Spike Estimation From Fluorescence Signals Using High-Resolution Property of Group Delay

TLDR: The proposed approach, GD spike, is compared with other spike estimation methods, including MLspike, Vogelstein de-convolution algorithm, and data-driven spike-triggered mixture model and shows superior results.

Abstract: Spike estimation from calcium (Ca $^{2+}$ ) fluorescence signals is a fundamental and challenging problem in neuroscience. Several models and algorithms have been proposed for this task over the past decade. Nevertheless, it is still hard to achieve accurate spike positions from the Ca $^{2+}$ fluorescence signals. While existing methods rely on data-driven methods and the physiology of neurons for modeling the spiking process, this paper exploits the nature of the fluorescence responses to spikes using signal processing. We first motivate the problem by a novel analysis of the high-resolution property of minimum-phase group delay (GD) functions for multi-pole resonators. The resonators could be connected either in series or in parallel. The Ca $^{2+}$ indicator responds to a spike with a sudden rise, that is followed by an exponential decay. We interpret the Ca $^{2+}$ signal as the response of an impulse train to the change in Ca $^{2+}$ concentration, where the Ca $^{2+}$ response corresponds to a resonator. We perform minimum-phase GD-based filtering of the Ca $^{2+}$ signal for resolving spike locations. The performance of the proposed algorithm is evaluated on nine datasets spanning various indicators, sampling rates, and mouse brain regions. The proposed approach, GDspike, is compared with other spike estimation methods, including MLspike, Vogelstein de-convolution algorithm, and data-driven spike-triggered mixture model. The performance of GDspike is superior to that of the Vogelstein algorithm and is comparable to that of MLspike. It can also be used to post-process the output of MLspike, which further enhances the performance.