ED Sciences Physiques et de l'Ingénieur
Deconvolution under Positivity Constraints with Joint Hyperparameter Estimation for High-Resolution Imaging
by Pierre MINIER (Laboratoire de l'Intégration du Matériau au Système)
The defense will take place at 10h00 - Amphithéâtre de l'IMS, Jean-Paul DOM 351 Cours de la Libération, Bâtiment A31, 33405 Talence
in front of the jury composed of
- Jean-François GIOVANNELLI - Professeur des universités - Université de Bordeaux - Directeur de these
- Pierre CHAINAIS - Professeur des universités - Centrale Lille - Rapporteur
- Loïc DENIS - Professeur des universités - Université de Saint-Étienne - Rapporteur
- François ORIEUX - Maître de conférences - Université de Paris-Saclay - CoDirecteur de these
- Angélique DRÉMEAU - Professeure - École Nationale Supérieure de Techniques Avancées - Examinateur
- Cornélia VACAR - Ingénieure de recherche - Commissariat à l'énergie atomique et aux énergies alternatives (CEA) - Examinateur
The work presented in this thesis focuses on deconvolution for high-resolution imaging. In these research works, we consider exclusively fully self-supervised approaches, meaning that they are capable of simultaneously estimating the instrument parameters, the structural and level parameters of the object, as well as the noise level, along with the object of interest itself. In addition, we aim to provide uncertainty quantification, including standard deviations, confidence intervals, and probabilities. Our attention is focused on positive objects, which raises several questions. First, we investigate the construction of the models themselves, whether they are based on truncated or rectified distributions, with or without auxiliary variables, or on filtering approaches. We also investigate their dependence on the model parameters, generally expressed through the partition function, as well as the development of efficient sampling algorithms. Although solutions have been proposed in the literature, these questions remain largely open. Given the relatively generic nature of the problem and of the developments proposed in this thesis, they may have applications in various fields, particularly physical imaging such as astronomy, as well as medical imaging and industrial monitoring. These fields may benefit from a fully self-supervised approach and from the explicit incorporation of constraints such as positivity, which prove to be valuable assets.