title: Least-square NUFFT methods applied to 2-D and 3-D radially encoded MR image reconstruction.
abstract: Radially encoded MRI has gained increasing attention due to its motion insensitivity and reduced artifacts. However, because its samples are collected nonuniformly in the k-space, multidimensional (especially 3-D) radially sampled MRI image reconstruction is challenging. The objective of this paper is to develop a reconstruction technique in high dimensions with on-the-fly kernel calculation. It implements general multidimensional nonuniform fast Fourier transform (NUFFT) algorithms and incorporates them into a k-space image reconstruction framework. The method is then applied to reconstruct from the radially encoded k-space data, although the method is applicable to any non-Cartesian patterns. Performance comparisons are made against the conventional Kaiser-Bessel (KB) gridding method for 2-D and 3-D radially encoded computer-simulated phantoms and physically scanned phantoms. The results show that the NUFFT reconstruction method has better accuracy-efficiency tradeoff than the KB gridding method when the kernel weights are calculated on the fly. It is found that for a particular conventional kernel function, using its corresponding deapodization function as a scaling factor in the NUFFT framework has the potential to improve accuracy. In particular, when a cosine scaling factor is used, the NUFFT method is faster than KB gridding method since a closed-form solution is available and is less computationally expensive than the KB kernel (KB griding requires computation of Bessel functions). The NUFFT method has been successfully applied to 2-D and 3-D in vivo studies on small animals.
authors.affiliation: Department of Electrical and Computer Engineering, Duke University, Durham, NC 27708, USA.
authors.forename: Jiayu
authors.initials: J
authors.lastname: Song
authors.forename: Yanhui
authors.initials: Y
authors.lastname: Liu
authors.forename: Sally L
authors.initials: SL
authors.lastname: Gewalt
authors.forename: Gary
authors.initials: G
authors.lastname: Cofer
authors.forename: G Allan
authors.initials: GA
authors.lastname: Johnson
authors.forename: Qing Huo
authors.initials: QH
authors.lastname: Liu
mesh_terms: D000818:Animals; D003198:Computer Simulation; D007091:Image Processing, Computer-Assisted / Q000379:methods*; D016018:Least-Squares Analysis; D008279:Magnetic Resonance Imaging / Q000379:methods*; D051379:Mice; D015233:Models, Statistical; D019047:Phantoms, Imaging