Combining algebraic approach with extreme value theory for spike detection

This paper uses the Extreme Value Theory (EVT) for threshold selection in a previously proposed algebraic spike detection method. The algebraic method characterizes the occurrence of a spike by an irregularity in the neural signal and devises a nonlinear (Volterra) filter which enhances the presence of such irregularities. These appear as (positive) high amplitude pulses in the output signal. The pulses are isolated. We then interpret the occurrence of a spike as a rare and extreme event that we model in the framework of EVT. With this model, we derive an explicit expression of the decision threshold corresponding to a given probability of false-alarm. Simulation results show that the empirical probability of false alarm is close to the predicted one by applying the derived theoretical threshold.