate$. Output: Two measurement matrices: ${\mathsf{\Phi }}_1$ and ${\mathsf{\Phi }}_2$. 1:Initialize two one-dimensional arrays $\mathbf{U}$ and $\mathbf{V}$ of size $N\times N$; 2:Let $\mathbf{U}\left(1\right)=x_0$ and $\mathbf{V}\left(1\right)=y_0$; 3:for $i=2:N\times N$ do 4:   $\mathbf{U}\left(i\right)={sin}^2(a\pi \mathbf{U}(i-1)+b\mathbf{V}(i-1))$; 5:   $\mathbf{V}\left(i\right)={cos}^2(b\pi /\mathbf{V}(i-1)+a\mathbf{U}(i-1))$; 6:end for 7:$\mathbf{U}=reshape(\mathbf{U},N,N)$; 8:$\mathbf{V}=reshape(\mathbf{V},N,N)$; 9:$M=round(\sqrt{subrate}\times N)$; 10:${\mathsf{\Phi }}_1=orth\left(\mathbf{U}\right)$; ${\mathsf{\Phi }}_1={\mathsf{\Phi }}_1(1:M,:)$; 11:${\mathsf{\Phi }}_2=orth\left(\mathbf{V}\right)$; ${\mathsf{\Phi }}_2={\mathsf{\Phi }}_2(1:M,:)$;