A Robust and Efficient Method to Recover Neural Events from Noisy and Corrupted Data Eva L. Dyer, Christoph Studer, Jacob T. Robinson, and Richard G. Baraniuk Dept. of Electrical & Computer Engineering, Rice University e-mail: {e.dyer, studer, jtrobinson, richb}@rice.edu Abstract—In a variety of neural data analysis problems, “neural events” such as action potentials or post-synaptic poten- tials (PSPs), must be recovered from noisy and possibly corrupted measurements. For instance, in calcium imaging, an action poten- tial or group of action potentials give rise to a stereotyped calcium signal with quick rise and slow decay. In this work, we develop a general-purpose method for learning a template waveform that characterizes the waveform of neural events and neural event recovery to determine the times at which such events occur. Our approach is based upon solving a sparse signal separation problem to separate the neural signal of interest from any noise and other corruptions that arise due to baseline drift, measurement noise, and breathing/motion artifacts. For both synthetic and real data, we demonstrate that our approach accurately detects neural events and learns the underlying template waveform, even in the presence of strong amounts of noise and corruptions. The method’s robustness and simplicity makes is amenable for use in the analysis of datasets arising in large-scale studies of both time-varying calcium imaging and whole cell electrophysiology. I. I NTRODUCTION Experimental neuroscience has experienced dramatic growth over the past few years. Out of this growth, experimen- talists now possess the tools necessary to modulate and record from increasingly large populations of neurons [1]. In order to analyze the data generated from large-scale experiments, computationally efficient, robust, and automated methods for neural data analysis are of paramount importance. While a great deal of work has focused on the detection and classification of spikes (the basic unit of information in neural systems) from both single and multi-electrode arrays, researchers are increasingly turning toward optical imaging techniques that have the potential to record from a greater number of individual neurons. The fact that these methods (voltage or calcium-sensitive imaging) rely on indirect optical measurements of the transmembrane voltage, the resulting estimates of spike timing are often imprecise. Further com- plicating things is the fact that the signal generated from a sequence of spikes is often corrupted by noise and/or an additive baseline or drift component that can vary in its structure, depending on the experimental setup and conditions. In many settings, neural signals that are associated with either the action potentials (APs) of the cell-under-test or the neural events generated by the pre-synaptic partners of the cell-under-test (post synaptic potentials), give rise to a stereotyped waveform that can be modeled by a common template waveform that approximates the time-course of the neural signal produced by a single spike event. Thus, a common method to extract the times at which events occur, is to use a matched filter to correlate the known template with the measured signal [2]. If the correlation between the template and the signal exceeds a certain threshold, then such algorithms declare the presence of a spike event. Previous studies of event detection in both the analysis of PSPs and calcium imaging data, have demonstrated that standard tem- plate matching-based approaches that rely on the correlation between the observations are unable to resolve events that occur in rapid succession or appear in noisy conditions [3], [4]. Hence, deconvolution methods that aim to reverse the effects of convolution on the data, are employed to improve the temporal resolution of correlation-based methods. In this work, we develop a novel, robust method for neural event detection that improves upon state-of-the-art deconvolution-based methods such as [5], [3] in a number of ways. First, we introduce a novel sparsity-based deconvolution approach that not only finds an estimate of the time and amplitude of neural events but also separates it from the baseline and noise components corrupting the measurement of the neural activity. By exploiting known signal structure in both the neuronal signal and the baseline component, we demonstrate that the proposed approach reliably recovers the neuronal signal from significant amounts of baseline drift and noise, in both real and synthetic data. The second contribution is the development of a alternating minimization framework for obtaining estimates of the underlying template waveform that generated the observed signal. This template learning method employs a constrained least-squares (LS) method to learn a kernel without any assumed parametric model; instead, we simply enforce the fact that the template must be non- negative and of limited duration relative to the length of the measurement. Our results on both synthetic and real data demonstrate that the proposed approach provides a nearly parameter-free method that enables accurate and robust event recovery from large-scale experimental datasets. II. SIGNAL MODEL AND SPARSE SIGNAL RECOVERY We start by introducing a convolution-based signal model for neuronal signals arising in calcium imaging and electro- physiology recordings. We then show how this model can be used to derive a robust and computationally efficient deconvolution approach to detect neural events.