PIMS/Shell Lunchbox Lecture: Compressed Sensing: Theory, Applications and Extensions

Many problems in science and engineering require the reconstruction of an object - an image or signal, for example - from a collection of measurements.  Due to time, cost or other constraints, one is often severely limited by the amount of data that can be collected.  Compressed sensing is a mathematical theory and set of techniques that aim to improve reconstruction quality from a given data set by leveraging the underlying structure of the unknown object; specifically, its sparsity.  

In this talk I will commence with an overview of the fundamentals of compressed sensing and discuss some of its applications.  However, I will next explain that, despite the large and growing body of literature on compressed sensing, many of these applications do not fit into the standard framework.  I will then describe a more general framework for compressed sensing which aims to bridge this gap.  Finally, I will show that this new framework is not just useful in explaining existing applications of compressed sensing.  The new insight it brings leads to substantially better compressed sensing-based approaches than the current state-of-the-art in a number of applications.