Dynamical sampling is a term describing an emerging set of problems related to recovering signals and evolution operators from space-time samples. For example, consider the abstract IVP in a separable Hilbert space $\mathcal{H}$:
\begin{equation} \begin{cases} \dot{u}(t) =Au(t) + F(t)\\ u(0)=u_{0} \end{cases}\,, \end{equation} $t\in \mathbb{R}_{+},u_{0}\in \mathcal{H}$,
where $t\in [0,\infty), u : \mathbb{R}_{+} \mapsto \mathcal{H}, \dot{u} : \mathbb{R}_{+} \mapsto \mathcal{H}$ is the time derivative of $u$, and $u_0$ is an initial condition. When, $F = 0, A$ is a known (or unknown) operator, and the goal is to recover $u_0$ from the samples $\{ u(t_{i},x_{j}) \}$ on a sampling set ${(t_i, x_j )}$, we get the so called space-time sampling problems. If the goal is to identify the operator $A$, or some of its characteristics, we get the system identification problems. If instead we wish to recover $F$, we get the source term problems. In this talk, I will present an overview of dynamical sampling, and some open problems.
De Eero Simoncelli
De Naoki Saito
De Maarten de Hoop
De Martin Vetterli
De Maureen Clerc
De Irène Waldspurger
De Jérôme Kalifa
De Gitta Kutyniok
De Michael Unser
De Edouard Oyallon
De Remi Gribonval
De Ronnie Pavlov
De Viviane Pons
De Wolfgang Arendt
De David Hewett
