A Tight Converse to the Spectral Resolution Limit via Convex Programming
Information Theory
2021-10-18 v2 Functional Analysis
math.IT
Abstract
It is now well understood that convex programming can be used to estimate the frequency components of a spectrally sparse signal from uniform temporal measurements. It is conjectured that a phase transition on the success of the total-variation regularization occurs when the distance between the spectral components of the signal to estimate crosses . We prove the necessity part of this conjecture by demonstrating that this regularization can fail whenever the spectral distance of the signal of interest is asymptotically equal to .
Cite
@article{arxiv.1801.04761,
title = {A Tight Converse to the Spectral Resolution Limit via Convex Programming},
author = {Maxime Ferreira Da Costa and Wei Dai},
journal= {arXiv preprint arXiv:1801.04761},
year = {2021}
}