## Ronald DeVore, University of South Carolina

Instance-optimal estimates in Compressed Sensing

**
Thursday April 20, 4:00PM,
Herman Brown 227**
The usual paradigm for encoding signals is based on the Shannon sampling theorem.
If the signal is broad-banded then this requires a high sampling rate even though the information
content in the signal may be small. Compressed Sensing is an attempt to get out of this dilemma
and sample at close to the information rate. The fact that this may be possible is embedded
in some old mathematical results in functional analysis, geometry and approximation.
This talk will be an excursion into these topics which will focus on the relation between the number of samples we take of a signal and how well we can approximate the signal. It will take place in the
discrete setting for vectors in Euclidean space. The talk should be understandable to graduate students
and non specialists.