We consider the problem of recovering spike times from extracellular voltage recordings, assuming the waveforms associated with each neuron are known. The voltage signal is assumed to be a noisy sum of the convolutions of the waveforms with their respective spike trains. This is a binary deconvolution problem that can be solved exactly only through exhaustive search, making it intractable in practice. Standard approximate solutions fall into two broad categories: (1) greedy algorithms based on thresholding a measure of distance between segments of the voltage signal and the waveforms (e.g., clustering [1] or matched filtering), and (2) penalized least squares methods [3, 4]. The first class often fails to correctly resolve spikes when two or more waveforms overlap in the signal (e.g., when two neurons have highly correlated activity). In typical implementations, both methods also suffer from the fact that they only seek solutions in terms of waveforms positioned on a discrete lattice. We propose a novel method, called continuous basis pursuit, that adapts the LASSO [3] for sparse linear inverse problems to explicitly handle continuous time shifts. We construct a dictionary of basis functions that can linearly combine to approximate superpositions of arbitrarily translated waveforms via interpolation, and derive a closed form expression for extracting the analog spike times from this linear representation. To obtain the coefficients, we formulate a convex optimization problem that can be efficiently solved using standard methods. We validate our method on simulated spike trains using waveforms taken from recordings in macaque retinal ganglion cells. We show that our method significantly outperforms standard greedy and penalized least squares methods in recovering the spike times, due to the fact that it accounts for both waveform superposition and the continuous nature of spike times. [1] M. S. Lewicki. A review of methods for spike sorting: the detection and classification of neural action potentials. Network, 9(4):R53-R78, Nov 1998.
[2] S. Mallat and Z. Zhang. Matching pursuits with time-frequency dictionaries. IEEE Trans Sig Proc, 41(12):3397-3415, Dec 1993.
[3] R. Tibshirani. Regression shrinkage and selection via the lasso. J Royal Statistical Society, Series B (Methodological), 58(1):267-288, 1996.
[4] S.S. Chen, D.L. Donoho, and M.A. Saunders. Atomic decomposition by basis pursuit. SIAM Journal on Scientific Computing, 20(1):33-61, 1998.
Related Publications: Ekanadham11, Ekanadham11aListing of all publications