FastLZeroSpikeInference: FastLZeroSpikeInference: FastLZeroSpikeInference: A package...
In FastLZeroSpikeInference: Fast Nonconvex Deconvolution of Calcium Imaging Data

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 != max(gam c_t-1, EPS)]

for the global optimum, where y_t is the observed fluorescence at the tth timestep.

Constrained 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 != max(gam c_t-1, EPS)]

subject to c_t >= max(gam c_t-1, EPS), t = 2, ..., T

We introduce the constant EPS > 0, to avoid arbitrarily small calcium concentrations that would result in numerical instabilities. In practice, this means that the estimated calcium concentration decays according to the AR(1) model for values greater than EPS and is equal to EPS thereafter.

When estimating the spikes, it is not necessary to explicitly compute the calcium concentration. Therefore, if only the spike times are required, the user can avoid this computation cost by setting the estimate_calcium boolean to false. By default, the calcium concentration is not estimated.

Given the set of estimated spikes produced from the estimate_spike, the calcium concentration can be estimated with the estimate_calcium function (see examples below).

For additional information see:

1. Jewell, Hocking, Fearnhead, and Witten (2018) <arXiv:1802.07380> and

2. Jewell, Sean; Witten, Daniela. Exact spike train inference via l0 optimization. Ann. Appl. Stat. 12 (2018), no. 4, 2457–2482. doi:10.1214/18-AOAS1162. https://projecteuclid.org/euclid.aoas/1542078052

Estimate spikes: estimate_spikes estimate_calcium

Simulate: simulate_ar1

sim <- simulate_ar1(n = 500, gam = 0.95, poisMean = 0.009, sd = 0.05, seed = 1)
plot(sim)

## Fits for a single tuning parameter

# AR(1) model
fit <- estimate_spikes(dat = sim$fl, gam = 0.95, lambda = 1)
print(fit)

# compute fitted values from prev. fit
fit <- estimate_calcium(fit)
plot(fit)

# or
fit <- estimate_spikes(dat = sim$fl, gam = 0.95, lambda = 1, estimate_calcium = TRUE)
plot(fit)

# Constrained AR(1) model
fit <- estimate_spikes(dat = sim$fl, gam = 0.95, lambda = 1, constraint = TRUE,
                                                    estimate_calcium = TRUE)
print(fit)
plot(fit)