Paper Info
Title
A Simplified Algorithm For Inverting Higher Order Diffusion Tensors
Abstract
In Riemannian geometry, a distance function is determined by an inner product on the tangent space. In Riemann-Finsler geometry, this distance function can be determined by a norm. This gives more freedom on the form of the so-called indicatrix or the set of unit vectors. This has some interesting applications, e.g., in medical image analysis, especially in diffusion weighted imaging (DWI). An important application of DWI is in the inference of the local architecture of the tissue, typically consisting of thin elongated structures, such as axons or muscle fibers, by measuring the constrained diffusion of water within the tissue. From high angular resolution diffusion imaging (HARDI) data, one can estimate the diffusion orientation distribution function (dODF), which indicates the relative diffusivity in all directions and can be represented by a spherical polynomial. We express this dODF as an equivalent spherical monomial (higher order tensor) to directly generalize the (second order) diffusion tensor approach. To enable efficient computation of Riemann-Finslerian quantities on diffusion weighted (DW)-images, such as the metric/norm tensor, we present a simple and efficient algorithm to invert even order spherical monomials, which extends the familiar inversion of diffusion tensors, i.e., symmetric matrices.
Year
DOI
Venue
2014
10.3390/axioms3040369
AXIOMS
Keywords
Field
DocType
Riemann-Finsler geometry, biomedical image analysis, HARDI, Einstein contracted product
Diffusion MRI,Tensor,Polynomial,Mathematical analysis,Metric (mathematics),Algorithm,Monomial,Riemannian geometry,Mathematics,Unit vector,Tangent space
Journal
Volume
Issue
ISSN
3
4
2075-1680
Citations 
PageRank 
References 
0
0.34
5
Authors
5
Name
Order
Citations
PageRank
Laura Astola1324.42
Neda Sepasian2122.32
Tom C. J. Dela Haije3213.22
Andrea Fuster4357.45
L. M. J. Florack51212210.47