Tensor dictionary learning for representing three-dimensional sound speed fields.

Ocean sound speed field (SSF) representation is often plagued with low resolution (i.e., the capability of explaining fine-scale fluctuations). This drawback, however, is inherent in a number of classical SSF basis functions, e.g., empirical orthogonal functions, Fourier basis functions, and more recent tensor-based basis functions learned via the higher-order orthogonal iterative algorithm. For two-dimensional depth-time SSF representation, recent attempts relying on dictionary learning have shown that fine-scale sound speed information can be well preserved by a large number of basis functions. They are learned from the historical data without imposing rigid constraints on their shapes, e.g., the orthogonal constraints. However, generalizing the dictionary learning idea to represent three-dimensional (3D) spatial ocean SSF is non-trivial, in terms of both problem formulation and algorithm development. It calls for integrating the dictionary learning framework and the tensor-based basis function learning framework, a recently proposed one that captures the 3D sound speed correlations well. To achieve this goal, we develop a 3D SSF-tailored tensor dictionary learning algorithm that learns a large number of tensor-based basis functions with flexible shapes in a data-driven fashion. Numerical results based on the South China Sea 3D SSF data have showcased the superiority of the proposed approach over the prior method.