Atomic Norm Minimization for Decomposition into Complex Exponentials and Optimal Transport in Fourier Domain

Laurent Condat (1, 2)

1 GIPSA-GAIA - GIPSA Pôle Géométrie, Apprentissage, Information et Algorithmes
2 KAUST - King Abdullah University of Science and Technology [Saudi Arabia]

This paper is devoted to the decomposition of vectors into sampled complex exponentials; or, equivalently, to the information over discrete measures captured in a finite sequence of their Fourier coefficients. We study existence, uniqueness, and cardinality properties, as well as computational aspects of estimation using convex semidefinite programs. We then explore optimal transport between measures, of which only a finite sequence of Fourier coefficients is known.

Mots clés: super-resolution; total variation norm; atomic norm; infinite dictionary; truncated moment problem; optimal transport; trigonometric moments

Domaines: Traitement du signal et de l'image [eess.SP]

Laurent Condat. Atomic Norm Minimization for Decomposition into Complex Exponentials and Optimal Transport in Fourier Domain. Journal of Approximation Theory, 2020, 258, pp.105456. ⟨10.1016/j.jat.2020.105456⟩. ⟨hal-02364499v2⟩