Contemporary sampling techniques and compressed sensing (Part III course)

Lecturers: Anders Hansen and Bogdan Roman
Time, location: Tue & Thu 10pm, MR11

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

  • Week 1: Introduction to compressed sensing.

    Intro lecture: Slides
    Reading list: (1) Ch1 in FH, LMS lecture series by Emmanuel Candes, and "On asymptotic structure in compressed sensing"

  • Week 2: Introduction to compressed sensing.

    Lecture 1: Slides
    Lecture 2: Slides
    Reading list: Ch1 in EK. For discussions on random Bernoulli and Gaussian matrices, see Chapter 9 of FR. 
For discussions on wavelets, see Chapter 6 and 9 (linear and non-linear approximation with wavelet) in "A wavelet tour of signal processing" by Stephane Mallat.