Reconstructing the ocean sound speed field via regularized tensor network decomposition

Existing methods for reconstructing oceanic three-dimensional sound speed fields (3D SSFs) often exhibit limited accuracy, primarily due to inadequate utilization of global correlations. To address this limitation, this work formulates the 3D SSF as a third-order tensor and introduces a low-rank tensor modeling framework termed the fully connected tensor network (FCTN) model. This model effectively captures the inherent global low-rank properties of the SSF. To further exploit local spatial smoothness, we incorporate factor-based Tikhonov regularization into the FCTN framework, thereby yielding the fully connected tensor network-Tikhonov regulation (FCTN-T) model. For efficient model optimization, we develop an algorithm based on proximal alternating minimization (PAM), integrated with an acceleration strategy to enhance its computational performance. Extensive numerical experiments demonstrate that the proposed FCTN-T method outperforms state-of-the-art approaches in terms of both reconstruction accuracy and computational speed, providing higher-fidelity approximations of the ground-truth SSF and marking a significant advancement in oceanic SSF reconstruction.