Abstract

In this talk we will introduce the basics of compressed sensing through the model examples of NMR and MRI , and discuss the various methods and tricks that can be used to improve reconstruction, depending on the situation. After this introduction, we’ll focus on the phenomenon of Superesolution, where the quality of reconstruction improves with scale keeping the sampling rate the same. An answer to this might be the principles of asymptotic sparsity, which means there is sparsity in the basis coefficients as we move along the ordering, and asymptotic incoherence, where coefficients of the sensing matrix decay. We’ll then discuss some results on asymptotic incoherence in the case of using the Fourier basis with wavelets and look at its consequences in finding a good sampling pattern.

The work to be presented was done jointly with Dr Anders Hansen at DAMTP and Dr Daniel Holland at the Chemical Engineering Department.