Algorithm 1: Orthogonal matching pursuit (OMP)

Input: $A,y,K$

Output: $\theta$

1 Initialization $r0=\theta$, ${\Lambda }_0=\varnothing ;$

2 Normalize all columns of $A$ to unit L2 norm;

3 for k = 1,2, …, K do

4            Step 1:      ${\lambda }_k{=}_{j\notin {\Lambda }_{k-1}}^{\mathit{arg}\mathit{max}\left|⟨a_j,r_{\kappa -1}⟩\right|};$

5            Step 2:      ${\Lambda }_k={\Lambda }_{K-1}\cup {\lambda }_k;$

6            Step 3:      $x_k\left(i\in {\Lambda }_k\right){=}_x^{\mathit{arg}\mathit{min}{‖A_{{\Lambda }_k}x-y‖}_2};$

7            Step 4:      $\widetilde{{\theta }_k}=A{x}_k;$

8            Step 5:      ${\gamma }_k=\theta -\widetilde{{\theta }_k};$

9 end