Tensor-based Basis Function Learning for Three-dimensional Sound Speed Fields

TL;DR

This paper introduces a tensor-based framework for learning basis functions to better represent 3D sound speed fields, leveraging tensor decomposition to improve over classical methods in ocean acoustic applications.

Contribution

It proposes a novel tensor-based basis function learning approach that unifies classical methods and enhances 3D sound speed field representation.

Findings

Tensor-based basis functions outperform classical methods.

Numerical results demonstrate improved representation of 3D SSF data.

Framework effectively captures 3D interactions in sound speed fields.

Abstract

Basis function learning is the stepping stone towards effective three-dimensional (3D) sound speed field (SSF) inversion for various acoustic signal processing tasks, including ocean acoustic tomography, underwater target localization/tracking, and underwater communications. Classical basis functions include the empirical orthogonal functions (EOFs), Fourier basis functions, and their combinations. The unsupervised machine learning method, e.g., the K-SVD algorithm, has recently tapped into the basis function design, showing better representation performance than the EOFs. However, existing methods do not consider basis function learning approaches that treat 3D SSF data as a third-order tensor, and thus cannot fully utilize the 3D interactions/correlations therein. To circumvent such a drawback, basis function learning is linked to tensor decomposition in this paper, which is the primary drive for recent multi-dimensional data mining. In particular, a tensor-based basis function learning framework is proposed, which can include the classical basis functions (using EOFs and/or Fourier basis functions) as its special cases. This provides a unified tensor perspective for understanding and representing 3D SSFs. Numerical results using the South China Sea 3D SSF data have demonstrated the excellent performance of the tensor-based basis functions.