Sparse Representation of Sound Speed Profiles Based on Dictionary Learning

The perturbations of sound speed profiles (SSPs) has great influence on sound propagation. Empirical orthogonal functions (EOFs) are often used to simplify the description of sound speed profiles. However, when the unevenness of seawater, such as internal wave and turbulence exists, the regularization operation will result in a significant decrease in the reconstruction accuracy of sound speed. In this paper, the dictionary learning, a form of unsupervised machine learning, is used to generate non-orthogonal entries of sound speed profiles, OMP algorithm is used in sparse coding, while K-SVD algorithm is used in dictionary updating. Because dictionary learning does not require the use of orthogonal conditions, it is more flexible for training data, and thus can use fewer atomic combinations to achieve higher reconstruction accuracy. The reconstruction performance of EOFs and LDs was tested with HYCOM data. The results show that compared with EOFs, LDs can better explain the perturbations of sound speed profiles with a few entries. Dictionary learning can improve the sparsity of sound speed profiles and improve the reconstruction accuracy of sound speed profiles.