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Session S13 - Harmonic Analysis, Fractal Geometry, and Applications

Tuesday, July 20, 20:15 ~ 20:45 UTC-3

Dynamical sampling: A source term inverse problem

Akram Aldroubi

Vanderbilt University, USA   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

Dynamical sampling is a term describing an emerging set of problems related to recovering signals and evolution operators from space-time samples. For example, one problem is to recover a function $f$ from space-time samples $\{(A_{t_i}f)(x_i)\} $ of its time evolution $f_t=(A_{t}f)(x)$, where $\{A_t\}_{t \in \mathcal T }$ is a known evolution operator and $\{(x_i,t_i)\}\subset \mathbb R^d\times \mathbb R^+.$

Applications of dynamical sampling include inverse problems in sensor networks, and source term recovery from physically driven evolutionary systems.

Dynamical sampling problems are tightly connected to frame theory as well as more classical areas of mathematics such as approximation theory, and functional analysis. In this talk, I will present a situation in which a function $u(t,x)$ is evolving under the action of a sum of two unknown terms: a bursts-like term and a background source term. The problem is to recover the driving bursts-like source term from noisy space-time samples of of $u$.

Joint work with Longxiu Huang (UCLA, USA), Keri Kornelson (University of Oklahoma, USA) and Ilya Krishtal (Northern Illinois University, USA).

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