Seminar on Compressive Sensing with Applications to Signal Processing and Parametric PDEs

Dr. Rauhut holds a chair in Mathematics (Analysis) at RWTH Aachen University, Germany. The research interests of Dr. Rauhut resolve around applied Harmonic Analysis, compressive sensing, mathematical signal processing, random matrices, convex optimization, and approximation theory.

Holger Rauhut is the co-author of the recently published book on Compressed Sensing, which gives a detailed account of the core theory upon which the field is build. It also serves as a reliable resource for practitioners and researchers in the fields of in mathematics, engineering, and computer science who want to acquire a careful understanding of the subject.

We are very much looking to welcoming you to the seminar!

Abstract:

Compressive sensing predicts that sparse vectors can be recovered from underdetermined linear measurements via efficient algorithms.

This finding has a large number of potential applications in signal and data processing. The talk gives an overview of the theory which builds on approximation theory, random matrices and convex optimization. I will highlight a few applications in signal processing such as magnetic resonance imaging and radar.

In the second part of the lecture, I will discuss applications of compressive sensing to the numerical solution of parametric operator equations (PDEs) when the parameter space is high-dimensional. I will give theoretical error rates and explain advantages with respect to other approaches.