Contemporary sampling techniques and compressed sensing (Part III course)

Lecturers: Anders Hansen and Bogdan Roman
Time, location: Tue & Thu 11am, MR11

Previous years: 2014-15.

This is a (non-examinable) graduate course on sampling theory and compressed sensing for use in signal processing and imaging. 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. Thus, we will take the word contemporary quite literally and emphasise the latest developments, however, no previous knowledge of the field is assumed. Although the main focus will be on compressed sensing, it will be presented in the general framework of sampling theory. The course will focus on how to get compressed sensing to work in real life applications and is aimed at students and post docs who want to learn how compressed sensing can be used in their research.

References: The course will be based on slides and references to the books:
Compressed Sensing (Eldar, Kutyniok), CUP 2012,
A Mathematical Introduction to Compressive Sensing (Foucart, Rauhut), Birkhauser 2014,

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

- Generalized sampling and infinite-dimensional compressed sensing