Multi-Pattern Recognition Through Maximization of Signal-to-Peak-Interference Ratio With Application to Neural Spike Sorting

In this paper, we propose three novel linear filter design methods for use in a multi-pattern recognition task with overlapping patterns and strong peak interferers. The recognition is based on a linear filter-and-threshold approach, which is particularly interesting when the task has to be performed in a computationally constrained environment. The first method optimizes the signal-to-peak-interference ratio (SPIR) of the filter output, where the focus is on minimization of the post-filtering peak interference instead of the pre-filtering peak interference as in existing methods. The second and third method are convex approximations of the first method and are shown to be closely related to support vector machines, which establishes a natural link between SPIR-optimal filtering and the maximum margin matched filter. The proposed methods only require a template of the target patterns as prior knowledge and do not require the training data to be labelled. An extensive case study is presented in the context of neural spike sorting, in which the proposed approaches are shown to significantly outperform existing filter-and-threshold approaches for spike sorting.