Tensor-based basis function learning for three-dimensional sound speed fields.

Area of Science:

• Acoustic Signal Processing
• Machine Learning
• Geophysics

Background:

• Basis function learning is crucial for 3D sound speed field (SSF) inversion in applications like ocean acoustic tomography and underwater target localization.
• Classical methods use empirical orthogonal functions (EOFs) or Fourier basis functions, while K-singular value decomposition (K-SVD) offers improved representation but doesn't leverage 3D tensor properties.

Purpose of the Study:

• To develop a unified tensor-based framework for basis function learning of 3D SSFs.
• To fully exploit the 3D interactions and correlations within SSF data.
• To provide a generalized approach encompassing classical basis functions.

Main Methods:

• Proposed a tensor-based basis function learning framework.
• Utilized tensor decomposition to model 3D SSF data.
• Demonstrated the framework's ability to include EOFs and Fourier basis functions as special cases.

Main Results:

• The tensor-based framework effectively represents 3D SSFs by leveraging multi-dimensional data mining techniques.
• Numerical results using South China Sea data confirmed the superior performance of tensor-based basis functions.
• The proposed method offers a unified tensor perspective for understanding and representing 3D SSFs.

Conclusions:

• The developed tensor-based basis function learning framework provides a significant advancement for 3D SSF inversion.
• This approach enhances acoustic signal processing tasks by fully utilizing 3D data characteristics.
• The unified tensor perspective offers a powerful tool for geophysical data analysis.