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

JOURNAL OF APPROXIMATION THEORY

卷:258

Article

Condat, Laurent¹ 

[1] King Abdullah Univ Sci & Technol KAUST, Visual Comp Ctr, Thuwal, Saudi Arabia

关键词: Atomic norm;    Infinite dictionary;    Truncated moment problem;    Trigonometric moments;    Total variation norm;    Super-resolution;    Optimal transport;   

DOI  :  10.1016/j.jat.2020.105456

来源: Elsevier

【 摘 要 】

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. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free