Denoising Smooth Signals Using a Bayesian Approach: Application to Altimetry

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 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.

3D Target Detection and Spectral Classification for Single-photon LiDAR Data

“…The CDA aims at maximizing the posterior in ( 14) with respect to the parameters of interest, namely 𝚯 = (𝒓, 𝑩, 𝒅, 𝒖, 𝒉, 𝒘). Due to the large number of parameters of interest and the complexity of the joint distribution, the CDA emerges as a great candidate to estimate the parameters of interest as in [13,[47][48][49]. Indeed, this algorithm iteratively updates the unknown parameters by maximizing their conditional distributions with respect to a single parameter while keeping the others fixed until a convergence criterion is met as detailed in Algo.…”

Altimetric Parameter Estimation in Long Coherent Processing by Airborne Delay/Doppler Altimetry Based on Bayesian Learning

“…For the sake of simplicity, we only express it as a function of τ r . Therefore, the echo mathematical model (23) can be used to re-track [5] and estimate the height parameters.…”

“…Conventional radar altimeters transmit and receive monopulse, whose coherent pulse interval (CPI) is burst length [5], [6]. The along-track resolution of altimeter depends on the number of the pulses in transmitted burst, where the CPI along-track is the burst period.…”