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

Area of Science:

• Oceanography
• Acoustics
• Data Science

Background:

• Ocean sound speed field (SSF) representation often suffers from low resolution, limiting the capture of fine-scale fluctuations.
• Classical SSF basis functions (e.g., EOFs, Fourier, tensor-based) have inherent limitations in resolving detailed spatial variations.
• Existing dictionary learning methods show promise for 2D SSF but generalizing to 3D is challenging.

Purpose of the Study:

• To develop a novel algorithm for accurate three-dimensional (3D) ocean sound speed field (SSF) representation.
• To integrate dictionary learning with tensor-based basis function learning for improved 3D SSF modeling.
• To enhance the preservation of fine-scale sound speed information in 3D oceanographic data.

Main Methods:

• Developed a 3D SSF-tailored tensor dictionary learning algorithm.
• Learned a large number of tensor-based basis functions with flexible shapes in a data-driven manner.
• Integrated dictionary learning and tensor-based basis function learning frameworks.

Main Results:

• The proposed algorithm successfully learns a large set of tensor-based basis functions with adaptable shapes.
• Numerical results demonstrated the superiority of the 3D tensor dictionary learning approach over prior methods.
• The method effectively preserves fine-scale sound speed information in 3D spatial ocean data.

Conclusions:

• The 3D tensor dictionary learning algorithm offers a significant advancement in ocean sound speed field representation.
• This data-driven approach overcomes limitations of traditional basis functions for 3D SSF.
• The method shows strong potential for applications requiring high-resolution 3D ocean acoustic modeling.