Sparse regularisation has proven its worth and effectiveness in many fields, such as medical imaging. In this sense, nuclear magnetic resonance spectroscopy (MRS) is one of the modalities that could greatly benefit from sparse regularisation. This paper introduces a novel Bayesian approach for MRS restoration that accounts for possible errors in the observation linear operator. The algorithm is tailored to the complex nature of MRS data, incorporating both real and imaginary parts of the spectrum. An MCMC (Markov chain Monte Carlo) inference is conducted using a Gibbs sampler strategy. The method has been successfully validated on both synthetic and clinical data of high-grade brain tumor glioblastoma (GBM) patients. This study will enable further analysis of metabolites of interest not conventionally considered in clinics because of their undetectable concentration.

This letter explores time-delay and Doppler estimation in the presence of unknown heavy-tailed disturbance. Conventional methods for achieving optimal mean squared error performance rely on the maximum likelihood estimator (MLE), which is consistent and asymptotically efficient under the unrealistic assumption of a perfect a-priori knowledge of the noise distribution. However, in practical situations, the noise distribution is often unknown, and classical parametric estimation procedures are no longer able to guarantee the statistical efficiency. In this work, by relying on the semiparametric theory, we present an original rank-based and distribution-free $R$-estimator which have the remarkable property to be parametrically efficient, i.e. it attains the “classical” Cramér-Rao Bound, irrespective of the unknown noise distribution, provided that the latter belongs to the family of Complex Elliptically Simmetric (CES) distributions.

The estimation of high resolution spectrometer Instrument Spectral Response Functions (ISRFs) is crucial because an imperfect knowledge of these functions can induce errors in the measurements. The state-of-the-art for this problem currently relies on the use of parametric models, which frequently lack flexibility to accurately model real-world ISRFs. To address this limitation, this paper proposes and investigates the use of sparse representations for modeling and estimating ISRFs, where the ISRFs are decomposed in a fixed dictionary of atoms. To estimate the sparse coefficient vector, a novel sparsity inducing regularization of the problem based on quadratic envelopes is studied and compared to the classical LASSO estimator and to a greedy method based on the Orthogonal Matching Pursuit (OMP) algorithm. Results for simulated ISRFs from the MicroCarb mission indicate that the proposed spectral representations yield excellent ISRF estimates, and that the use of quadratic envelopes can yield significantly better precision than competing methods.

In this talk, we present a hybrid approach to predicting the future performance of a fuel cell. The idea is to combine the physical laws governing system dynamics with machine learning algorithms. The data used come from an aging campaign carried out under a dynamic load profile and variable operating conditions. The proposed approach is based on a simplified formulation of the well-known quasi-static model. Evolution laws are proposed for certain parameters related to activation and diffusion losses. The ohmic resistance, which determines the ohmic losses, is modeled by random forests. To estimate the evolution of other parameters over time, these methods are used in conjunction with an extended Kalman filter (EKF). To predict future performance, a long-term memory is used to learn the evolution of these parameters, estimated by the EKF.

This article presents a comprehensive review of recent advances in intrinsic Cramér-Rao bounds (ICRBs) for Lie groups (LGs), which play a pivotal role in addressing estimation problems involving parameters and/or observations constrained by geometric structures. The review encompasses both deterministic and Bayesian frameworks, with a detailed examination of their formulation, derivation, and theoretical foundations. Furthermore, we underscore significant theoretical contributions and extend the discussion to practical estimation challenges, offering insights into their applicability. Emphasis is placed on methodologies for validating these bounds, providing a robust framework for performance evaluation across a variety of estimation problems in engineering and applied sciences.

Diffusion models have emerged as a powerful tool in generative modeling, demonstrating remarkable capabilities in synthesizing high-fidelity data across various domains. These models transform an initial simple distribution into a more complex one through a denoising process, making them particularly effective for generating detailed and realistic data. In this seminar, we will explore how to integrate diffusion models within a mathematical framework to solve inverse problems, that is, to reconstruct data from partial observations. By leveraging diffusion models as prior knowledge of the data, we introduce a new approach that enables precise generation of conditional data under various noise and artifact conditions. We validate our approach through extensive experiments using various public image datasets, demonstrating its versatility and effectiveness. Furthermore, we demonstrate the practical implications of our method by applying it to reconstruct electrocardiograms (ECGs), where it enhances the quality and reliability of ECG signals, paving the way for broader applications in medical diagnostics and real-time health monitoring.

Cette présentation a pour but d’introduire le radar météorologique et de présenter son fonctionnement global.

In this talk, Colin Cros will focus on the problem of cooperative positioning in the context of GNSS (Global Navigation Satellite Systems). The presentation is divided into two parts. The first examines the solvability of the problem from a theoretical point of view, where the specificity comes from the type of measurements made: pseudo-distances. The approach adopted is based on a study of the measurement graph and the theory of rigidity. The second part deals with practical aspects, presenting how to integrate a cooperative measurement into a Kalman-type navigation filter. The difficulty arises from the lack of knowledge of the correlations between the agents' errors, which means that so-called conservative filters have to be used. This presentation is based on my doctoral thesis, which is available at: https://theses.fr/2024GRALT032

If P1, . . . , Pn and Q1, . . . , Qn are probability measures on Rd and P1 ∗ · · · ∗ Pn and Q1 ∗ · · · ∗ Qn are their respective convolutions, the Rényi divergence Dλ of order λ ∈ (0, 1] satisfies Dλ(P1 ∗ · · · ∗ Pn||Q1 ∗ · · · ∗ Qn) ≤ ni=1 Dλ(Pi ||Qi ). When Pi belongs to the natural exponential family generated by Qi , with the same natural parameter θ for any i = 1, . . . , n, the equality sign holds. The present note tackles the inverse problem, namely “does the equality Dλ(P1 ∗ · · · ∗ Pn||Q1 ∗ · · · ∗ Qn) = ni=1 Dλ(Pi ||Qi ) imply that Pi belongs to the natural exponential family generated by Qi for every i = 1, . . . , n?” The answer is not always positive and depends on the set of solutions of a generalization of the celebrated Cauchy functional equation. We discuss in particular the case P1 = · · · = Pn = P and Q1 = · · · = Qn = Q, with n = 2 and n = ∞, the latter meaning that the equality holds for all n. Our analysis is mainly devoted to P and Q concentrated on non-negative integers, and P and Q with densities with respect to the Lebesgue measure. The results cover the Kullback– Leibler divergence (KL), this being the Rényi divergence for λ = 1. We also show that the only f -divergences such that Df (P∗2||Q∗2) = 2Df (P||Q), for P and Q in the same exponential family, are mixtures of KL divergence and its dual.

This article addresses the problem of computing a Cramér-Rao bound when the likelihood of Euclidean observations is parameterized by both unknown Lie group (LG) parameters and covariance matrix. To achieve this goal, we leverage the LG structure of the space of positive definite matrices. In this way, we can assemble a global LG parameter that lies on the product of the two groups, on which LG's intrinsic tools can be applied. From this, we derive an inequality on the intrinsic error, which can be seen as the equivalent of the Slepian-Bangs formula on LGs. Subsequently, we obtain a closed-form expression of this formula for Euclidean observations. The proposed bound is computed and implemented on two real-world problems involving observations lying in $\mathbb{R}^{p}$, dependent on an unknown LG parameter and an unknown noise covariance matrix: the Wahba's estimation problem on $SE(3)$, and the inference of the pose in $SE(3)$ of a camera from pixel detections.