In this talk, we describe a variational model for spatio-temporal Magnetic Resonance Imaging (MRI) that allows linking the computation - in a single model - of the reconstruction of an image sequence from Fourier measurements to the inherent dynamics in the scene. More precisely, we recast the image formation and motion estimation problems as an unconstrained minimisation problem that is solved, iteratively, by breaking it up into two more computationally tractable problems. Particularly, we focus our model to solve the central limitation of MRI, which is the linear relation between the necessary measures to form an image and the acquisition time. We show that injecting physical motion into the compressed sensing computation produces a better approximation of the image formation, that, in fact, is closer to the gold-standard. We also demonstrate that the synergy created by our variational model turns out to have positive clinical potentials in terms of improving image quality. Finally, we shall close this talk by suggesting a further improvement of our model by creating a connection between our variational model and machine learning.

This presentation is part of Minisymposium “MS72 - Inverse problems with imperfect forward models (2 parts)”
organized by: Yury Korolev (University of Cambridge) , Martin Burger (University of Muenster) .

Authors:

Carola-Bibiane Schönlieb (University of Cambridge)

Angelica I. Aviles-Rivero (University of Cambridge)

Keywords:

image reconstruction, inverse problems, medical imaging, motion estimation, partial differential equation models