For each iteration:

begin

For each pixel j:

begin $$\begin{array}{c}\hfill {\widehat{\mu }}_j^{\mathrm{old}}:={\widehat{\mu }}_j;\\ \hfill {\widehat{\mu }}_j^{\mathrm{new}}:=\frac{{\mathbf{A}}_j^T{\Sigma }^{-1}\widehat{\mathbf{r}}+{\lambda }_j{\widehat{\mu }}_j^{\mathrm{old}}+\beta \sum _{m\in A{W}_j}{b}_{jm}^{N{D}_{\_}predict}{\mu }_m}{{\lambda }_j+\beta \sum _{m\in A{W}_j}{b}_{jm}^{N{D}_{\_}predict}};\\ \hfill {\widehat{\mu }}_j:=\max \{0,{\widehat{\mu }}_j^{\mathrm{new}}\};\\ \hfill \widehat{\mathbf{r}}:=\widehat{\mathbf{r}}+{\mathbf{A}}_j\left({\widehat{\mu }}_j^{\mathrm{old}}-{\widehat{\mu }}_j\right);\end{array}$$

end

end