Dictionary Learning on the Manifold of Square Root Densities and Application to Reconstruction of Diffusion Propagator Fields^*

Jiaqi Sun¹, Yuchen Xie², Wenxing Ye³, Jeffrey Ho¹, Alireza Entezari¹, Stephen J. Blackband⁴, and Baba C. Vemuri¹

¹CISE Department, University of Florida, Gainesville, FL 32611, USA

²Qualcomm Inc., San Diego, CA 92121, USA

³Google Inc., Mountain View, CA 94043, USA

⁴Department of Neuroscience, McKnight Brian Institute, University of Florida, Gainesville, FL 32611, USA

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.

Keywords: Dictionary learning, Manifold, DW-MRI, Diffusion propagator reconstruction

^*This research was in part funded by the NIH grant NS066340 to Baba C. Vemuri, and the following grants AFOSR FA9550-12-1-0304, ONR N000141210862, NSF CCF-1018149 to Alireza Entezari.

LNCS 7917, p. 619 ff.

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