Dictionary learning on the manifold of square root densities and application to reconstruction of diffusion propagator fields

Authors:
Jiaqi Sun;Yuchen Xie;Wenxing Ye;Jeffrey Ho;Alireza Entezari;Stephen J. Blackband;Baba C. Vemuri
Affiliations:
CISE Department, University of Florida, Gainesville, FL;Qualcomm Inc., San Diego, CA;Google Inc., Mountain View, CA;CISE Department, University of Florida, Gainesville, FL;CISE Department, University of Florida, Gainesville, FL;Department of Neuroscience, McKnight Brian Institute, University of Florida, Gainesville, FL;CISE Department, University of Florida, Gainesville, FL
Venue:
IPMI'13 Proceedings of the 23rd international conference on Information Processing in Medical Imaging
Year:
2013

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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.