Windowed State Space Filters for Peak Interference Suppression in Neural Spike Sorting

Signal-to-peak-interference ratio (SPIR) optimal filters are template matching filters with peak interference suppression properties. Such max-SPIR filters are used in multi-pattern recognition problems, such as neural spike sorting in micro-electrode array probes, where cellular action potentials need to be detected and clustered according to their firing neuron cells.
In high-density probes with hundreds of channels, such max-SPIR filter banks can require unacceptable high computational resources, in particular for applications with real-time demands and/or on-probe spike sorting. In this paper, we present a computationally attractive substitute for max-SPIR filters by recursively computed Autonomous Linear State Space Model (ALSSM) filters. In our approach, we approximate the impulse
response of max-SPIR filters by low order ALSSMs and perform the signal convolution in the new, low-dimensional ALSSM vector space. We demonstrate our method on real neural recordings from high-density probes and show only minimal loss in detection quality while the computational complexity drops by up to a factor 10.