Atomic norm minimization for decomposition into complex exponentials and optimal transport in Fourier domain

Condat, Laurent

Atomic norm minimization for decomposition into complex exponentials and optimal transport in Fourier domain

Files

Condat-atomic.pdf (335.85 KB)

Type

Article

Authors

Condat, Laurent

KAUST Department

Visual Computing Center (VCC)
Visual Computing Center, King Abdullah University of Science and Technology (KAUST), Thuwal, Saudi Arabia

Online Publication Date

2020-07-13

Print Publication Date

2020-10

Date

2020-07-13

Submitted Date

2018-09-25

Abstract

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.

Citation

Condat, L. (2020). Atomic norm minimization for decomposition into complex exponentials and optimal transport in Fourier domain. Journal of Approximation Theory, 258, 105456. doi:10.1016/j.jat.2020.105456