SWOMP algorithm:

Input parameters: observation y, measurement matrix Φ, number of iterations S, threshold value $\alpha$.

Output parameters: sparse signal $\stackrel{\wedge }{\theta }$.

Initialization: signal margin r = y, sparse signal $\stackrel{\wedge }{\theta }=0$, index set ${\Lambda }_0=\varnothing$, number of iterations k = 1, support set $A_0=\varnothing$.

(1) Calculate the correlation coefficient $u=\left\{u_i|u_i=|\langle r,{\phi }_i\rangle |,i=1,2,\cdots ,N\right\}$.

(2) Select a value greater than $Th=\alpha \underset{i=1,2,\cdots ,N}{argmax}|\langle r,{\phi }_i\rangle |$ in u and constitute the serial number corresponding to the selected value to form set $J_0$.

(3) Update the index set and the support set; let ${\Lambda }_k={\Lambda }_{k-1}{{\displaystyle \cup }}^{\text{}}{J}_0$ and $A_k=A_{k-1}{{\displaystyle \cup }}^{\text{}}{\phi }_{J_0}$. If ${\Lambda }_k={\Lambda }_{k-1}$, stop iteration, and turn to Step (6).

(4) Calculate the least-squares solution of $y=A_k{\stackrel{\wedge }{\theta }}_k,$ ${\stackrel{\wedge }{\theta }}_k={\left(A_k^T{A}_K\right)}^{-1}{A}_k^{T}y$, and update the residual $r_k=y-A_k{\stackrel{\wedge }{\theta }}_k=y-{\left(A_k^T{A}_k\right)}^{-1}{A}_k^{T}y$.

(5) Let k = k + 1. If $k\le S$, return to Step (2); otherwise, stop iteration.

(6) Output sparse signal.