Abstract

In this work I will describe a few recent results for the generation of sampling patterns in MRI . In the first part of my talk, I will provide mathematical models describing the sampling problem in MRI . This will allow me to show that the traditional way mathematicians look at an MRI scanner is usually way too idealized and that important ingredients are currently missing in the theories. The mathematical modelling shows that a natural way to generate a pattern consists in projecting a density onto a set of admissible measures. I will then describe two projection algorithms. The first one is based on a distance defined through a convolution mapping the measures to L^{2, while the second is based on the L}2 transportation distance. After describing a few original applications of this formalism, I will show how it allows to significantly improve scanning times in MRI systems with real in vivo experiments. An outcome of this work is that compressed sensing, as it stands, only allows for moderate acceleration factors, while other ideas that take advantage of all the degrees of freedom of an MRI scanner yield way more significant improvements.