Abstract
We consider two popular nonparametric models describing measurements obtained from low and high angular resolution diffusion tensor imaging. The balance between the number of distinct directions for measurements and the number of repetitions is investigated from the statistical point of view. We show that designs with multiple independent repetitions using one set of six directions for the low resolution case yield smaller norms of the estimator’s covariance function than designs where a large set of directions with no repetitions is used, assuming that norms of covariances of image components are similar for both types of designs. The difference is inversely proportional to the number of repetitions. Similar result is obtained for the high resolution case. This yields a practical guideline on how to choose the number of gradient directions and the number of repetitions for estimation problems in this imaging context.
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Acknowledgement
Research is partially supported by NSF grant DMS-1208238. The author is grateful to professor Hira Koul for his guidance, help, and contagious enthusiasm for statistics.
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Sakhanenko, L. (2014). How to Choose the Number of Gradient Directions for Estimation Problems from Noisy Diffusion Tensor Data. In: Lahiri, S., Schick, A., SenGupta, A., Sriram, T. (eds) Contemporary Developments in Statistical Theory. Springer Proceedings in Mathematics & Statistics, vol 68. Springer, Cham. https://doi.org/10.1007/978-3-319-02651-0_19
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DOI: https://doi.org/10.1007/978-3-319-02651-0_19
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