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 totalvariation 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.
On the other hand, it is known that TV-regularization can fail whenever ∆ < 2/N REF .
A Tight Converse to the Spectral Resolution Limit via Convex Programming
2018 IEEE International Symposium on Information Theory (ISIT)
2018 IEEE International Symposium on Information Theory (ISIT)
Computer Science Mathematics