On strong basins of attractions for non-convex sparse spike estimation: upper and lower bounds
Language
en
Article de revue
This item was published in
Journal of Mathematical Imaging and Vision. 2023-09-28
Springer Verlag
English Abstract
In this article, we study the size of strong basins of attractions for the non-convex sparse spike estimation problem. We first extend previous results to obtain a lower bound on the size of sets where gradient descent ...Read more >
In this article, we study the size of strong basins of attractions for the non-convex sparse spike estimation problem. We first extend previous results to obtain a lower bound on the size of sets where gradient descent converges with a linear rate to the minimum of the non-convex objective functional. We then give an upper bound that shows that the dependency of the lower bound with respect to the number of measurements reflects well the true size of basins of attraction for random Gaussian Fourier measurements. These theoretical results are confirmed by experiments.Read less <
ANR Project
Régularisation performante de problèmes inverses en grande dimension pour le traitement de données - ANR-20-CE40-0001
Origin
Hal imported