# Compressed Sensing - Applications and Theory

### University of Oslo, 23 -25 March, 2015

Vilhelm Bjerknes' Hus (Auditorium 2), Blindern: 12:15-14:00 Monday and Tuesday, 14:15-16:00 Wednesday

This will be a short 6 lectures course on contemporary compressed sensing designed for researchers from engineering, physics, mathematics, life sciences etc. on how to get compressed sensing to work in their own field.

Compressed sensing is a theory of randomisation, sparsity and non-linear optimisation techniques that breaks traditional barriers in sampling theory. Since its introduction in 2004 the field has exploded and is rapidly growing and changing. The course will be introductory but aims at providing the latest developments in the field. The course will focus on how to get compressed sensing to work in real life applications and is aimed at students, post docs and professors who want to learn how compressed sensing can be used in their research. The course is designed to be very accessible to people outside the math department and applications will be emphasised. Typical examples include Magnetic Resonance Imaging (MRI), Computerised Tomography (CT), Electron microscopy, Fluorescence microscopy, Helium atom scattering, radio interferometry and imaging in general.

For a recent article in Apollon about compressed sensing see: Apollon (in Norwegian)

**References:** The course will be based on slides and references to books and papers:

Compressed Sensing (Eldar, Kutyniok), CUP 2012,

A Mathematical Introduction to Compressive Sensing (Foucart, Rauhut), Birkhauser 2014

The books mentioned above are excellent for covering compressed sensing up to about 2011. Chapter 1 in EK is an excellent introduction to the basics. The field has changes considerably since then, and we will emphasise more recent developments. Thus, the following papers will also be useful:

- *On asymptotic structure in compressed sensing*

- *Breaking the coherence barrier: A new theory for compressed sensing*

- *The quest for optimal sampling: computationally efficient, structure-exploiting measurements for compressed sensing*

- *Generalized sampling: stable reconstructions, inverse problems and compressed sensing over the continuum*