Graph-guided Bayesian matrix completion for ocean sound speed field reconstruction

Reconstructing ocean sound speed field (SSF) from limited and noisy measurements/estimates is crucial for many ocean acoustic applications, including underwater tomography, target localization/tracking, and communications. Classical reconstruction methods include deterministic approaches (e.g., spline interpolation) and geostatistical methods (e.g., kriging). They exhibit a strong link to linear regression and Gaussian process regression in machine learning (ML) literature, by uniformly viewing them as supervised regression models that learn the mapping from the geographical locations to the sound speed outputs. From a unified ML perspective, theoretical analysis indicates that classical reconstruction methods have several drawbacks, such as the sensitivity to noises and high computational cost. To overcome these drawbacks, inspired by the recent thriving development of graph machine learning, we introduce graph-guided Bayesian low-rank matrix completions (LRMCs) for fine-scale and accurate ocean SSF reconstruction. In particular, a more general graph-guided LRMC model is proposed that encompasses the state-of-the-art one as a special case. The proposed model and the associated inference algorithm simultaneously exploit the global (low-rankness) and local (graph structure) information of ocean sound speed data, thus striking an outstanding balance of reconstruction accuracy and computational complexity. Numerical results using real-life ocean SSF data have demonstrated the encouraging performances of the proposed approaches.