title: Dictionary learning on the manifold of square root densities and application to reconstruction of diffusion propagator fields.
abstract: In this paper, we present a novel dictionary learning framework for data lying on the manifold of square root densities and apply it to the reconstruction of diffusion propagator (DP) fields given a multi-shell diffusion MRI data set. Unlike most of the existing dictionary learning algorithms which rely on the assumption that the data points are vectors in some Euclidean space, our dictionary learning algorithm is designed to incorporate the intrinsic geometric structure of manifolds and performs better than traditional dictionary learning approaches when applied to data lying on the manifold of square root densities. Non-negativity as well as smoothness across the whole field of the reconstructed DPs is guaranteed in our approach. We demonstrate the advantage of our approach by comparing it with an existing dictionary based reconstruction method on synthetic and real multi-shell MRI data.
authors.forename: Jiaqi
authors.initials: J
authors.lastname: Sun
authors.forename: Yuchen
authors.initials: Y
authors.lastname: Xie
authors.forename: Wenxing
authors.initials: W
authors.lastname: Ye
authors.forename: Jeffrey
authors.initials: J
authors.lastname: Ho
authors.forename: Alireza
authors.initials: A
authors.lastname: Entezari
authors.forename: Stephen J
authors.initials: SJ
authors.lastname: Blackband
authors.forename: Baba C
authors.initials: BC
authors.lastname: Vemuri
mesh_terms: D000465:Algorithms; D000818:Animals; D001185:Artificial Intelligence; D001921:Brain / Q000033:anatomy & histology*; D003198:Computer Simulation; D007089:Image Enhancement / Q000379:methods; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D008279:Magnetic Resonance Imaging / Q000379:methods*; D051379:Mice; D015233:Models, Statistical; D010363:Pattern Recognition, Automated / Q000379:methods*; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity