Leveraging data-driven low-dimensional signal representations to solve inverse problems

Ricardo Borsoi (CNRS, CRAN Laboratory, Nancy)
March 01, 2024 — 11:00 — "new L2S location (IBM building), 3rd floor room" (and Teams)

Abstract

Inverse problems, such as image reconstruction, deconvolution, or hyperspectral unmixing, typically involve the recovery of high-dimensional signals from a small amount of measurements. One of the key elements in successfully solving inverse problems is the design of priors that accurately describe the signals to be recovered. A wide range of priors have been considered for this task, such as the Tikhonov and sparsity regularizations. Recently, data-driven, low-dimensional representations (such as deep generative models) have been investigated to represent the signals using a small number of parameters, making the reconstruction problem well-posed. In this talk, we will present recent results on the use of generative/latent variable models as priors for inverse problems. Theoretical results concerning the capacity of such approaches to accurately recover the correct solution, which is one of the features that makes them appealing, will be presented. We will discuss some of the challenges to their use in practical problems, and how such models can be used to solve the unsupervised hyperspectral unmixing problem.

Bio

Ricardo Borsoi received the the masters degree from Federal University of Santa Catarina, Brazil, in 2016 and the Ph.D. degree in cotutelle from the Federal University of Santa Catarina, Brazil, and Côte d’Azur University, France, in 2021. His thesis was selected by the Brazilian research council among the 3 best theses in electrical, computer and biomedical engineering defended in 2021. During 2022, he was a Postdoctoral Researcher with the CRAN Laboratory, Nancy, France, where he now works as a chargée de recherche after joining the French National Center for Scientific Research (CNRS) as a chargée de recherche in October 2022. His works works on developing interpretable machine learning solutions to inverse problems and data fusion based on tensor decomposition, deep generative models, with applications in hyperspectral and medical image analysis.