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Denoising Smooth Signals Using a Bayesian Approach Application to Altimetry


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Abstract


This paper presents a novel Bayesian strategy for the estimation of smooth signals corrupted by Gaussian noise. The method assumes a smooth evolution of a succession of continu-ous signals that can have a numerical or an analytical expression with respect to some parameters. The proposed Bayesian model takes into account the Gaussian properties of the noise and the smooth evolution of the successive signals. In addition, a gamma Markov randomfield prior is assigned to the signal energies and to the noise variances to account for their known properties. The re-sulting posterior distribution is maximized using a fast coordinate descent algorithm whose parameters are updated by analytical ex-pressions. The proposed algorithm is tested on satellite altimetric data demonstrating good denoising results on both synthetic and real signals. In comparison with state-of-the-art algorithms, the proposed strategy provides a good compromise between denoising quality and necessary reduced computational cost. The proposed algorithm is also shown to improve the quality of the altimetric parameters when combined with a parameter estimation or a clas-sification strategy.

KeyWords
Altimetry, Bayesian algorithm, coordinate de-scent algorithm (CDA), gamma Markov random fields (gamma-MRFs).



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