### Generalized Sampling and Infinite-Dimensional Compressed Sensing

**Hansen, A ***(University of Cambridge)*

Friday 26 August 2011, 14:45-15:30

Seminar Room 1, Newton Institute

#### Abstract

I will discuss a generalization of the Shannon Sampling Theorem that allows for reconstruction of signals in arbitrary bases (and frames). Not only can one reconstruct in arbitrary bases, but this can also be done in a completely stable way. When extra information is available, such as sparsity or compressibility of the signal in a particular basis, one may reduce the number of samples dramatically. This is done via Compressed Sensing techniques, however, the usual finite-dimensional framework is not sufficient. To overcome this obstacle I'll introduce the concept of Infinite-Dimensional Compressed Sensing.

#### Presentation

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