Authors:
Theodosios Gkamas
1
;
Félix Renard
2
;
Christian Heinrich
1
and
Stéphane Kremer
1
Affiliations:
1
University of Strasbourg - CNRS and Fédération de Médecine Translationnelle de Strasbourg (FMTS), France
;
2
Gipsa-lab, France
Keyword(s):
Diffusion-weighted MRI, Fourth Order Tensor, Non Euclidean Metric, Nonlinear Dimension Reduction, Permutation Testing.
Related
Ontology
Subjects/Areas/Topics:
Applications
;
Classification
;
Embedding and Manifold Learning
;
Feature Selection and Extraction
;
Medical Imaging
;
Pattern Recognition
;
Software Engineering
;
Theory and Methods
Abstract:
In this communication, we propose an original statistical model for diffusion-weighted magnetic resonance
imaging, in order to determine new biomarkers. Second order tensor (T2) modeling of Orientation Distribution
Functions (ODFs) is popular and has benefited of specific statistical models, incorporating appropriate metrics.
Nevertheless, the shortcomings of T2s, for example for the modeling of crossing fibers, are well identified. We
consider here fourth order tensor (T4) models for ODFs, thus alleviating the T2 shortcomings. We propose
an original metric in the T4 parameter space. This metric is incorporated in a nonlinear dimension reduction
procedure. In the resulting reduced space, we represent the probability density of the two populations, normal
and abnormal, by kernel density estimation with a Gaussian kernel, and propose a permutation test for the
comparison of the two populations. Application of the proposed model on synthetic and real data is achieved.
The relevance of t
he approach is shown.
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