Algorithm 1 The MM1-CD algorithm for spatially non-uniform white noise.

1:Give ${\mathbf{r}}_0$ and $ϵ$, 2:$u=0$, 3: repeat 4:    ${\mathbf{W}}_u=\mathbf{B}Diag\left({\mathbf{r}}_u\right){\mathbf{B}}^H+{\mathbf{J}}_m$, 5:    Calculate ${\mathbf{M}}_u$ and ${\mathbf{w}}_u$, 6:    $d=0$, 7:    ${\mathbf{r}}^0={\mathbf{r}}_u$, $\mathbf{r}={\mathbf{r}}^0$, 8:    repeat 9:        for $i=1:k+m-1$ do 10:           ${\mathbf{N}}_i={\sum }_{l\ne i}{r}_l{\mathbf{b}}_l{\mathbf{b}}_l^H+{\mathbf{J}}_m$, 11:           Calculate ${\alpha }_i$, ${\beta }_i$ and ${\gamma }_i$, 12:           if ${\beta }_i\le {\alpha }_i$ then 13:               $r_i=0$, 14:           else 15:               $r_i=(\sqrt{{\beta }_i/{\alpha }_i}-1)/{\gamma }_i$, 16:           end if 17:        end for 18:        $d=d+1$, 19:        ${\mathbf{r}}^d={[r_1,\dots ,r_{k+m-1}]}^T$, 20:    until $\parallel {\mathbf{r}}^d-{\mathbf{r}}^{d-1}{\parallel }_2/{\parallel {\mathbf{r}}^{d-1}\parallel }_2<ϵ$, 21:    $u=u+1$, 22:    ${\mathbf{r}}_u={\mathbf{r}}^d$, 23:until$\parallel {\mathbf{r}}_u-{\mathbf{r}}_{u-1}{\parallel }_2/{\parallel {\mathbf{r}}_{u-1}\parallel }_2<ϵ$.