TV- based methods for sparse reconstruction in continuous-domain
| Quand ? |
Le 08/02/2021, de 10:30 à 11:30 |
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| S'adresser à | Titouan Vayer |
| Participants |
Julien Fageot |
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Title: TV- based methods for sparse reconstruction in continuous-domain
Abstract: We consider the problem of reconstructing an unknown function from some finitely many and possibly corrupted linear measurements. This is achieved by considering an optimization task using a sparsity-promoting regularization. More precisely, we consider the total-variation norm on Radon measures - which is the infinite-dimensional counterpart of the classic L1 norm used for sparse reconstruction in sparse statistical learning and compressed sensing - and a regularization operator that controls the smoothness of the reconstruction. The goal of this presentation is to discuss some theoretical and computational aspects of this infinite-dimensional optimization problem (form of the solutions, connection with spline theory, uniqueness issues, algorithmic strategies) and to illustrate the potential of the method for continuous-domain signal reconstruction.