IPMI 2013 - LNCS 7917

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

Jia Du¹, A. Pasha Hosseinbor^{3, 4}, Moo K. Chung^{4, 5}, Barbara B. Bendlin⁶, Gaurav Suryawanshi⁴, Andrew L. Alexander^{3, 4}, and Anqi Qiu^{1, 2}

¹Department of Bioengineering, National University of Singapore, Singapore

²Clinical Imaging Research Center, National University of Singapore, Singapore

³Department of Medical Physics, University of Wisconsin-Madison, USA

⁴Waisman Laboratory for Brain Imaging and Behavior, University of Wisconsin-Madison, USA

⁵Biostatistics and Medical Informatics, University of Wisconsin-Madison, USA

⁶Department of Medicine, University of Wisconsin-Madison, USA

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.

LNCS 7917, p. 147 ff.

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