FoCM 2014 conference

Workshop A2 - Computational Harmonic Analysis, Image and Signal Processing

December 12, 14:30 ~ 14:55 - Room C21

## FUNDAMENTALS OF DYNAMICAL SAMPLING

### Carlos Cabrelli

### Dept. of Mathematics, FCEyN, UBA and IMAS-UBA-CONICET, Argentina - cabrelli@dm.uba.ar

Dynamical sampling refers to the process that results from sampling an evolving signal $f$ at various times. The fundamental question of this spatial-temporal sampling is: when do coarse samplings taken at varying times contain the same information as a finer sampling taken at the earliest time? In other words, under what conditions on an evolving system, can time samples be traded for spatial samples?

Because dynamical sampling uses samples from varying time levels for a single reconstruction, it departs from classical sampling theory in which a signal $f$ does not evolve in time and is to be reconstructed from its samples at a single time $t=0$.

In this talk we study this problem in finite dimensional spaces, and for a large class of self adjoint operators in infinite dimensional spaces.

Joint work with Akram Aldroubi (Vanderbilt University, US), Ursula Molter (University of Buenos Aires, Argentina), Sui Tang (Vanderbilt University, US)..