Spikes super-resolution with random Fourier sampling

Abstract : 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.
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https://hal.archives-ouvertes.fr/hal-01509863
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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⟩

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