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Diffusion Tensor Magnetic Resonance Imaging in the Analysis of Neurodegenerative Diseases
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A computational Framework for generating rotation invariant features and its application in diffusion MRI.

Mauro Zucchelli1, Samuel Deslauriers-Gauthier1, Rachid Deriche1

  • 1Athena Project-Team, Inria Sophia Antipolis - Méditerranée, Université Côte D'Azur, France.

Medical Image Analysis
|December 7, 2019
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Summary
This summary is machine-generated.

We developed a computational framework to generate Rotation Invariant Features (RIF) for spherical functions. These new RIFs offer advanced analysis of diffusion MRI data for brain microstructure estimation.

Keywords:
BiomarkersDiffusion MRIGaunt coefficientsRotation invariantsSpherical harmonics

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Area of Science:

  • Computational mathematics
  • Medical imaging analysis
  • Neuroscience

Background:

  • Spherical functions are crucial for analyzing data on a sphere, common in fields like medical imaging.
  • Existing rotation invariant features have limitations in capturing the full complexity of spherical data.
  • Spherical Harmonic (SH) representations are widely used but require robust invariant features for analysis.

Purpose of the Study:

  • To introduce a novel computational framework for analytically generating a complete set of algebraically independent Rotation Invariant Features (RIF).
  • To provide closed-form solutions for new invariants that expand upon existing measures like spherical mean, power-spectrum, and bispectrum.
  • To demonstrate the utility of these RIFs in modeling and analyzing diffusion MRI (dMRI) data for brain microstructure.

Main Methods:

  • Developed a computational framework to derive Rotation Invariant Features (RIF) from Laplace-series expansion of spherical functions.
  • Derived closed-form solutions for a complete set of algebraically independent RIFs.
  • Applied the framework to model dMRI signals, including Apparent Diffusion Coefficient (ADC), diffusion signal, and fiber Orientation Distribution Function (fODF).

Main Results:

  • Generated a novel set of algebraically independent RIFs with closed-form solutions.
  • Established links between new RIFs and statistical/geometrical measures (mean, variance, volume) of spherical signals.
  • Demonstrated successful application in dMRI signal modeling and microstructure estimation using synthetic and real data.

Conclusions:

  • The proposed framework provides a powerful tool for generating comprehensive Rotation Invariant Features.
  • These RIFs enhance the analysis of spherical data, particularly in dMRI for brain microstructure recovery.
  • The framework offers greater flexibility and potential for innovative developments in microstructure imaging.