Algorithm 3: SeededInitialization
Require: Input data matrix $Y$, matrix of binary masks $M$, number of background components ${\displaystyle n_b.}$
1:	${\displaystyle \mathbf{p}=\mathrm{f}\mathrm{i}\mathrm{n}\mathrm{d}(M\mathbf{1}==0)}$	Find the pixels not covered by any component.
2:	${\displaystyle [\sim ,\mathbf{f}]\leftarrow \mathrm{N}\mathrm{N}\mathrm{M}\mathrm{F}(Y[\mathbf{p},:],n_b)}$	Run NMF on these pixels just to get temporal backgrounds ${\displaystyle \mathbf{f}}$
3:	${\displaystyle \mathbf{b}\leftarrow {\mathrm{a}\mathrm{r}\mathrm{g}\mathrm{m}\mathrm{i}\mathrm{n}}_{\mathbf{b}\ge 0}\Vert Y-\mathbf{b}\mathbf{f}\Vert }$	Obtain spatial background ${\displaystyle \mathbf{b}}$.
4:	${\displaystyle C\leftarrow max\left((M^{\mathrm{\top }}M{)}^{-1}{M}^{\mathrm{\top }}(Y-\mathbf{b}\mathbf{f}),0\right)}$	Initialize temporal traces.
5:	${\displaystyle A\leftarrow {\mathrm{a}\mathrm{r}\mathrm{g}\mathrm{m}\mathrm{i}\mathrm{n}}_{A\ge 0,A(\sim M)==0}\Vert Y-\mathbf{b}\mathbf{f}-AC\Vert .}$	Initialize spatial footprints constrained within the masks.
6:	repeat	Optionally keep updating $A,C,\mathbf{𝐛},\mathbf{𝐟}$ using HALS
7:	${\displaystyle [\mathbf{b},\mathbf{f}]\leftarrow \mathrm{N}\mathrm{N}\mathrm{M}\mathrm{F}(Y-AC,n_b)}$
8:	${\displaystyle C\leftarrow {\mathrm{a}\mathrm{r}\mathrm{g}\mathrm{m}\mathrm{i}\mathrm{n}}_{C\ge 0}\Vert Y-\mathbf{b}\mathbf{f}-AC\Vert }$
9:	${\displaystyle A\leftarrow {\mathrm{a}\mathrm{r}\mathrm{g}\mathrm{m}\mathrm{i}\mathrm{n}}_{A\ge 0,A(\sim M)==0}\Vert Y-\mathbf{b}\mathbf{f}-AC\Vert }$
10:	until Convergence
11:	return $A,C,\mathbf{𝐛},\mathbf{𝐟}$