title: Phase reconstruction from velocity-encoded MRI measurements--a survey of sparsity-promoting variational approaches.
abstract: 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.
authors.affiliation: Magnetic Resonance Research Centre, Department of Chemical Engineering and Biotechnology, c/o Cavendish Stores, JJ Thomson Avenue, Cambridge CB3 0HE, United Kingdom. Electronic address: mb941@cam.ac.uk.
authors.forename: Martin
authors.initials: M
authors.lastname: Benning
authors.affiliation: Magnetic Resonance Research Centre, Department of Chemical Engineering and Biotechnology, c/o Cavendish Stores, JJ Thomson Avenue, Cambridge CB3 0HE, United Kingdom.
authors.forename: Lynn
authors.initials: L
authors.lastname: Gladden
authors.affiliation: Magnetic Resonance Research Centre, Department of Chemical Engineering and Biotechnology, c/o Cavendish Stores, JJ Thomson Avenue, Cambridge CB3 0HE, United Kingdom.
authors.forename: Daniel
authors.initials: D
authors.lastname: Holland
authors.affiliation: Department of Applied Mathematics and Theoretical Physics (DAMTP), University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK; Magnetic Resonance Research Centre, Department of Chemical Engineering and Biotechnology, c/o Cavendish Stores, JJ Thomson Avenue, Cambridge CB3 0HE, United Kingdom.
authors.forename: Carola-Bibiane
authors.initials: CB
authors.lastname: Schönlieb
authors.affiliation: Department of Applied Mathematics and Theoretical Physics (DAMTP), University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK; Magnetic Resonance Research Centre, Department of Chemical Engineering and Biotechnology, c/o Cavendish Stores, JJ Thomson Avenue, Cambridge CB3 0HE, United Kingdom.
authors.forename: Tuomo
authors.initials: T
authors.lastname: Valkonen
mesh_terms: D000465:Algorithms; D007089:Image Enhancement / Q000379:methods; D007090:Image Interpretation, Computer-Assisted / Q000379:methods; D007091:Image Processing, Computer-Assisted / Q000379:methods*; D008279:Magnetic Resonance Imaging / Q000379:methods*; D015233:Models, Statistical; D016011:Normal Distribution; D059629:Signal-To-Noise Ratio; D014867:Water / Q000737:chemistry; D058067:Wavelet Analysis
chemical_list: D014867:Water
keywords: Bregman iteration; Compressed sensing; Higher-order regularisation; Phase-encoded magnetic resonance; Total variation; Velocity imaging