Enhancing the robustness of ocean sound speed profile representation via interpretable deep matrix decomposition

Developing an effective and robust representation model for ocean sound speed profiles (SSPs) is crucial for numerous ocean acoustic applications. However, the performance of existing sound speed profile (SSP) representation methods, such as empirical orthogonal function and K-singular value decomposition, heavily relies on the number of selected basis functions. This could lead to overfitting of noise, as these methods are unable to distinguish between signals and noise during the basis function learning process. To overcome these limitations and effectively learn a large number of basis functions with strong representation power from potentially noisy SSP data, we propose a novel algorithm called deep matrix decomposition (deep MD). This algorithm utilizes untrained deep neural networks as priors to reject noise within the interpretable matrix decomposition framework. To achieve optimal performance with deep MD, we propose a stopping strategy based on the rank estimate to determine the termination epoch. Experimental results using real-life datasets demonstrate that deep MD is robust against various types of noise and outperforms traditional SSP representation methods in terms of SSP reconstruction and characterizing the transmission loss in underwater acoustics.