Algorithm 1: General DP-ADMM approach for image restoration variational models of the TV-KL form in (8) and (9) and automatic selection of $\mu$ via DP.
inputs: observed degraded image $\mathit{y}\in {\mathbb{N}}^m$, emission background $\mathit{b}\in {\mathbb{R}}_{+}^m$, blur and regularization operators $\mathbf{H}\in {\mathbb{R}}^{m\times n}$, $\mathbf{D}\in {\mathbb{R}}^{2n\times n}$
output: estimated restored image $\widehat{\mathit{x}}\in {\mathbb{R}}^n$
1. initialise: set ${\mathit{x}}^{\left(0\right)}=\mathit{y}$
2. for k = 0, 1, 2, $\dots$ until convergence do:
3.    $·$ compute ${\gamma }^{(k+1)}={\mu }^{(k+1)}/{\beta }_{\lambda }$	by (61) and (62)
4.    $·$ compute ${\mathit{\lambda }}^{(k+1)}$	by (63)
5.    $·$ compute ${\mathbf{g}}^{(k+1)}$	by (49)
6.    $·$ compute ${\mathit{z}}^{(k+1)}$	by (51)
7.    $·$ compute ${\mathit{x}}^{(k+1)}$	by (53)
8.    $·$ compute ${\mathit{\rho }}_{\lambda }^{(k+1)},{\mathit{\rho }}_g^{(k+1)},{\mathit{\rho }}_z^{(k+1)}$	by (45)–(47)
9. end for
10. $\widehat{\mathit{x}}={\mathit{x}}^{(k+1)}$