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 \(\ell_1\) penalty was proposed for this task. In this paper, we slightly modify that recent proposal by replacing the \(\ell_1\) penalty with an \(\ell_0\) penalty. In stark contrast to the conventional wisdom that \(\ell_0\) 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 \(\ell_1\) proposal, in simulations as well as on two calcium imaging data sets. 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....

Exact Spike Train Inference Via \(\ell_0\) Optimization