Algorithm 4: Orthogonal matching pursuit

Input: Measurement vector y, M × N matrix A, signal sparsity K ▪Set initial residual: $r_0\leftarrow y$ ▪Set initial indices: ${\mathsf{\Omega }}_0\leftarrow \mathbf{\varnothing }$ ▪Set matrix of chosen columns: ${\mathsf{\Theta }}_0\leftarrow []$ ▪for$i\leftarrow 1\hspace{1em}\mathbf{to}\hspace{1em}K$     ${\omega }_i=\underset{j=1,\dots ,N}{\arg \max }\left|\langle r_{i-1},{\mathbf{A}}_j\rangle \right|$    - maximum correlation column     ${\mathsf{\Omega }}_i\leftarrow {\mathsf{\Omega }}_{i-1}\cup {\mathit{\omega }}_i$        - update set of indices     ${\mathsf{\Theta }}_i\leftarrow \left[{\mathsf{\Theta }}_{i-1}{A}_{{\mathit{\omega }}_i}\right]$        - update set of chosen columns     $x_i=\underset{x}{\arg \min }{\left|\left|r_{i-1}-{\mathsf{\Theta }}_{i}x\right|\right|}_2^2$     $a_i\leftarrow {\mathsf{\Theta }}_i{x}_i$     $r_i\leftarrow y-a_i$ ▪end for Output: xK and ${\mathsf{\Omega }}_K$