Unsupervised Dolphin Whistle Signal Dereverberation Based on β-Divergence Convolutive Nonnegative Matrix Factorization With Mixed Constraints

Reverberation significantly affects the feature extraction and detection performance of dolphin whistle signals in underwater passive acoustic monitoring (PAM). To mitigate this interference, we propose a unsupervised signal deconvolution method based on generalized <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\beta $ </tex-math></inline-formula>-divergence convolutive nonnegative matrix factorization with mixed constraints (<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\beta $ </tex-math></inline-formula>-CNMF-MC) for dolphin whistles. First, we employ dictionary learning to capture the contour structures of whistle spectrograms from t–f segments of observed dolphin calls. Then, using the learned dictionary, we reconstruct the pure whistle signals by applying mixed constraints of underwater acoustic channel (UAC) characteristics. Both stages are formulated as the minimization of a unified cost function incorporating a mixed penalty term, solved via an agent-assisted optimization algorithm tailored for local minima convergence. Among them, the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\beta $ </tex-math></inline-formula>-divergence is used as a nonnegative fidelity term, utilizing the inherent sparsity to enhance the fidelity of the time-frequency (t–f) representation of the whistle signals amidst reverberation. The optimal parameter selection of the proposed method is identified using a two-stage optimization algorithm to ensure the most accurate dereverberation outcome. The proposed method was validated on a dataset involving two Southern Bottlenose Dolphins, with experimental results indicating robust performance across varying degrees of reverberant interference.