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A Tight Converse to the Spectral Resolution Limit via Convex Programming

by   Maxime Ferreira Da Costa, et al.
Imperial College London

It is now well understood that convex programming can be used to estimate the frequency components of a spectrally sparse signal from m 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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