Algorithm 1.

SALSA Algorithm

Input: A, η, b, k = 0, u0, f0

Output: x k+1

Repeat till convergence is satisfied

$x_{k+1}=\text{arg}\hspace{0.17em}{\mathit{min}}_x{\Vert \mathbf{A}x-b\Vert }_2^2+\eta {\Vert x-u_k-f_k\Vert }_2^2$

$u_{k+1}=\text{arg}\hspace{0.17em}{\mathit{min}}_u\tau \varphi (u)+(\eta /2){\Vert x_{k+1}-u-f_k\Vert }_2^2$

fk+1 = fk − (xk+1 − uk+1)

k = k + 1