Table 2 Pseudocode of the QR-CS reconstruction algorithm.

Require:\(Y\in {R}^{N\times P}\), \(X\in {R}^{N\times P}\) and \(U\in {R}^{M\times P}\)

Ensure: \(A\in {R}^{N\times N}\) and \(B\in {R}^{N\times M}\)

1: input \(U\in {R}^{M\times P}\), set \({\parallel B\parallel }_{0}=k\)

2: for \(i=1\) to \(P+1\) do

3: \({X}^{i}={({x}_{1},{x}_{2},\cdots ,{x}_{N})}^{T}.\)

4: \({Y}^{i}={({y}_{1},{y}_{2},\cdots ,{y}_{N})}^{T}.\)

5: end for

6: \(X\in {R}^{N\times P}\mathop{\to }\limits^{QR\,decomposition}[{S}_{1},{S}_{2}][\begin{array}{c}{R}_{1}\\ 0\end{array}]\)

7: for \(i=1\) to \(N\) do

8: \({B}^{i}\mathop{\leftarrow }\limits^{CS\,reconstruction\,algorithm}({{{\rm{S}}}_{2}}^{T}* {Y}^{i},{{{\rm{S}}}_{2}}^{T}{* U}^{T}).\)

9: end for

10: \({B}_{i}\to {A}_{i}\)

11: \(A=[{A}^{1},{A}^{2},\cdots ,{A}^{N}]\in {R}^{N}.\)

12: return A.