Abstract: How much can we learn about an evolving system when we observe only a small part of it? This question arises in sensor networks, environmental monitoring, and data-driven modeling, where measurements may be expensive, incomplete, or corrupted. Temporal observations offer an opportunity to compensate for limited spatial access, but reliable recovery depends on the interplay between the system dynamics, the sampling strategy, and the structure of the unknown quantities. In this talk, I will present sampling and reconstruction methods that exploit this interplay. I will first discuss dynamical sampling on graphs, focusing on the joint recovery of an initial state and a persistent source from partial space–time measurements. The analysis identifies how graph structure and sampling distributions influence the number of measurements needed for stable reconstruction. I will then consider the recovery of spectral information about unknown convolutional dynamics when some temporal observations contain large errors. By exploiting the low-rank structure of Hankel matrices formed from the measurements, we can connect this identification problem to robust matrix recovery and completion. Throughout the talk, I will emphasize the mathematical principles behind sampling design, stability, and computational efficiency, together with numerical examples illustrating their practical consequences. These results offer perspectives on sensing and identification under limited measurement resources.
Bio: Longxiu Huang is an Assistant Professor in the Department of Computational Mathematics, Science and Engineering and the Department of Mathematics at Michigan State University. She received her Ph.D. in Mathematics from Vanderbilt University in 2019, advised by Akram Aldroubi. She was subsequently an Assistant Adjunct Professor in the Department of Mathematics at UCLA, working with Deanna Needell. Her research sits at the interface of applied harmonic analysis and randomized numerical linear algebra. She works on sampling theory, low-rank matrix and tensor recovery, and CUR-type decompositions — with a recurring emphasis on methods that are fast, provably accurate, and interpretable in terms of the original data.
Zoom Link: https://msu.zoom.us/j/97383731374
Password: 680558