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arXiv · 1801.04761

A Tight Converse to the Spectral Resolution Limit via Convex Programming

Maxime Ferreira Da Costa·Wei Dai
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Abstract

It is now well understood that convex programming can be used to estimate the frequency components of a spectrally sparse signal from $2m+1$ 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 $1/m$. 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 $1/m$.

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Maxime Ferreira Da Costa, Wei Dai. 2018-01-15. A Tight Converse to the Spectral Resolution Limit via Convex Programming. https://doi.org/10.1109/isit.2018.8437490

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