Diffeomorphic Metric Mapping of Hybrid Diffusion Imaging Based on BFOR Signal Basis

Abstract

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 L 2 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.

Diffeomorphic metric mapping and probabilistic atlas generation of hybrid diffusion imaging based on BFOR signal basis

“…We derived the gradient of this variational problem with the explicit computation of the mDWI reorientation and provided a numeric algorithm without a need of the discretization in the q -space. Comparing with our existing work (Du et al, 2013), we further derived the EM algorithm for the estimation of the atlas in the Bayesian framework. Moreover, we provided the extensive evaluation on the mapping accuracy based on a new dataset of 36 healthy adults and compared LDDMM-HYDI with that of the diffeomorphic mapping based on diffusion tensors.…”

“…Unlike the work in Dhollander et al (2011), we will incorporate the BFOR signal basis into the LDDMM framework and derive the gradient descent algorithm for solving the LDDMM-HYDI variational problem with explicit orientation optimization. Even though the LDDMM-HYDI algorithm is largely based on our previous work (Du et al, 2013), in this paper we further develop a Bayesian probabilistic model to estimate the brain white matter atlas from the q -space. This probabilistic model is the extension of the previous Bayesian atlas estimation for scalar-based intensity images (Ma et al, 2008).…”