When:
Thursday, February 27, 2025
3:00 PM - 4:00 PM CT
Where: Lunt Hall, 107, 2033 Sheridan Road, Evanston, IL 60208 map it
Audience: Faculty/Staff - Student - Public - Post Docs/Docs - Graduate Students
Contact:
Rachel Greenfeld
Group: Department of Mathematics: Analysis Seminar
Category: Lectures & Meetings
Title: Exact signal recovery, restriction phenomenon, and applications
Abstract: Let $f: {\mathbb Z}_N^d \to {\mathbb C}$ be a signal and suppose that the frequencies ${\{\widehat{f}(m)\}}_{m \in S}$ are missing, where
$$\widehat{f}(m)=N^{-\frac{d}{2}} \sum_{x \in {\mathbb Z}_N^d} e^{-\frac{2 \pi i x \cdot m}{N}} f(x).$$
Under what reasonable assumption can we recover the original signal? We are going to discuss the connections between this problem and the classical restriction phenomenon in harmonic analysis. Bourgain's celebrated $\Lambda(q)$ theorem and its variants by Talagrand and others play an important role in our investigations.