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We propose a large deformation diffeomorphic metric mapping algorithm toalign multiple b-value diffusion weighted imaging (mDWI) data, specificallyacquired via hybrid diffusion imaging (HYDI), denoted as LDDMM-HYDI. We thenpropose a Bayesian model for estimating the white matter atlas from HYDIs. Weadopt the work given in Hosseinbor et al. (2012) and represent the q-spacediffusion signal with the Bessel Fourier orientation reconstruction (BFOR)signal basis. The BFOR framework provides the representation of mDWI in theq-space and thus reduces memory requirement. In addition, since the BFOR signalbasis is orthonormal, the L2 norm that quantifies the differences in theq-space signals of any two mDWI datasets can be easily computed as the sum ofthe squared differences in the BFOR expansion coefficients. In this work, weshow that the reorientation of the $q$-space signal due to spatialtransformation can be easily defined on the BFOR signal basis. We incorporatethe BFOR signal basis into the LDDMM framework and derive the gradient descentalgorithm for LDDMM-HYDI with explicit orientation optimization. Additionally,we extend the previous Bayesian atlas estimation framework for scalar-valuedimages to HYDIs and derive the expectation-maximization algorithm for solvingthe HYDI atlas estimation problem. Using real HYDI datasets, we show theBayesian model generates the white matter atlas with anatomical details.Moreover, we show that it is important to consider the variation of mDWIreorientation due to a small change in diffeomorphic transformation in theLDDMM-HYDI optimization and to incorporate the full information of HYDI foraligning mDWI.

Diffeomorphic Metric Mapping and Probabilistic Atlas Generation of Hybrid Diffusion Imaging based on BFOR Signal Basis