学术报告（唐穗 2024.8.30）

Abstract：

Modern applications frequently involve evolving network data in fields such as sensor networks, neural networks, transportation systems, and social networks. These networks often consist of a large number of nodes, posing significant challenges in both data processing and storage. To address these challenges, it is essential to minimize the data volume while retaining critical information. Mathematically, this is achieved through the optimal selection of space-time samples—a problem known as dynamical sampling—and the development of algorithms to accurately reconstruct the dynamical system from these sparse samples.

While a substantial body of literature has focused on the deterministic aspects of dynamical sampling, this talk will explore the randomized dynamical sampling problem. We will present recent advances in two key areas: (1) Theoretical Insights on Recoverability: We will discuss conditions under which dynamical systems can be reconstructed from space-time samples, considering both known (linear inverse problems) and unknown (nonlinear inverse problems) evolution operators. (2) Reconstruction Algorithms: Leveraging and extending techniques from compressive sensing and matrix completion, we will introduce novel algorithms designed for efficient system recovery.

This talk is based on collaborative work with Akram Aldroubi (Vanderbilt University), Jiahui Cheng (Georgia Tech), Longxiu Huang (Michigan State University), Christian Kummerer (University of North Carolina Wilmington), Mauro Maggioni (Johns Hopkins University), and Deanna Needell (University of California, Los Angeles).