Signal Recovery, Restriction Theory, and Applications - Lecture 4

Explore signal recovery and restriction theory in this 58-minute lecture by Alex Iosevich from the Hausdorff Center for Mathematics. Delve into the problem of recovering a signal transmitted via its Fourier transform when certain frequencies are missing. Examine the conditions under which exact signal recovery is possible, including the Matolcsi-Szuchs and Donoho-Stark theorems. Discover how non-trivial restriction estimates can significantly improve recovery conditions, and learn about 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. Gain insights from joint work with Azita Mayeli (CUNY) on this advanced topic in mathematical signal processing and harmonic analysis.