Regularization of geophysical inversion using dictionary learning

Densely sampled dynamic geophysical data are often modeled using principal components analysis (PCA, a.k.a. empirical orthogonal function or EOF analysis) to provide constraints for their inversion with remote sensing techniques. We show that overcomplete sparsifying dictionaries, generated using dictionary learning, provide a more informative basis for geophysical signal representation. Relative to EOFs, all the vectors in learned dictionaries represent significant variance in the geophysical signals. Since many geophysical inverse problems are ill-posed, this behavior makes learned dictionaries ideal for both minimizing the solution dimension and improving the resolution of parameter estimates. The K-SVD algorithm is applied to ocean sound speed profile (SSP) data. It is shown that learned dictionaries improves SSP inversion resolution.