Estimation of templates and timings of spikes in extracellular voltage signals containing overlaps of the arbitrary number of spikes

Development of methods to detect and classify neural spikes in extracellular voltage signals (e.g. commonly referred to as spike sorting) have been one of important subjects in neuroscience and neural engineering. Most of previous spike sorting methods suffer from unresolved overlaps of spike waveforms which make timings and shapes of spikes unclear. Some methods have got a handle on this problem, but they had restrictions about the type of electrodes or complexity of overlaps. In this paper, we attempted to develop a spike sorting method for the signal containing overlaps of the arbitrary number of spikes recorded with arbitrary electrodes. We estimated templates and timings of spikes by the inference based on hidden Markov model. In order to avoid the problem of too high computational cost and too much decomposition caused by assuming arbitrary overlaps, we imposed the weak probabilistic penalty on overlaps in the model and reduced computation of estimation by approximating low probabilities to zero. As the result of assessments using simulated signal and real extracellular recordings, we showed that proposed method could robustly detect and sort complexly overlapped spikes.