  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.
