Algorithm 2 OMP

Input: $A=\Phi \Psi ,y,k$  Initialize:  $\left\{\begin{array}{cc}{r}_0=y\hfill & //residual\hfill \\ A_0=\varnothing \hfill & //columns\\ t=0\hfill & \end{array}\right.$  Output: k-sparse coefficient vector x  while$t<k$ do   ${\lambda }_t=\underset{j}{argmax}\left|a_j^T{r}_{t-1}\right|$  // find the column of A that is most strongly correlated with the residual   $A_t=\left[A_{t-1}{a}_{{\lambda }_t}\right]$  // merge the new column   $x_t=A_t^{†}y$  // find the best coefficients $x_t$ from (31)   $r_t=y-A_t{x}_t$  // update the residual   $t=t+1$  end while