Advanced Sparse Representation Techniques for Ocean Sound Velocity and Comparative Performance Analysis

Objectives: Ocean sound velocity is a fundamental element of marine environmental observation, and accurate sound velocity information is critical for ocean exploration, underwater communication, navigation, and localization. Accurately reconstructing two-dimensional sound velocity profiles (SVPs) and three-dimensional ocean sound velocity fields (SVFs) is crucial for various ocean acoustics applications. However, the spatial and temporal variations and uncertainties in sound velocity across the vast ocean make this a challenging task, necessitating further investigation into sparse representations of ocean sound velocity. Methods: To address the problem of limited reconstruction accuracy of ocean sound velocity information, this study proposes a sparse representation method based on three mainstream approaches: Empirical Orthogonal Function (EOF), Dictionary Learning (DL), and Tensor Decomposition (TD). The sparse representation effects and data reconstruction accuracies of 2D SVPs and 3D ocean SVFs are investigated using global ocean Argo (Array for Real-time Geostrophic Oceanography) grid data. For 2D sound velocity information, the study extends to a global scale, analyzing the determination of EOF order and grid sparsity, and comprehensively comparing the reconstruction results of the EOF and DL methods. For the 3D sound velocity field, the Central Pacific Ocean serves as the experimental area. The parameter information for EOF, DL, and TD methods is determined based on the training set, and the reconstruction results for the test set are analyzed to assess the data reconstruction accuracies of the three methods. Results: The results demonstrate that in the sparse representation of 2D sound velocity data, DL method demonstrates superior reconstruction performance on a global scale, achieving reconstruction errors as low as 0.2 m·s^-1 in most sea regions. Additionally, DL method shows greater stability in both the depth and time dimensions compared to EOF method, making them more suitable for sparse representation of two-dimensional sound velocity data. For the threedimensional sound velocity field, the tensor decomposition method effectively captures the spatial variability of sound velocity through multiple factor matrices. This approach is well-suited for the sparse representation of three-dimensional sound velocity data, significantly reducing the number of parameters while delivering more stable and accurate reconstruction results, with an overall reconstruction error of 0.21 m·s^-1. Conclusions: To draw a conclusion, these experimental findings provide practical guidance for the compression and feature extraction of multidimensional sound velocity information, thereby improving the reconstruction and inversion accuracy of ocean sound velocity.