Algorithm 1 Orthogonal Matching Pursuit (OMP)

Input: A signal $\mathit{y}\in {ℝ}^N$, a matrix $A\in {ℝ}^{M\times N}$. Initialize: Set the support set ${\mathsf{\Omega }}_0=\varnothing$, the residual error ${\mathit{r}}_0=\mathit{y}$ and put the counter $k=1$. Identify: Find a column ${\mathit{a}}_n$ from A that most correlates with the residual error and record the correlation coefficient: $$n_k\in \arg \underset{n=1,2,\dots N}{\max }\left|\langle {\mathit{r}}_{k-1},{\mathit{a}}_n\rangle \right|,{\mathsf{\Omega }}_k={\mathsf{\Omega }}_{k-1}\cup \left\{n_k\right\}$$ Estimate: compute the best approximating coefficients: $${\mathit{x}}_k=\arg {\min }_x{\Vert \mathit{y}-A_{{\mathsf{\Omega }}_k}\mathit{x}\Vert }_2$$ Iterate: Update the residual and counter: $${\mathit{r}}_k=\mathit{y}-A_{{\mathsf{\Omega }}_k}{\mathit{x}}_k,k=k+1$$ Until: Stopping criterion holds. Output: The vector $\widehat{\mathit{x}}$ with components $\widehat{x}(n)=x_k(n)(n\in {\mathsf{\Omega }}_k)$ and $\widehat{x}(n)=0$ otherwise.