Denoising Smooth Signals Using a Bayesian Approach: Application to Altimetry
Résumé
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 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 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. 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 classification strategy.
Mots clés
noise Gaussian properties
successive signals
gamma Markov random field
signal energies
noise variances
posterior distribution
fast coordinate descent algorithm
satellite altimetric data
synthetic signal
real signal
state-of-the-art algorithms
denoising quality
computational cost
altimetric parameter quality
classification strategy
Logic gates
Noise reduction
Signal processing algorithms
Computational modeling
Correlation
Satellites
Altimetry
Bayesian algorithm
coordinate descent algorithm (CDA)
gamma Markov random fields (gamma-MRFs)
Bayesian inference
Bayes methods
Gaussian noise
height measurement
Markov processes
parameter estimation
random processes
signal denoising
smoothing methods
statistical distributions
denoising smooth signals
Bayesian approach
Bayesian strategy
smooth signals estimation
smooth evolution
continuous signals
| Origine | Publication financée par une institution |
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