Reconstruction of 3-D Sound Speed Fields Based on Tensor Tucker Decomposition

Sound velocity is a key marine environmental parameter that strongly influences sound propagation in the ocean. In oceanographic research and exploration, the precise reconstruction of 3-D sound speed fields (3-D SSFs) serves as a fundamental prerequisite for improving the measurement and positioning accuracy of marine acoustic equipment and maintaining the reliability of underwater wireless communication. However, conventional empirical orthogonal function (EOF)-based SSF reconstruction algorithms exhibit inherent limitations due to their inability to account for 3-D structural features of ocean SSFs and their inadequate capacity for deep feature extraction. In this regard, this study proposes a modified conjugate gradient (MCG) algorithm incorporating the Tucker tensor decomposition. The integration of the conjugate gradient optimization framework and tensor-based high-order principal component analysis (PCA) can extract spatial structural features of 3-D SSF and robustly estimate missing values through an advanced tensor imputation mechanism. Experimental validation utilizes the Global Ocean Argo gridded data set (BOA_Argo) from the South China Sea, with comparative analyses conducted against conventional EOF and steepest descent (SD) algorithms. The raw data set is partitioned into training and testing sets to independently evaluate the algorithm’s modeling performance and missing-data imputation capability. The proposed MCG algorithm achieves substantial performance improvements, yielding 96.3% and 85.4% enhancements in modeling accuracy relative to conventional EOF and SD approaches, respectively. Furthermore, the algorithm exhibits superior imputation capabilities, with accuracy gains of 84.3% and 80.7% compared to these baseline methods. Crucially, the proposed method maintains exceptional stability and reliability even under challenging acoustic conditions and limited prior information.