Algorithm 1. NMF algorithm using localization constraints and spatio-temporal decimation.

Required: data $Y\in {\mathbb{R}}_{+}^{D\times T}$, N neuron centers, number of iterations $\tilde{I}$ and I
1: successively take mean of e.g. 30 frames        ⊳ operate on decimated data
2: initialize centers using greedy (or group lasso) method from [8]
3: downscale spatially using local mean: $Y\to \tilde{Y}\in {\mathbb{R}}_{+}^{\tilde{D}\times \tilde{T}}$
4: generate patches $\tilde{P}$ around centers
5: initialize spatial background as 20% percentile, neural shapes as Gaussians within patch: $\tilde{A}\in {\mathbb{R}}_{+}^{\tilde{D}\times (N+1)}$
6: initialize temporal background as ${\mathbf{1}}_{\tilde{T}}$, neural activities as data at centers: $\tilde{C}\in {\mathbb{R}}_{+}^{(N+1)\times \tilde{T}}$
7: fori = 1, …, $\tilde{I}$do
8:  $\tilde{C}$ ← HALSactivity($\tilde{Y},\tilde{A},\tilde{C}$)
9:  $\tilde{A}$ ← HALSshape($\tilde{Y},\tilde{A},\tilde{C},\tilde{P}$)
10: initialize activities $C\in {\mathbb{R}}_{+}^{(N+1)\times T}$ as mean of $\tilde{C}$ for each neuron     ⊳ back to full data
11: initialize shapes $A\in {\mathbb{R}}_{+}^{D\times (N+1)}$ by zero-order-hold upsampling of $\tilde{A}$
12: generate patches P
13: fori = 1, …, Ido
14:  C ← HALSactivity(Y, A, C, 5)          ⊳ note the increased inner iterations
15:  A ← HALSshape(Y, A, C, P, 5)
16: denoise C using OASIS [18]
17: returnA, C
1: function HALSactivity(Y, A, C, I = 1)	1: function HALSshape(Y, A, C, P, I = 1)
2:  U = A⊤Y	2:  U = CY⊤
3:  V = A⊤A	3:  V = CC⊤
4:  fori = 1, …, Ido	4:  fori = 1, …, Ido
5:   forn = 1, …, Ndo	5:   forn = 1, …, N + 1 do
6:    $C_{n,:}\leftarrow \text{max}(0,C_{n,:}+\frac{U_{n,:}-{\sum }_j{V}_{n,j}{C}_{j,:}}{V_{n,n}})$	6:    $A_{n,:}\leftarrow P_{n,:}\odot \text{max}0,\left(A_{n,:}+\frac{U_{n,:}-{\Sigma }_j{V}_{n,j}{A}_{j,:}^{\top }}{V_{n,n}}\right)$
7:   $C_{N+1,:}\leftarrow C_{N+1,:}+\frac{U_{N+1,:}-{\sum }_j{V}_{N+1,j}{C}_{j,:}}{V_{N+1,N+1}}$	7:
8:  returnC	8:  returnA