From conventional to delay/Doppler altimetry

For more than twenty years, conventional altimeters like Topex, Poseidon-2 or Poseidon-3, have been delivering waveforms that are used to estimate many parameters such as the range between the satellite and the observed scene, the wave height and the wind speed. Several waveform models and estimation processing have been developed for the oceanic data in order to improve the quality of the estimated altimetric parameters. Moreover, a great e ffort has been devoted to process coastal echoes in order to move the altimetric measurements closer to the coast. In this thesis, we are interested in resolving these two problems, i.e., processing coastal waveforms and improving the quality of the estimated oceanic parameters. The fi rst part of the study considers the problem of coastal waveforms and proposes a new altimetric model taking into account the possible presence of peaks a ffecting altimetric echoes. In a second part of our work, we have been interested in the delay/Doppler altimetry. This new technology aims at reducing the measurement noise and increasing the along-track resolution when compared to conventional altimetry. Two altimetric models have been developed in order to estimate the resulting delay/Doppler echoes. These models allow a clear improvement in parameter estimation when compared to conventional altimetry.Depuis plus de vingt ans, les altimètres classiques comme Topex, Poseidon-2 ou Poséidon-3, ont fourni des formes d'onde qui sont utilisées pour estimer de nombreux paramètres tels que la distance entre le satellite et la scène observée, la hauteur des vagues et la vitesse du vent. L'amélioration de la qualité des paramètres altimétriques a nécessité le développement de plusieurs modèles d'échos et d'algorithmes d'estimation paramétrique. Par ailleurs, un grand effort est récemment dédié au traitement des échos côtiers afin d'analyser les mesures altimétriques le plus près possible des côtes. Cette thèse s'intéresse à la résolution de ces deux problèmes, à savoir, le traitement des formes d'onde côtières et l'amélioration de la qualité des paramètres océaniques estimés. La première partie de l'étude traite le problème des formes d'onde côtières en proposant un nouveau modèle altimétrique tenant compte de la présence éventuelle d'un pic sur l'écho altimétrique. Dans la seconde partie de notre travail, nous nous sommes intéressés à l'étude de l'altimétrie SAR/Doppler. Cette nouvelle technologie vise à réduire le bruit de mesure et à augmenter la résolution le long de la trace par rapport à l'altimétrie conventionnelle. Deux modèles altimétriques ont été développés afin d'estimer les paramètres associés aux échos SAR/Doppler. Ces modèles montrent une nette amélioration de la qualité des paramètres estimés par rapport à l'altimétrie conventionnelle

Correntropy Maximization via ADMM - Application to Robust Hyperspectral Unmixing

In hyperspectral images, some spectral bands suffer from low signal-to-noise ratio due to noisy acquisition and atmospheric effects, thus requiring robust techniques for the unmixing problem. This paper presents a robust supervised spectral unmixing approach for hyperspectral images. The robustness is achieved by writing the unmixing problem as the maximization of the correntropy criterion subject to the most commonly used constraints. Two unmixing problems are derived: the first problem considers the fully-constrained unmixing, with both the non-negativity and sum-to-one constraints, while the second one deals with the non-negativity and the sparsity-promoting of the abundances. The corresponding optimization problems are solved efficiently using an alternating direction method of multipliers (ADMM) approach. Experiments on synthetic and real hyperspectral images validate the performance of the proposed algorithms for different scenarios, demonstrating that the correntropy-based unmixing is robust to outlier bands.Comment: 23 page

Bayesian Based Unrolling for Reconstruction and Super-resolution of Single-Photon Lidar Systems

Deploying 3D single-photon Lidar imaging in real world applications faces several challenges due to imaging in high noise environments and with sensors having limited resolution. This paper presents a deep learning algorithm based on unrolling a Bayesian model for the reconstruction and super-resolution of 3D single-photon Lidar. The resulting algorithm benefits from the advantages of both statistical and learning based frameworks, providing best estimates with improved network interpretability. Compared to existing learning-based solutions, the proposed architecture requires a reduced number of trainable parameters, is more robust to noise and mismodelling of the system impulse response function, and provides richer information about the estimates including uncertainty measures. Results on synthetic and real data show competitive results regarding the quality of the inference and computational complexity when compared to state-of-the-art algorithms. This short paper is based on contributions published in [1] and [2].Comment: Presented in ISCS2

Parameter estimation for peaky altimetric waveforms

Much attention has been recently devoted to the analysis of coastal altimetric waveforms. When approaching the coast, altimetric waveforms are sometimes corrupted by peaks caused by high reflective areas inside the illuminated land surfaces or by the modification of the sea state close to the shoreline. This paper introduces a new parametric model for these peaky altimetric waveforms. This model assumes that the received altimetric waveform is the sum of a Brown echo and an asymmetric Gaussian peak. The asymmetric Gaussian peak is parameterized by a location, an amplitude, a width, and an asymmetry coefficient. A maximum-likelihood estimator is studied to estimate the Brown plus peak model parameters. The Cramér–Rao lower bounds of the model parameters are then derived providing minimum variances for any unbiased estimator, i.e., a reference in terms of estimation error. The performance of the proposed model and the resulting estimation strategy are evaluated via many simulations conducted on synthetic and real data. Results obtained in this paper show that the proposed model can be used to retrack efficiently standard oceanic Brown echoes as well as coastal echoes corrupted by symmetric or asymmetric Gaussian peaks. Thus, the Brown with Gaussian peak model is useful for analyzing altimetric easurements closer to the coast

Sparsity-based blind deconvolution of neural activation signal in FMRI

International audienceThe estimation of the hemodynamic response function (HRF) in functional magnetic resonance imaging (fMRI) is critical to deconvolve a time-resolved neural activity and get insights on the underlying cognitive processes. Existing methods propose to estimate the HRF using the experimental paradigm (EP) in task fMRI as a surrogate of neural activity. These approaches induce a bias as they do not account for laten-cies in the cognitive responses compared to EP and cannot be applied to resting-state data as no EP is available. In this work, we formulate the joint estimation of the HRF and neu-ral activation signal as a semi blind deconvolution problem. Its solution can be approximated using an efficient alternate minimization algorithm. The proposed approach is applied to task fMRI data for validation purpose and compared to a state-of-the-art HRF estimation technique. Numerical experiments suggest that our approach is competitive with others while not requiring EP information

Hyperspectral unmixing accounting for spatial correlations and endmember variability

International audienceThis paper presents an unsupervised Bayesian algorithm for hyperspectral image unmixing accounting for endmember variability. This variability is obtained by assuming that each pixel is a linear combination of random endmembers weighted by their corresponding abundances. An additive noise is also considered in the proposed model generalizing the normal compositional model. The proposed model is unsupervised since it estimates the abundances and both the mean and the covariance matrix of each endmember. A classification map indicating the class of each pixel is also obtained based on the estimated abundances. Simulations conducted on a real dataset show the potential of the proposed model in terms of unmixing performance for the analysis of hyperspectral images

Supervised nonlinear spectral unmixing using a post-nonlinear mixing model for hyperspectral imagery

This paper presents a nonlinear mixing model for hyperspectral image unmixing. The proposed model assumes that the pixel reflectances are nonlinear functions of pure spectral components contaminated by an additive white Gaussian noise. These nonlinear functions are approximated using polynomial functions leading to a polynomial postnonlinear mixing model. A Bayesian algorithm and optimization methods are proposed to estimate the parameters involved in the model. The performance of the unmixing strategies is evaluated by simulations conducted on synthetic and real data

Bayesian Estimation of Smooth Altimetric Parameters: Application to Conventional and Delay/Doppler Altimetry

International audienceThis paper proposes a new Bayesian strategy for the smooth estimation of altimetric parameters. The altimetric signal is assumed to be corrupted by a thermal and speckle noise distributed according to an independent and non-identically Gaussian distribution. We introduce a prior enforcing a smooth temporal evolution of the altimetric parameters which improves their physical interpretation. The posterior distribution of the resulting model is optimized using a gradient descent algorithm which allows us to compute the maximum a posteriori estimator of the unknown model parameters. This algorithm has a low computational cost that is suitable for real-time applications. The proposed Bayesian strategy and the corresponding estimation algorithm are evaluated using both synthetic and real data associated with conventional and delay/Doppler altimetry. The analysis of real Jason-2 and CryoSat-2 waveforms shows an improvement in parameter estimation when compared to state-of-the-art estimation algorithms