TY - JOUR
T1 - Tensor decomposition processes for interpolation of diffusion magnetic resonance imaging
AU - Vargas-Cardona, Hernán Darío
AU - Orozco, Álvaro A.
AU - Álvarez, Andrés M.
AU - Álvarez, Mauricio A.
N1 - Funding Information:
H. D. Vargas-Cardona is funded by Colciencias under the program: formación de alto nivel para la ciencia, la tecnología y la innovación - Convocatoria 617 de 2013. M. A. Álvarez has been partially supported by the Engineering and Physical Research Council (EPSRC) Research Project EP/N014162/1 . This research is developed under the project: Desarrollo de un sistema de soporte clínico basado en el procesamiento estocástico para mejorar la resolución espacial de la resonancia magnética estructural y de difusión con aplicación al procedimiento de ablación de tumores, financed by Colciencias with code 111074455860 . Data collection and sharing for this project was provided by the MGH-USC Human Connectome Project (HCP; Principal Investigators: Bruce Rosen, M.D., Ph.D., Arthur W. Toga, Ph.D., Van J. Weeden, MD). HCP funding was provided by the National Institute of Dental and Craniofacial Research (NIDCR), the National Institute of Mental Health (NIMH), and the National Institute of Neurological Disorders and Stroke (NINDS). HCP data are disseminated by the Laboratory of Neuro Imaging at the University of California, Los Angeles.
Publisher Copyright:
© 2018
PY - 2019/3/15
Y1 - 2019/3/15
N2 - Diffusion magnetic resonance imaging (dMRI) is an established medical technique used for describing water diffusion in an organic tissue. Typically, rank-2 or 2nd-order tensors quantify this diffusion. From this quantification, it is possible to calculate relevant scalar measures (i.e. fractional anisotropy) employed in the clinical diagnosis of neurological diseases. Nonetheless, 2nd-order tensors fail to represent complex tissue structures like crossing fibers. To overcome this limitation, several researchers proposed a diffusion representation with higher order tensors (HOT), specifically 4th and 6th orders. However, the current acquisition protocols of dMRI data allow images with a spatial resolution between 1 mm3 and 2 mm3, and this voxel size is much bigger than tissue structures. Therefore, several clinical procedures derived from dMRI may be inaccurate. Concerning this, interpolation has been used to enhance the resolution of dMRI in a tensorial space. Most interpolation methods are valid only for rank-2 tensors and a generalization for HOT data is missing. In this work, we propose a probabilistic framework for performing HOT data interpolation. In particular, we introduce two novel probabilistic models based on the Tucker and the canonical decompositions. We call our approaches: Tucker decomposition process (TDP) and canonical decomposition process (CDP). We test the TDP and CDP in rank-2, 4 and 6 HOT fields. For rank-2 tensors, we compare against direct interpolation, log-Euclidean approach, and Generalized Wishart processes. For rank-4 and 6 tensors, we compare against direct interpolation and raw dMRI interpolation. Results obtained show that TDP and CDP interpolate accurately the HOT fields in terms of Frobenius distance, anisotropy measurements, and fiber tracts. Besides, CDP and TDP can be generalized to any rank. Also, the proposed framework keeps the mandatory constraint of positive definite tensors, and preserves morphological properties such as fractional anisotropy (FA), generalized anisotropy (GA) and tractography.
AB - Diffusion magnetic resonance imaging (dMRI) is an established medical technique used for describing water diffusion in an organic tissue. Typically, rank-2 or 2nd-order tensors quantify this diffusion. From this quantification, it is possible to calculate relevant scalar measures (i.e. fractional anisotropy) employed in the clinical diagnosis of neurological diseases. Nonetheless, 2nd-order tensors fail to represent complex tissue structures like crossing fibers. To overcome this limitation, several researchers proposed a diffusion representation with higher order tensors (HOT), specifically 4th and 6th orders. However, the current acquisition protocols of dMRI data allow images with a spatial resolution between 1 mm3 and 2 mm3, and this voxel size is much bigger than tissue structures. Therefore, several clinical procedures derived from dMRI may be inaccurate. Concerning this, interpolation has been used to enhance the resolution of dMRI in a tensorial space. Most interpolation methods are valid only for rank-2 tensors and a generalization for HOT data is missing. In this work, we propose a probabilistic framework for performing HOT data interpolation. In particular, we introduce two novel probabilistic models based on the Tucker and the canonical decompositions. We call our approaches: Tucker decomposition process (TDP) and canonical decomposition process (CDP). We test the TDP and CDP in rank-2, 4 and 6 HOT fields. For rank-2 tensors, we compare against direct interpolation, log-Euclidean approach, and Generalized Wishart processes. For rank-4 and 6 tensors, we compare against direct interpolation and raw dMRI interpolation. Results obtained show that TDP and CDP interpolate accurately the HOT fields in terms of Frobenius distance, anisotropy measurements, and fiber tracts. Besides, CDP and TDP can be generalized to any rank. Also, the proposed framework keeps the mandatory constraint of positive definite tensors, and preserves morphological properties such as fractional anisotropy (FA), generalized anisotropy (GA) and tractography.
KW - Diffusion magnetic resonance imaging
KW - Higher order tensors
KW - Interpolation
KW - Probabilistic models
KW - Tensor decomposition
UR - http://www.scopus.com/inward/record.url?scp=85054463035&partnerID=8YFLogxK
U2 - 10.1016/j.eswa.2018.10.005
DO - 10.1016/j.eswa.2018.10.005
M3 - Article
AN - SCOPUS:85054463035
SN - 0957-4174
VL - 118
SP - 92
EP - 108
JO - Expert Systems with Applications
JF - Expert Systems with Applications
ER -