  Accurately reconstructing a three-dimensional ocean sound speed field (3D
SSF) is essential for various ocean acoustic applications, but the sparsity and
uncertainty of sound speed samples across a vast ocean region make it a
challenging task. To tackle this challenge, a large body of reconstruction
methods has been developed, including spline interpolation, matrix/tensor-based
completion, and deep neural networks-based reconstruction. However, a
principled analysis of their effectiveness in 3D SSF reconstruction is still
lacking. This paper performs a thorough analysis of the reconstruction error
and highlights the need for a balanced representation model that integrates
both expressiveness and conciseness. To meet this requirement, a 3D
SSF-tailored tensor deep neural network is proposed, which utilizes tensor
computations and deep neural network architectures to achieve remarkable 3D SSF
reconstruction. The proposed model not only includes the previous tensor-based
SSF representation model as a special case, but also has a natural ability to
reject noise. The numerical results using the South China Sea 3D SSF data
demonstrate that the proposed method outperforms state-of-the-art methods. The
code is available at https://github.com/OceanSTARLab/Tensor-Neural-Network.
