Non-Smooth Variational Data Assimilation with Sparse Priors

TL;DR

This paper introduces a Bayesian extension to 3D variational data assimilation that incorporates transform-domain sparsity priors, improving analysis accuracy for geophysical signals, demonstrated on a synthetic example.

Contribution

It extends classical 3D variational data assimilation by integrating sparsity priors in a Bayesian framework, enhancing analysis quality.

Findings

Effective incorporation of sparsity priors in data assimilation.

Demonstrated improved analysis on synthetic data.

Framework applicable to geophysical signals.

Abstract

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.