SCAIM Seminar: Ben Adcock

Abstract: Compressed sensing has been one of the great successes of applied mathematics in the last decade. It allows one to reconstruct sparse signals from seemingly incomplete collections of measurements, and thereby circumvent the classical Nyquist barrier. However, compressed sensing is currently a finite-dimensional theory: it concerns the recovery of vectors in finite-dimensional vector spaces. With this in mind, the purpose of this talk is to introduce a new framework that extends the current theory and techniques to infinite-dimensional problems.

This new framework originates from recent developments in classical (i.e. Nyquist rate) signal recovery, known as generalized sampling. Generalized sampling, which I will introduce in the first part of the talk, allows for signal reconstruction in arbitrary bases in a manner which is both numerically stable and, in a certain sense, optimal. The infinite-dimensional compressed sensing framework builds on this approach by allowing one to take advantage of sparsity to obtain significant subsampling.

This is joint work with Anders Hansen (Cambridge)