Convergence of grid-based inverse problems toward their continuous limit
Julien Fageot

Meeting • 2023-07-11

Abstract
We consider optimization problems over function spaces to reconstruct an unknown function from some finite-dimensional measurements. We tackle the ill-posedness of the reconstruction task using sparsity-promoting regularization (total variation norm of functions with bounded variation). In order to go from the infinite-dimensional mathematical world to its discrete computer-based implementation, we consider grid-based approximations of the initial continuous-domain inverse problems. I will present a general framework which allows to say when a sequence of optimization problems (Pn) converge to a limiting optimization problem (P) and see how this can be used to show the convergence of grid-based methods towards their continuous limit.