Irène Waldspurger, “Sketching semidefinite programs for super-resolution problems”
“Sketching semidefinite programs for super-resolution problems”
Irene Waldspurger, PhD
CNRS Researcher
Université Paris-Dauphine
Abstract: In this talk, we will consider the canonical example of a super-resolution problem: the recovery of a measure on [0;1] from its first Fourier coefficients, assuming that the measure is the sum of a few spikes. Under weak assumptions, it is known that the measure to be recovered is the solution of a convex infinite-dimensional problem, which is in turn equivalent to a semidefinite program. This property yields a polynomial-time reconstruction algorithm with strong correctness guarantees. Unfortunately, the size of the semidefinite program can be extremely large, even when the measure contains a very small number of spikes. I will present a sketching approach to reduce this size. Proving that this approach retains the correctness guarantees is still an ongoing work. I will present a byproduct of our efforts to find a proof, namely an algorithm to automatically find (simple) upper bounds on some integrals with parameters. This work is a collaboration with Augustin Cosse and Gabriel Peyré
Biography: Irene Waldspurger, PhD, is a CNRS researcher, working at Université Paris Dauphine and at Inria, (Mokaplan team). She is especially interested in inverse problems and non-convex optimization. Irene received her doctoral degree under the supervision of Stéphane Mallat at ENS Paris, (France). Her dissertation was on phase retrieval for the wavelet transform, and on the scattering transform. Irene defended in 2015, and then spent a year at MIT IDSS, (Cambridge, United States), as a post-doctoral fellow mentored by Philippe Rigollet.
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Meeting ID: 986 2441 3365