# LZeroSpikeInference: A package for estimating spike times from calcium imaging data using an L0 penalty

This package implements an algorithm for deconvolving calcium imaging data for a single neuron in order to estimate the times at which the neuron spikes.

This algorithm solves the optimization problems ### AR(1) model minimize_{c1,…,cT} 0.5 sum_{t=1}^T ( y_t - c_t )^2 + lambda sum_{t=2}^T 1_{c_t neq gamma c_{t-1} }

for the global optimum, where y_t is the observed fluorescence at the tth timepoint. We also solve the above problem with the constraint that c_t >= 0 (hardThreshold = T).

### AR(1) with intercept

minimize_{c1,…,cT,b1,…,bT} 0.5 sum_{t=1}^T (y_t - c_t - b_t)^2 + lambda sum_{t=2}^T 1_{c_t neq gamma c_{t-1}, b_t neq b_{t-1} }

where the indicator variable 1_{(A,B)} equals 1 if the event A cup B holds, and equals zero otherwise.

## Install

In R, if `devtools`

is installed type

`devtools::install_github("jewellsean/LZeroSpikeInference")`

## Usage

Once installed type

```
library(LZeroSpikeInference)
?LZeroSpikeInference
```

## Python

This package can be called from Python using the py2 package. To install LZeroSpikeInference and rpy2 for use in Python first

- Install R (for example
`apt-get install r-base`

)

and then from within R install this package (as above). Then pip install rpy2

- pip install –user rpy2

The following example illustrates use of the LZeroSpikeInference package from python

```
from numpy import array
import rpy2.robjects.packages
lzsi = rpy2.robjects.packages.importr("LZeroSpikeInference")
d = lzsi.simulateAR1(n = 500, gam = 0.998, poisMean = 0.009, sd = 0.15, seed = 8)
fit = lzsi.estimateSpikes(d[1], **{'gam':0.998, 'lambda':8, 'type':"ar1"})
spikes = array(fit[0])
fittedValues = array(fit[1])
```

Thanks to Luke Campagnola for suggesting this approach!

## Reference

See Jewell and Witten, Exact Spike Train Inference Via L0 Optimization (2017)