Signal Recovery, Restriction Theory, and Applications - Part I

Explore signal recovery and restriction theory in this 59-minute lecture by Alex Iosevich from the Hausdorff Center for Mathematics. Delve into the problem of recovering a signal f : Zd N → C transmitted via its Fourier transform when certain frequencies are missing. Learn about the Matolcsi-Szuchs and Donoho-Stark theorem, which provides conditions for exact signal recovery. Discover how non-trivial restriction estimates can significantly improve recovery conditions. Examine the application of multi-linear restriction theory to enhance recovery in multiple transmissions. Investigate continuous aspects of the problem and understand the restriction conjecture as a signal recovery mechanism. This lecture presents joint work with Azita Mayeli (CUNY) and offers valuable insights into advanced signal processing techniques.