Algorithm 1 ISTA

1: Input: measurement matrix $\mathbf{D}$, measurement signal $x$.

2: Initialization: $\eta \in \left(0,1/\left|\right|D^{T}D\left|\right|\right)$, $\lambda >0,{\mathsf{\alpha }}_0=0,k=0$

3: Main iteration: increment $k$ by 1

4: ${\mathsf{\alpha }}_k=$ ${\pi }_{\lambda \eta }$ $\left({\mathsf{\alpha }}_{k-1}-\eta \nabla f\left({\mathsf{\alpha }}_{k-1}\right)\right)$

5: Stopping rule: stop if ${\mathsf{\alpha }}_k$ has converged

6: Output: sparse signal $\mathsf{\alpha }$