# Lab Meeting 11/12/13: Spike Identification Using Continuous Basis Pursuit

In a previous lab meeting (7/9/13) we discussed the Continuous Basis Pursuit algorithm presented in Ekanadham et al., 2011.  In today’s meeting, we considered the recent work by the authors in applying this method to the problem of identifying action potentials of different neurons from extracellular electrode recordings (Ekanadham et al., 2013).   Most current methods for automatic spike sorting involve identifying candidate regions where a spike may have occurred, projecting the data from these candidate time intervals onto some lower dimensional feature space, and then using clustering methods to group segments with similar voltage traces.   These methods tend to perform badly when the waveforms corresponding to spikes from different neurons overlap.

The authors of this paper model the voltage trace as the (noisy) linear combination of waveforms that are translated continuously in time:  $V(t) = \sum_n^N \sum_i^C a_{n,i}W_n(t-\tau_{n,i}) + \epsilon(t)$.

The method proceeds, roughly, by alternately using least square to estimate the shape the waveforms $W_{n}$, and then using Continuous Basis Pursuit to estimate locations and amplitude ($\tau_{n,i}, a_{n,i}$) of the waveforms present in the signal.

References

• Ekanadham, Chaitanya, Daniel Tranchina, and Eero P. Simoncelli. “A unified framework and method for automatic neural spike identification.” Journal of neuroscience methods (2013).
• Ekanadham, Chaitanya, Daniel Tranchina, and Eero P. Simoncelli. “Recovery of sparse translation-invariant signals with continuous basis pursuit.” Signal Processing, IEEE Transactions on 59.10 (2011): 4735-4744.
• Ekanadham, Chaitanya, Daniel Tranchina, and Eero P. Simoncelli. “A blind sparse deconvolution method for neural spike identification.” Advances in Neural Information Processing Systems. 2011.