# Super-resolution via Convex Programming

In this project we consider the problem of super-resolving a signal from low-pass data via convex programming and the related problem of super-resolving the spectrum of a multisinusoidal signal from a finite number of samples. Exact recovery under a minimum separation condition is proved in [1] and [4]. Stability guarantees are derived in [2] in terms of the increase in resolution that we demand from the recovery process. Complementary support-detection guarantees that do not depend on the amplitude of the signal are established in [3]. Finally, [5] illustrates the flexibility of an optimization-based framework by describing an extension to the demixing of sines and spikes, which allows to provably achieve robust spectral super-resolution in the presence of outliers.