Frames for Source Recovery in Dynamical Systems

Akram Aldroubi

Session: Frames, Riesz bases, and related topics (Jorge Antezana)

Keywords: Space-time sampling, discrete dynamical systems, frames, inverse problems, stable reconstruction

TL;DR: Recovering source terms driving a discrete dynamical system from dynamical samples obtained from spatially located frame vectors

Abstract: dynamical systems described by $x_{n+1} = Ax_n + w$, where $x_n$ represents the state in a Hilbert space $\mathcal H$, $A$ is a bounded linear operator, and $w$ is a source term within a closed subspace $W \subseteq \mathcal H$. Using time-space sampling measurements, we establish necessary and sufficient conditions for stable recovery of $w$, independent of the unknown initial state $x_0$. This work has practical applications in areas such as environmental monitoring, where precise source identification is critical.

Submission Number: 8