Timing based source separation

Abstract

The motivation of this work is to use statistical signal processing to help to separate mixtures of marine mammal vocalizations, in particular sperm whale click trains. It is observed that clicks from a single whale are spaced at regular intervals which we exploit to do the separation. To begin, we consider an idealized problem: each source emits at impulses at iid intervals according to some distribution. That is, the impulse times for each source constitute a renewal process. These timing distributions induce a likelihood function for the impulse times given some assignment. We present an algorithm inspired by the Viterbi algorithm to give assignments that maximizes this likelihood. Additionally, we provide more computationally feasible approximations of this algorithm. We verify these algorithms with a derived lower bound. Furthermore, we provide methods to estimate the timing distribution parameters and the total number of sources using alternating maximization and the minimum description length. We also attempted to use timing to help improve detection methods for impulses using a Bayesian framework. Unfortunately, the results were impractical, but the concepts were used to generate a classification using impulse shape information timing information. Finally we explore modifications to make the algorithm work on actual sperm whale click mixtures.