5 papers
Statistical Estimation of Monge Transport Maps via Brenier Potentials
Elsa Cazelles, Edouard Pauwels, Léo Portales
We introduce and analyze a statistical estimator for Monge transport maps: solutions to the quadratic optimal transport problem in the Euclidean space. For absolutely continuous so…
An analytic theory of convolutional neural network inverse problems solvers
Minh Hai Nguyen, Quoc Bao Do, Edouard Pauwels +1
Supervised convolutional neural networks (CNNs) are widely used to solve imaging inverse problems, achieving state-of-the-art performance in numerous applications. However, despite…
A Morse-Bott Framework for Blind Inverse Problems: Local Recovery Guarantees and the Failure of the MAP
Minh-Hai Nguyen, Edouard Pauwels, Pierre Weiss
Maximum A Posteriori (MAP) estimation is a cornerstone framework for blind inverse problems, where an image and a forward operator are jointly estimated as the maximizers of a post…
Sample complexity of optimal transport barycenters with discrete support
Léo Portales, Edouard Pauwels, Elsa Cazelles
Computational implementation of optimal transport barycenters for a set of target probability measures requires a form of approximation, a widespread solution being empirical appro…
On the sequential convergence of Lloyd's algorithms
Léo Portales, Elsa Cazelles, Edouard Pauwels
Lloyd's algorithm is an iterative method that solves the quantization problem, i.e. the approximation of a target probability measure by a discrete one, and is particularly used in…