So far, the problem of unmixing large or multitemporal hyperspectral datasets has been specifically addressed in the remote sensing literature only by a few dedicated strategies. Among them, some attempts have been made within a distributed estimation framework, in particular relying on the alternating direction method of multipliers (ADMM). In this paper, we propose to study the interest of a partially asynchronous distributed unmixing procedure based on a recently proposed asynchronous algorithm. Under standard assumptions, the proposed algorithm inherits its convergence properties from recent contributions in non-convex optimization, while allowing the problem of interest to be efficiently addressed. Comparisons with a distributed synchronous counterpart of the proposed unmixing procedure allow its interest to be assessed on synthetic and real data. Besides, thanks to its genericity and flexibility, the procedure investigated in this work can be implemented to address various matrix factorization problems.

This research study is the result of a 3 years CIFRE PhD thesis between the Airbus design office (Aircraft Control domain) and TéSA laboratory in Toulouse. The main goal is to propose, develop and validate a software solution for the detection and diagnosis of a specific type of elevator and rudder vibration, called limit cycle oscillation (LCO), based on existing signals available in flight control computers on board in-series aircraft. LCO is a generic mathematical term defining an initial condition-independent periodic mode occurring in nonconservative nonlinear systems. This study focuses on the LCO phenomenon induced by mechanical freeplays in the control surface of a civil aircraft. The LCO consequences are local structural load augmentation, flight handling qualities deterioration, actuator operational life reduction, cockpit and cabin comfort deterioration and maintenance cost augmentation. The state-of-the-art for freeplay induced LCO detection and diagnosis is based on the pilot sensitivity to vibration and to periodic freeplay check on the control surfaces. This study is thought to propose a data-driven solution to help LCO and freeplay diagnosis. The goal is to improve even more aircraft availability and reduce the maintenance costs by providing to the airlines a condition monitoring signal for LCO and freeplays. For this reason, two algorithmic solutions for vibration and freeplay diagnosis are investigated in this PhD thesis. A real time detector for LCO diagnosis is first proposed based on the theory of the generalized likelihood ratio test (GLRT). Some variants and simplifications are also proposed to be compliant with the industrial constraints. In a second part of this work, a mechanical freeplay detector is introduced based on the theory of Wiener model identification. Parametric (maximum likelihood estimator) and nonparametric (kernel regression) approaches are investigated, as well as some variants to well-known nonparametric methods. In particular, the problem of hysteresis cycle estimation (as the output nonlinearity of a Wiener model) is tackled. Moreover, the constrained and unconstrained problems are studied. A theoretical, numerical (simulator) and experimental (flight data and laboratory) analysis is carried out to investigate the performance of the proposed detectors and to identify limitations and industrial feasibility. The obtained numerical and experimental results confirm that the proposed GLR test (and its variants / simplifications) is a very appealing method for LCO diagnostic in terms of performance, robustness and computational cost. On the other hand, the proposed freeplay diagnostic algorithm is able to detect relatively large freeplay levels, but it does not provide consistent results for relatively small freeplay levels. Moreover, specific input types are needed to guarantee repetitive and consistent results. Further studies should be carried out in order to compare the GLRT results with a Bayesian approach and to investigate more deeply the possibilities and limitations of the proposed parametric method for Wiener model identification.

We propose a new fusion method for magnetic resonance imaging (MRI) and ultrasound (US) data combining two inverse problems: MRI reconstruction using super-resolution and US image despeckling, using a model relating the two modalities through an unknown polynomial function. We demonstrate the accuracy of the proposed fusion algorithm by quantitative and qualitative evaluation using synthetic data. The resulting fused image is shown to have an improved signal to noise ratio and spatial resolution compared to the native MRI and US images.

Multipath (MP) remains the main source of error when using global navigation satellite systems (GNSS) in a constrained environment, leading to biased measurements and thus to inaccurate estimated positions. This paper formulates the GNSS navigation problem as the resolution of an overdetermined system whose unknowns are the receiver position and speed, clock bias and clock drift, and the potential biases affecting GNSS measurements. We assume that only a part of the satellites are affected by MP, i.e., that the unknown bias vector has several zero components, which allows sparse estimation theory to be exploited. The natural way of enforcing this sparsity is to introduce an ℓ1 regularization associated with the bias vector. This leads to a least absolute shrinkage and selection operator problem that is solved using a reweighted- ℓ1 algorithm. The weighting matrix of this algorithm is designed carefully as functions of the satellite carrier-to-noise density ratio ( C/N0 ) and the satellite elevations. Experimental validation conducted with real GPS data show the effectiveness of the proposed method as long as the sparsity assumption is respected.

This paper introduces a robust 2-D cardiac motion estimation method. The problem is formulated as an energy minimization with an optical flow-based data fidelity term and two regularization terms imposing spatial smoothness and the sparsity of the motion field in an appropriate cardiac motion dictionary. Robustness to outliers, such as imaging artefacts and anatomical motion boundaries, is introduced using robust weighting functions for the data fidelity term as well as for the spatial and sparse regularizations. The motion fields and the weights are computed jointly using an iteratively re-weighted minimization strategy. The proposed robust approach is evaluated on synthetic data and realistic simulation sequences with available ground-truth by comparing the performance with state-of-the-art algorithms. Finally, the proposed method is validated using two sequences of in vivo images. The obtained results show the interest of the proposed approach for 2-D cardiac ultrasound imaging.

Change-point estimation has received much attention in the literature as it plays a significant role in several signal processing applications. However, the study of the optimal estimation performance in such context is a difficult task since the unknown parameter vector of interest may contain both continuous and discrete parameters, namely the parameters associated with the noise distribution and the change-point locations. In this paper, we handle this by deriving a lower bound on the mean square error of these continuous and discrete parameters. Specifically, we propose a Hybrid Cramér-Rao– Weiss-Weinstein bound and derive its associated closed-form expressions. Numerical simulations assess the tightness of the proposed bound in the case of Gaussian and Poisson observations.

L’évolution des technologies électroniques (miniaturisation, diminution des coûts) a permis aux GNSS (systèmes de navigation par satellites) d’être de plus en plus accessibles et donc utilisés au quotidien, par exemple par le biais d’un smartphone, ou de récepteurs disponibles dans le commerce à des prix raisonnables (récepteurs bas-coûts). Ces récepteurs fournissent à l’utilisateur plusieurs informations, comme par exemple sa position et sa vitesse, ainsi que des mesures des temps de propagation entre le récepteur et les satellites visibles entre autres. Ces récepteurs sont donc devenus très répandus pour les utilisateurs souhaitant évaluer des techniques de positionnement sans développer tout le hardware nécessaire. Les signaux issus des satellites GNSS sont perturbés par de nombreuses sources d’erreurs entre le moment où ils sont traités par le récepteurs pour estimer la mesure correspondante. Il est donc nécessaire de compenser chacune des ces erreurs afin de fournir à l’utilisateur la meilleure position possible. Une des sources d’erreurs recevant beaucoup d’intérêt, est le phénomène de réflexion des différents signaux sur les éventuels obstacles de la scène dans laquelle se trouve l’utilisateur, appelé multitrajets. L’objectif de cette thèse est de proposer des algorithmes permettant de limiter l’effet des multitrajets sur les mesures GNSS. La première idée développée dans cette thèse est de supposer que ces signaux multitrajets donnent naissance à des biais additifs parcimonieux. Cette hypothèse de parcimonie permet d’estimer ces biais à l’aide de méthodes efficaces comme le problème LASSO. Plusieurs variantes ont été développés autour de cette hypothèse visant à contraindre le nombre de satellites ne souffrant pas de multitrajet comme non nul. La deuxième idée explorée dans cette thèse est une technique d’estimation des erreurs de mesure GNSS à partir d’une solution de référence, qui suppose que les erreurs dues aux multitrajets peuvent se modéliser à l’aide de mélanges de Gaussiennes ou de modèles de Markov cachés. Deux méthodes de positionnement adaptées à ces modèles sont étudiées pour la navigation GNSS.

L’évolution des technologies électroniques (miniaturisation, diminution des coûts) a permis aux GNSS (systèmes de navigation par satellites) d’être de plus en plus accessibles et donc utilisés au quotidien, par exemple par le biais d’un smartphone, ou de récepteurs disponibles dans le commerce à des prix raisonnables (récepteurs bas-coûts). Ces récepteurs fournissent à l’utilisateur plusieurs informations, comme par exemple sa position et sa vitesse, ainsi que des mesures des temps de propagation entre le récepteur et les satellites visibles entre autres. Ces récepteurs sont donc devenus très répandus pour les utilisateurs souhaitant évaluer des techniques de positionnement sans développer tout le hardware nécessaire. Les signaux issus des satellites GNSS sont perturbés par de nombreuses sources d’erreurs entre le moment où ils sont traités par le récepteurs pour estimer la mesure correspondante. Il est donc nécessaire de compenser chacune des ces erreurs afin de fournir à l’utilisateur la meilleure position possible. Une des sources d’erreurs recevant beaucoup d’intérêt, est le phénomène de réflexion des différents signaux sur les éventuels obstacles de la scène dans laquelle se trouve l’utilisateur, appelé multitrajets. L’objectif de cette thèse est de proposer des algorithmes permettant de limiter l’effet des multitrajets sur les mesures GNSS. La première idée développée dans cette thèse est de supposer que ces signaux multitrajets donnent naissance à des biais additifs parcimonieux. Cette hypothèse de parcimonie permet d’estimer ces biais à l’aide de méthodes efficaces comme le problème LASSO. Plusieurs variantes ont été développés autour de cette hypothèse visant à contraindre le nombre de satellites ne souffrant pas de multitrajet comme non nul. La deuxième idée explorée dans cette thèse est une technique d’estimation des erreurs de mesure GNSS à partir d’une solution de référence, qui suppose que les erreurs dues aux multitrajets peuvent se modéliser à l’aide de mélanges de Gaussiennes ou de modèles de Markov cachés. Deux méthodes de positionnement adaptées à ces modèles sont étudiées pour la navigation GNSS.

Light detection and ranging (Lidar) data can be used to capture the depth and intensity profile of a 3D scene. This modality relies on constructing, for each pixel, a histogram of time delays between emitted light pulses and detected photon arrivals. In a general setting, more than one surface can be observed in a single pixel. The problem of estimating the number of surfaces, their reflectivity, and position becomes very challenging in the low-photon regime (which equates to short acquisition times) or relatively high background levels (i.e., strong ambient illumination). This paper presents a new approach to 3D reconstruction using single-photon, single-wavelength Lidar data, which is capable of identifying multiple surfaces in each pixel. Adopting a Bayesian approach, the 3D structure to be recovered is modelled as a marked point process, and reversible jump Markov chain Monte Carlo (RJ-MCMC) moves are proposed to sample the posterior distribution of interest. In order to promote spatial correlation between points belonging to the same surface, we propose a prior that combines an area interaction process and a Strauss process. New RJ-MCMC dilation and erosion updates are presented to achieve an efficient exploration of the configuration space. To further reduce the computational load, we adopt a multiresolution approach, processing the data from a coarse to the finest scale. The experiments performed with synthetic and real data show that the algorithm obtains better reconstructions than other recently published optimization algorithms for lower execution times.