Diffeomorphic metric mapping of hybrid diffusion imaging based on BFOR signal basis

Authors:
Jia Du;A. Pasha Hosseinbor;Moo K. Chung;Barbara B. Bendlin;Gaurav Suryawanshi;Andrew L. Alexander;Anqi Qiu
Affiliations:
Department of Bioengineering, National University of Singapore, Singapore;Department of Medical Physics, University of Wisconsin-Madison and Waisman Laboratory for Brain Imaging and Behavior, University of Wisconsin-Madison;Waisman Laboratory for Brain Imaging and Behavior, University of Wisconsin-Madison and Biostatistics and Medical Informatics, University of Wisconsin-Madison;Department of Medicine, University of Wisconsin-Madison;Waisman Laboratory for Brain Imaging and Behavior, University of Wisconsin-Madison;Department of Medical Physics, University of Wisconsin-Madison and Waisman Laboratory for Brain Imaging and Behavior, University of Wisconsin-Madison;Department of Bioengineering, National University of Singapore, Singapore,Clinical Imaging Research Center, National University of Singapore, Singapore
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 propose a large deformation diffeomorphic metric mapping algorithm to align multiple b-value diffusion weighted imaging (mDWI) data, specifically acquired via hybrid diffusion imaging (HYDI), denoted as LDDMM-HYDI. We adopt the work given in Hosseinbor et al. (2012) and represent the q-space diffusion signal with the Bessel Fourier orientation reconstruction (BFOR) signal basis. The BFOR framework provides the representation of mDWI in the q-space and thus reduces memory requirement. In addition, since the BFOR signal basis is orthonormal, the L2 norm that quantifies the differences in q-space signals of any two mDWI datasets can be easily computed as the sum of the squared differences in the BFOR expansion coefficients. In this work, we show that the reorientation of the q-space signal due to spatial transformation can be easily defined on the BFOR signal basis. We incorporate the BFOR signal basis into the LDDMM framework and derive the gradient descent algorithm for LDDMM-HYDI with explicit orientation optimization. Using real HYDI datasets, we show that it is important to consider the variation of mDWI reorientation due to a small change in diffeomorphic transformation in the LDDMM-HYDI optimization.