Unsupervised selection of the singular spectrum components based on information theory for bioacoustic signal filtering

In this work, we present a comprehensive study of Singular Spectrum Analysis (SSA) applied to bioacoustics signal enhancement. The SSA method decomposes the signal into oscillatory components with physical meaning, allowing us to analyze different sound frequencies. One of the major SSA's challenges is how to choose those oscillatory components that will result in a better signal reconstruction, with less noise and distortion. We thus examine three entropy-based criterions for choosing such components. The quantifiers evaluated are: Amplitude Entropy, Spectral Entropy, and Permutation Entropy. The convergence of these quantifiers for different contamination conditions is provided. We then propose a grouping algorithm to arrange these components according to their entropy values. With the proposed rule, it is possible to identify the predominantly deterministic inner structure of the signal, in an unsupervised manner. We perform two different evaluations. First, we test a synthetic amplitude modulated signal contaminated with white, blue, pink, red, and violet color noises at 0 dB. Second, we analyze three audio calls of different anuran species recorded in the rainforest. The best quality of the recovered signal assessed through the Mean Square Error and the Signal-to-Distortion Ratio are 0.21 and 7.23 respectively for a white noise contamination applying the Permutation Entropy-based rule. Therefore, we conclude that our criterion is suitable for real scenarios under severe noise conditions, easily identifying trends and low-frequency components with a narrow band spectrum. Furthermore, we show how to derive an optimal FIR filter from SSA's components to build a specific filter bank for each species. We then present the magnitude-frequency response of the FIR filters of a bioacoustic anuran call.