PhD position on generative modeling for constrained Bayesian inverse problems in imaging at IMT Atlantique

The goal of this PhD thesis project is to develop generative models that are able to generate constrained-valued images, in contrast to 1) classical unconstrained approaches that work well for images, or 2) methods that handle constrained supports. Here our targets are 2D-fields of constrained values. The models are to be used as supervised priors for inverse problems in remote sensing. We will consider constrained Gaussian Processes as an unsupervised baseline, before moving to the design of flow-matching based techniques for more realistic priors. A first instance of such problems is the spectral unmixing problem in hyperspectral images, where we aim to estimate images for which each pixel is classically constrained to live in the probability simplex. Depening on the findings, other types of constraints and applications will be envisioned.