Non-Smooth Variational Data Assimilation with Sparse Priors

This paper proposes an extension to the classical 3D variational data assimilation approach by explicitly incorporating as a prior information, the transform-domain sparsity observed in a large class of geophysical signals. In particular, the proposed framework extends the maximum likelihood estimation of the analysis state to the maximum a posteriori estimator, from a Bayesian perspective. The promise of the methodology is demonstrated via application to a 1D synthetic example.