A Tight Converse to the Spectral Resolution Limit via Convex Programming

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 $1/m$.

References in corpus (1)

• Super-resolution, Extremal Functions and the Condition Number of Vandermonde Matrices

Cited by in corpus (5)

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• Two-Dimensional Super-Resolution via Convex Relaxation
• Compressed Super-Resolution of Positive Sources
• On the Stable Resolution Limit of Total Variation Regularization for Spike Deconvolution