Exact spike train inference via $\ell_{0}$ optimization

Abstract

In recent years new technologies in neuroscience have made it possible to measure the activities of large numbers of neurons simultaneously in behaving animals. For each neuron a fluorescence trace is measured; this can be seen as a first-order approximation of the neuron’s activity over time. Determining the exact time at which a neuron spikes on the basis of its fluorescence trace is an important open problem in the field of computational neuroscience. Recently, a convex optimization problem involving an ℓ1 penalty was proposed for this task. In this paper we slightly modify that recent proposal by replacing the ℓ1 penalty with an ℓ0 penalty. In stark contrast to the conventional wisdom that ℓ0 optimization problems are computationally intractable, we show that the resulting optimization problem can be efficiently solved for the global optimum using an extremely simple and efficient dynamic programming algorithm. Our R-language implementation of the proposed algorithm runs in a few minutes on fluorescence traces of 100,000 timesteps. Furthermore, our proposal leads to substantial improvements over the previous ℓ1 proposal, in simulations as well as on two calcium imaging datasets. R-language software for our proposal is available on CRAN in the package LZeroSpikeInference. Instructions for running this software in python can be found at https://github.com/jewellsean/LZeroSpikeInference.

SCALPEL: Extracting neurons from calcium imaging data

“…If this is the case, it may be desirable to incorporate more sophisticated modeling of the background noise, like that employed in Zhou et al (2016). Additionally, in future work we could modify Step 3 of SCALPEL to make use of a more refined model for neuron spiking, as in Friedrich, Zhou and Paninski (2017), Vogelstein et al (2010), Jewell and Witten (2018).…”

Inferring the Spiking Rate of a Population of Neurons from Wide-Field Calcium Imaging

“…Problem (5) closely resembles the optimization problem (2) used to deconvolve the fluorescence trace for a single neuron (Friedrich et al 2017, Jewell & Witten 2018, Jewell et al 2019. For that task, the authors considered the use of a sparsity-inducing penalty, because a neuron is not expected to spike at most timepoints.…”

“…The problem of inferring the underlying neuronal activity from a fluorescence trace has recently been considered by a number of authors, in the case of fluorescence traces that result from the activity of a single neuron (Jewell & Witten 2018, Jewell et al 2019, Friedrich et al 2017, Pnevmatikakis et al 2016). These papers make use of an auto-regressive model, originally proposed in Vogelstein et al (2009), that associates the fluorescence y t of a single neuron at the tth timepoint with the unobserved calcium c t at the tth timepoint,…”

“…In (1), β 0 corresponds to the baseline fluorescence, which must be estimated; however, we can set β 1 = 1 without loss of generality, as this simply amounts to scaling the calcium by a constant factor. To fit the model (1) with β 1 = 1, Friedrich et al (2017), Jewell & Witten (2018), and Jewell et al (2019) solve the optimization problem…”

“…where λ is a nonnegative tuning parameter, and where P (·) is a penalty function designed to induce sparsity in its argument -that is, to encourage c t − γc t−1 = s t = 0 -so that at most timepoints, no spike is estimated to occur. Friedrich et al (2017) makes use of an 1 penalty (Tibshirani 1996), while Jewell & Witten (2018) and Jewell et al (2019) instead use an 0 penalty. However, fluorescence traces that result from wide-field calcium imaging recordings correspond to the activity of a collection of neurons rather than the activity of a single neuron.…”