EXACT SPIKE TRAIN INFERENCE VIA ℓ0 OPTIMIZATION

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.
Comment: 28 pages, 6 figures