Bayesian Filtering of Smooth Signals: Application to Altimetry

TL;DR

This paper introduces a Bayesian filtering method for smooth signals corrupted by Gaussian noise, specifically applied to satellite altimetry, demonstrating effective denoising and improved parameter estimation on synthetic and real data.

Contribution

A novel Bayesian approach with a gamma Markov random field prior for denoising smooth signals, optimized with a fast coordinate descent algorithm, applied to altimetry data.

Findings

Effective denoising of synthetic and real altimetric signals.

Improved accuracy of altimetric parameter estimation.

Fast convergence of the proposed algorithm.

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 continuous signals that can have a numerical or an analytical expression with respect to some parameters. The Bayesian model proposed takes into account the Gaussian properties of the noise and the smooth evolution of the successive signals. In addition, a gamma Markov random field prior is assigned to the signal energies and to the noise variances to account for their known properties. The resulting posterior distribution is maximized using a fast coordinate descent algorithm whose parameters are updated by analytical expressions. The proposed algorithm is tested on satellite altimetric data demonstrating good denoising results on both synthetic and real signals. The proposed algorithm is also shown to improve the quality of the altimetric parameters when combined with a parameter estimation strategy.