Linear transforms for Fourier data on the sphere: application to high angular resolution diffusion MRI of the brain

Area of Science:

• Medical Imaging
• Signal Processing
• Computational Neuroscience

Background:

• Diffusion Magnetic Resonance Imaging (dMRI) is crucial for studying white matter fiber orientations in the central nervous system.
• The Funk-Radon Transform (FRT) has been used for orientation estimation in dMRI, but limitations exist in accuracy and resolution.
• Analyzing data on the surface of a 2-sphere in Fourier space presents unique challenges for signal processing.

Purpose of the Study:

• To introduce a novel family of linear transforms generalizing the FRT for 2-sphere data analysis.
• To present the Funk-Radon and Cosine Transform (FRACT) as a specific, advanced transform within this new family.
• To demonstrate the theoretical and practical superiority of FRACT for orientation estimation in dMRI.

Main Methods:

• Theoretical characterization of a new family of linear transforms.
• Development of efficient numerical implementations using spherical harmonic bases.
• Application and simulation of the Funk-Radon and Cosine Transform (FRACT).
• Validation using simulated data and real diffusion-weighted MRI brain data.

Main Results:

• The new transforms, particularly FRACT, are theoretically expected to offer improved accuracy and angular resolution.
• Simulations confirm FRACT's enhanced performance characteristics compared to the standard FRT.
• Experiments with real dMRI data show FRACT outperforms state-of-the-art methods in angular resolution and robustness.

Conclusions:

• The proposed Funk-Radon and Cosine Transform (FRACT) represents a significant advancement in analyzing 2-sphere data.
• FRACT provides superior orientation estimation for diffusion MRI data, enhancing accuracy and angular resolution.
• This novel approach offers practical benefits for neuroscience research and clinical applications.