The basins of attraction of the global minimizers of non-convex inverse problems with low-dimensional models in infinite dimension
Language
en
Article de revue
This item was published in
Information and Inference. 2022
Oxford University Press (OUP)
English Abstract
Non-convex methods for linear inverse problems with low-dimensional models have emerged as an alternative to convex techniques. We propose a theoretical framework where both finite dimensional and infinite dimensional ...Read more >
Non-convex methods for linear inverse problems with low-dimensional models have emerged as an alternative to convex techniques. We propose a theoretical framework where both finite dimensional and infinite dimensional linear inverse problems can be studied. We show how the size of the the basins of attraction of the minimizers of such problems is linked with the number of available measurements. This framework recovers known results about low-rank matrix estimation and off-the-grid sparse spike estimation, and it provides new results for Gaussian mixture estimation from linear measurements. keywords: low-dimensional models, non-convex methods, low-rank matrix recovery, off-the-grid sparse recovery, Gaussian mixture model estimation from linear measurements.Read less <
ANR Project
Super-résolution d'images multi-échelles en sciences des matériaux avec des attributs géométriques - ANR-18-CE92-0050
Régularisation performante de problèmes inverses en grande dimension pour le traitement de données - ANR-20-CE40-0001
Régularisation performante de problèmes inverses en grande dimension pour le traitement de données - ANR-20-CE40-0001
Origin
Hal imported