Application of Graph-guided Low-rank Matrix Completion in Underwater Target Scattered Acoustic Pressure Field Reconstruction

During the measurement of the scattered acoustic pressure field of underwater targets, limitations such as insufficient measurement coverage and resolution often lead to pressure field data that fail to meet the required standards. Therefore, accurate reconstruction of the scattered acoustic pressure field is essential. Inspired by the development of graph-based machine learning, this paper employs a Graph-guided Bayesian Low-rank Matrix Completion (BMCG) method for reconstructing the scattered acoustic pressure field. The proposed method leverages both global (low-rank) and local (graph-based) structural information from the scattered acoustic pressure field to formulate an optimization problem. This problem is then solved by a Bayesian algorithm based on the Student's <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$t$</tex> prior and another Bayesian algorithm based on the generalized hyperbolic distribution, which allows for automatic learning of the hyperparameters to achieve optimal results. The method is validated using the Finite Element Method (FEM) and compared with classical reconstruction methods, including spline interpolation and kriging interpolation. The results demonstrate that the proposed method achieves high reconstruction accuracy in reconstructing the underwater target scattering field and exhibits robustness to noisy measurements.