Sparse Deconvolution with Applications to Spike Sorting

Chronic extracellular recording is the use of implanted electrodes to measure the electrical activity of nearby neurons over a long period of time. It presents an unparalleled view of neural activity over a broad range of time scales, offering sub-millisecond resolution of single action potentials while also allowing for continuous recording over the course of many months. These recordings pick up a rich collection of neural phenomena -- spikes, ripples, and theta oscillations, to name a few -- that can elucidate the activity of individual neurons and local circuits. However, this also presents an interesting challenge for data analysis. Chronic extracellular recordings contain overlapping signals from multiple sources, requiring these signals to be detected and classified before they can be properly analyzed. The combination of fine temporal resolution with long recording durations produces large datasets, requiring efficient algorithms that can operate at scale. In this thesis, I consider the problem of spike sorting: detecting spikes (the extracellular signatures of individual neurons' action potentials) and clustering them according to their putative source. First, I introduce a sparse deconvolution approach to spike detection, which seeks to detect spikes and represent them as the linear combination of basis waveforms. This approach is able to separate overlapping spikes without the need for source templates, and produces an output that can be used with a variety of clustering algorithms. Second, I introduce a clustering algorithm based around a mixture of drifting t-distributions. This model captures two features of chronic extracellular recordings -- cluster drift over time and heavy-tailed residuals in the distribution of spikes -- that are missing from previous models. This enables us to reliably track individual neurons over longer periods of time. I will also show that this model produces more accurate estimates of classification error, which is an important component to proper interpretation of the spike sorting output. Finally, I present a few theoretical results that may assist in the efficient implementation of sparse deconvolution.</p