Geophysical inversion by dictionary learning

Dictionary learning, a form of unsupervised machine learning, has recently been applied to ocean sound speed profile (SSP) data to obtain compact dictionaries of shape functions which explain SSPs using as few as one non-zero coefficient. In this presentation, the results of this analysis and potential applications of dictionary learning techniques to the inversion of real acoustic data are discussed. The estimation of true geophysical parameters from acoustic observations often is an ill-conditioned problem that is regularized by enforcing prior constraints such as sparsity or energy penalities, and by reducing the size of the parameter search. Traditionally, empirical orthogonal functions (EOFs) and overcomplete wavelet and curvelet dictionaries have been used to represent complex geophysical structures with few parameters. Using the K-SVD dictionary learning algorithm, the representation of ocean SSP data is significantly compressed relative to EOF analysis. The regularization performance of these learned dictionaries is evaluated against EOFs in the estimation of ocean sound speed structure from ocean acoustic observations and the limitations of such unsupervised methods are considered.