Phase reconstruction from velocity-encoded MRI measurements – A survey of sparsity-promoting variational approaches

Martin Benning, Lynn Gladden, Daniel Holland, Carola-Bibiane Schönlieb, Tuomo Valkonen

Research output: Contribution to journalArticlepeer-review

51 Scopus citations


In recent years there has been significant developments in the reconstruction of magnetic resonance velocity images from sub-sampled k-space data. While showing a strong improvement in reconstruction quality compared to classical approaches, the vast number of different methods, and the challenges in setting them up, often leaves the user with the difficult task of choosing the correct approach, or more importantly, not selecting a poor approach. In this paper, we survey variational approaches for the reconstruction of phase-encoded magnetic resonance velocity images from sub-sampled k-space data. We are particularly interested in regularisers that correctly treat both smooth and geometric features of the image. These features are common to velocity imaging, where the flow field will be smooth but interfaces between the fluid and surrounding material will be sharp, but are challenging to represent sparsely. As an example we demonstrate the variational approaches on velocity imaging of water flowing through a packed bed of solid particles. We evaluate Wavelet regularisation against Total Variation and the relatively recent second order Total Generalised Variation regularisation. We combine these regularisation schemes with a contrast enhancement approach called Bregman iteration. We verify for a variety of sampling patterns that Morozov's discrepancy principle provides a good criterion for stopping the iterations. Therefore, given only the noise level, we present a robust guideline for setting up a variational reconstruction scheme for MR velocity imaging. © 2013 Elsevier Inc. All rights reserved.
Original languageEnglish (US)
Pages (from-to)26-43
Number of pages18
JournalJournal of Magnetic Resonance
StatePublished - Jan 2014
Externally publishedYes

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUK-I1-007-43
Acknowledgements: This work has been financially supported by the King Abdullah University of Science and Technology (KAUST) Award No. KUK-I1-007-43, and the EPSRC/Isaac Newton Trust Small Grant 2012/13 "Non-smooth geometric reconstruction for high resolution MRI imaging of fluid transport in bed reactors", EPSRC Grant EP/F047991/1, and Microsoft Research Connections.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.


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