Table 1:

Algorithm for SAR update

Flatten Z(k), U(k) into vectors z(k), u(k)

GIVEN: z(k), u(k), y[j] = z(k) − u(k); j, G[j], w[j] from prior ADMM iterations

REPEAT:

1. Update the matrix of normal vectors G[j] by appending the normal vector at y[j].

2. Update the vector of intercepts w[j] by appending the intercept at y[j].

3. Update pulse by minimizing the PLA + PENALTY function with the refined piecewise linear approximation:

${\underset{\_}{\mathit{y}}}^{[j+1]}={\mathrm{a}\mathrm{r}\mathrm{g}\mathrm{m}\mathrm{i}\mathrm{n}}_{\underset{\_}{\mathit{y}}}(\text{max}\left(G^{\left[j\right]T}\underset{\_}{\mathit{y}}+w^{\left[j\right]}\right)+\frac{\rho }{2}{\Vert \underset{\_}{\mathit{y}}-{\underset{\_}{\mathit{z}}}^{\left(k\right)}+{\underset{\_}{\mathit{u}}}^{\left(k\right)}\Vert }_2^2)$

4. j = j + 1

UNTIL: COST stops changing

Reshape y[j] into Y(k)