Vectorial total variation regularisation of orientation distribution functions in diffusion weighted MRI.

Area of Science:

• Medical Imaging
• Diffusion MRI
• Computational Neuroscience

Background:

• Orientation Distribution Functions (ODFs) are crucial for understanding tissue microstructures in diffusion MRI.
• Existing methods often struggle with accurate reconstruction and regularisation, leading to noisy or blurred results.
• Spherical harmonic functions are commonly used to represent ODFs.

Purpose of the Study:

• To develop a novel model for simultaneous ODF reconstruction and regularisation.
• To improve the accuracy and directional fidelity of reconstructed ODFs.
• To efficiently solve the proposed model using advanced numerical methods.

Main Methods:

• ODF reconstruction using real spherical harmonic functions.
• Spatial regularisation via minimising Vectorial Total Variation (VTV) of spherical harmonic coefficients.
• Angular regularisation using the Laplace-Beltrami operator on the unit sphere.
• Efficient model solution using a modified primal-dual hybrid gradient algorithm.

Main Results:

• The proposed model successfully reconstructs ODFs with enhanced directional structures.
• Simultaneous spatial and angular regularisation leads to improved ODF quality.
• Experimental results demonstrate the effectiveness of the VTV and Laplace-Beltrami regularisation terms.
• The modified primal-dual hybrid gradient algorithm provides an efficient solution.

Conclusions:

• The proposed model offers a robust framework for ODF reconstruction and regularisation.
• This approach advances the analysis of diffusion MRI data by providing clearer directional information.
• The method has potential applications in neuroimaging and other fields requiring microstructure analysis.