Sketching Semidefinite Programs for Super-Resolution Problems

Explore a lecture on sketching semidefinite programs for super-resolution problems, focusing on the recovery of measures from Fourier coefficients. Delve into the canonical example of recovering a measure on [0;1] from its first Fourier coefficients, assuming the measure is the sum of a few spikes. Learn about the convex infinite-dimensional problem and its equivalent semidefinite program, which provides a polynomial-time reconstruction algorithm with strong correctness guarantees. Discover a sketching approach to reduce the size of large semidefinite programs and gain insights into ongoing work to prove the correctness of this method. Examine a byproduct of this research: an algorithm for automatically finding simple upper bounds on integrals with parameters. This 33-minute talk, presented by Irène Waldspurger from CNRS & Dauphine at the Institut des Hautes Etudes Scientifiques (IHES), is a collaboration with Augustin Cosse and Gabriel Peyré.