Algorithm 2. SIRA

Input:     Measurement vector y; M × N matrix A; signal sparsity K ○Set desired probability (e.g., $P\leftarrow 0.99$) ○ Calculate variance—variance is calculated by using one of the relations, depending on the chosen transformation domain. The corresponding equations are in the following table: Transformation domain DFT DCT HT Variance $\begin{array}{c}\hspace{1em}{\mathit{\sigma }}_{MS}^2=\\ =M\frac{N-M}{N-1}{\displaystyle \sum _{i=1}^M\frac{y{(i)}^2}{M}}\end{array}$ $\begin{array}{c}\hspace{1em}{\mathit{\sigma }}_{MS}^2=\\ =M\frac{N-M}{N^2(N-1)}{\displaystyle \sum _{i=1}^K{A}_i^2},\end{array}$ $\begin{array}{c}\hspace{1em}{\mathit{\sigma }}_{MS}^2=\\ =\frac{(N-M)M-{(N-M)}^2}{M^2(M-1)}{\displaystyle \sum _{i=1}^K{A}_i^2}\end{array}$ $\begin{array}{c}\hspace{1em}{\displaystyle \sum _{i=1}^K{A}_i^2}=\frac{N}{M}{\displaystyle \sum _{n\in M}^{}{s}^2(n),}\\ \\ \hspace{1em}s(n)-\mathrm{available} \mathrm{samples}\end{array}$ ○For a given P calculate threshold according to relation (13); ○$\mathrm{Calculate} \mathrm{the} \mathrm{initial} \mathrm{transform} \mathrm{domain} \mathrm{vector} {\mathbf{X}}_{\mathbf{0}}: {\mathbf{X}}_{\mathbf{0}}={\mathbf{A}}^{-1}\mathbf{y}$; ○$\mathrm{Find} \mathrm{positions} \mathrm{of} \mathrm{components} \mathrm{in} \mathbf{X} \mathrm{higher} \mathrm{than} \mathrm{normalized} \mathrm{threshold} T, \mathbf{k}=\arg \{\left|{\mathbf{X}}_{\mathbf{0}}\right|>T/N\}$; ○$\mathrm{Form} \mathrm{CS} \mathrm{matrix} \mathrm{by} \mathrm{using} \mathrm{only} \mathbf{k} \mathrm{columns} \mathrm{from} \mathbf{A}, {\mathbf{A}}_{CS}\leftarrow \mathbf{A}(\mathbf{k})$ ○$\mathrm{Calculate} {\mathbf{X}}_R={\left({\mathbf{A}}_{CS}^T{\mathbf{A}}_{CS}\right)}^{-1}{\mathbf{A}}_{CS}^T\mathbf{y}$;  Output: XR