"Sampling rates for l1-synthesis"Weiss, PierreIn this talk, I will try to shed some light on the geometry of l1-based signal recovery. This setting has been studied extensively in the last decade with the advent of compressed sensing and super-resolution. There is however clear evidence that the best existing theories are still unable to predict some of the observed numerical behaviours, especially when using redundant dictionaries. I will work in the simple framework of under-sampled noisy Gaussian measurements, and try to explain how the geometry of high dimensional convex cones enters in the game and how the circumangle of a descent cone can provide tight bounds on the number of measurements sufficient for efficient recovery. This is a joint work with M. März, C. Boyer and J. Kahn, published in FoCM 2022. |
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