This problem is exacerbated in multi-electrode recordings, in which each neuron may produce waveforms on multiple electrodes, and each electrode may contain waveforms arising from many cells. Although a variety of clustering methods have been developed to discriminate the waveforms of multiple neurons measured with a multi-electrode array, these methods still rely on the assumption that spikes occur in isolation, and fail to account for the linear superposition of spike waveforms. This problem is particularly severe when the problem of interest is the correlated activity from a neural population.

Here, we propose a Bayesian spike-sorting methodology that is robust to superposition of spiking waveforms. We explicitly model the raw signal data as a superposition of sparsely occurring multi-electrode waveforms, whose occurrences are governed by a Bernoulli process, against a background of correlated spatio-temporal Gaussian noise. We develop an algorithm for jointly estimating the spike trains and associated waveforms of each neuron, by approximately maximizing the posterior distribution for these parameters given the observed data. We illustrate the method's efficacy using several physiological datasets. We show that in many cases, our algorithm identifies significantly more spikes than than can be detected with standard thresholding or multi-dimensional clustering procedures, and that it corrects spike-train artifacts resulting from failures to detect synchronous activity.