SEMINAR:Exact signal recovery, uncertainty principle...

Guest: Alex Iosevich, University of Rochester

Title: Exact signal recovery, uncertainty principle, and Fourier restriction

Abstract:In their seminal paper from the late 80s, Donoho and Stark considered the following problem. Suppose that    is a function (sometimes called a signal) that is transmitted via its Fourier transform where  . Suppose that the frequencies    are lost, or unobserved. Under what conditions  can  be recovered the original signal exactly? Donoho and Stark showed using the Fourier uncertainty principle that the exact recovery is possible if the number of non-zero values of the signal multiplied by the size of   is smaller than . We are going to study this problem under the assumption that the set of missing frequencies is generic. Fourier restriction and Bourgain's results on Rudin's celebrated    problem play an important role.