Abstract
Low spatial resolution of diffusion resonance magnetic imaging (dMRI) restricts its clinical applications. Usually, the measures are obtained in a range from 1 to 2 \(\mathrm{mm}^3\) per voxel, and some structures cannot be studied in detail. Due to clinical acquisition protocols (exposure time, field strength, among others) and technological limitations, it is not possible to acquire images with high resolution. In this work, we present a methodology for enhancing the spatial resolution of diffusion tensor (DT) fields obtained from dMRI. The proposed methodology assumes that a DT field follows a generalized Wishart process (GWP), which is a stochastic process defined over symmetric and positive definite matrices indexed by spatial coordinates. A GWP is modulated by a set of Gaussian processes (GPs). Therefore, the kernel hyperparameters of the GPs control the spatial dynamic of a GWP. Following this notion, we employ a non-stationary kernel for describing DT fields whose statistical properties are not constant over the space. We test our proposed method in synthetic and real dMRI data. Results show that non-stationary GWP can describe complex DT fields (i.e. crossing fibers where the shape, size and orientation properties change abruptly), and it is a competitive methodology for interpolation of DT fields, when we compare with methods established in literature evaluating Frobenius and Riemann distances.
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Acknowledgments
This research is developed under the project “Desarrollo de un sistema de soporte clínico basado en el procesamiento estócasitco para mejorar la resolución espacial de la resonancia magnética estructural y de difusión con aplicación al procedimiento de la ablación de tumores” financed by COLCIENCIAS with code 111074455860. H.D. Vargas is funded by Colciencias under the program: Convocatoria 617 de 2013. J.F. Cuellar is funded by Colciencias under program: Jóvenes investigadores e innovadores-Convocatoria 761 de 2016. We thank to the program of master in electrical engineering of the Universidad Tecnológica de Pereira.
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Cuellar-Fierro, J.F., Vargas-Cardona, H.D., Álvarez, A.M., Orozco, Á.A., Álvarez, M.A. (2018). Non-stationary Generalized Wishart Processes for Enhancing Resolution over Diffusion Tensor Fields. In: Bebis, G., et al. Advances in Visual Computing. ISVC 2018. Lecture Notes in Computer Science(), vol 11241. Springer, Cham. https://doi.org/10.1007/978-3-030-03801-4_33
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DOI: https://doi.org/10.1007/978-3-030-03801-4_33
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