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An improved OPDT model in high angular resolution diffusion imaging

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Abstract

Orientation probability density transform (OPDT) is a single-shell high angular resolution diffusion imaging (HARDI) estimator proposed by Tristán-Vega et al. for orientation probability density function (OPDF), i.e. marginal orientation distribution function (ODF) of white matter fibers in the brain. Unlike ODF in Q-Ball imaging (QBI), the Jacobian of the spherical coordinate is included in OPDF. OPDT is based on the Funk-Radon transform (FRT), so there is blurring introduced by FRT. Aganj et al. have proved that the radial part of the OPDF equals a constant, which is independent of the diffusion signal. With this consideration, we propose an improved form of OPDT with a closed form expression, which can reduce the FRT blurring in OPDT by replacing the radial part (a non-constant function) with its mean value over the sphere. Compared with OPDT, the proposed FRT-based single-shell HARDI estimator improves the angular resolution, and almost maintains the higher angular accuracy, robustness to noise and computational efficiency. Results on synthetic data and real human brain data are provided to demonstrate the effectiveness of the proposed model.

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Acknowledgements

The authors are sincerely grateful to all the anonymous reviewers for valuable comments and suggestions that have considerably improved the manuscript. The authors would like to thank Professor Ching-Po Lin for providing the human brain dataset. This work was supported by grants from the National Basic Research Program of China (973 program, 2011CB707800) and the National Natural Science Foundation of China (91132301 and 11171300).

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Authors and Affiliations

  1. Department of Mathematics, Zhejiang University, Hangzhou, 310027, P.R. China

    Na Zhang & Chong Li

  2. Center for Computational Medicine, National Laboratory of Pattern Recognition, Institute of Automation, Chinese Academy of Sciences, Beijing, 100190, P.R. China

    Na Zhang & Tianzi Jiang

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  1. Na Zhang
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  2. Chong Li
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  3. Tianzi Jiang
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Correspondence to Tianzi Jiang.

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Zhang, N., Li, C. & Jiang, T. An improved OPDT model in high angular resolution diffusion imaging. J Math Imaging Vis 48, 385–395 (2014). https://doi.org/10.1007/s10851-012-0412-5

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