Spikes super-resolution with random Fourier sampling

Yann Traonmilin (1) , Nicolas Keriven (1) , Rémi Gribonval (1) , Gilles Blanchard (2)

1 PANAMA - Parcimonie et Nouveaux Algorithmes pour le Signal et la Modélisation Audio
2 Institut für Mathematik [Potsdam]

We leverage recent results from machine learning to show theoretically and practically that it is possible to stably recover a signal made of few spikes (in the gridless setting) from few random weighted Fourier measurements. Given a free choice of frequencies, a number of measurements lower than with the traditional low-pass filter (uniform sampling of low frequencies) guarantees stable recovery.

Domaines: Traitement du signal et de l'image [eess.SP]; Théorie de l'information et codage [math.IT]

Yann Traonmilin, Nicolas Keriven, Rémi Gribonval, Gilles Blanchard. Spikes super-resolution with random Fourier sampling. SPARS workshop 2017, Jun 2017, Lisbonne, Portugal. 2017. ⟨hal-01509863⟩