title: A fast wavelet-based reconstruction method for magnetic resonance imaging.
abstract: In this work, we exploit the fact that wavelets can represent magnetic resonance images well, with relatively few coefficients. We use this property to improve magnetic resonance imaging (MRI) reconstructions from undersampled data with arbitrary k-space trajectories. Reconstruction is posed as an optimization problem that could be solved with the iterative shrinkage/thresholding algorithm (ISTA) which, unfortunately, converges slowly. To make the approach more practical, we propose a variant that combines recent improvements in convex optimization and that can be tuned to a given specific k-space trajectory. We present a mathematical analysis that explains the performance of the algorithms. Using simulated and in vivo data, we show that our nonlinear method is fast, as it accelerates ISTA by almost two orders of magnitude. We also show that it remains competitive with TV regularization in terms of image quality.
authors.affiliation: Biomedical Imaging Group, École Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland.
authors.forename: M
authors.initials: M
authors.lastname: Guerquin-Kern
authors.forename: M
authors.initials: M
authors.lastname: Häberlin
authors.forename: K P
authors.initials: KP
authors.lastname: Pruessmann
authors.forename: M
authors.initials: M
authors.lastname: Unser
mesh_terms: D000465:Algorithms; D001921:Brain / Q000033:anatomy & histology; D006801:Humans; 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*; D009682:Magnetic Resonance Spectroscopy / Q000379:methods; D017711:Nonlinear Dynamics; D019047:Phantoms, Imaging; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity