Fast Optimal Transport Averaging of Neuroimaging Data

Area of Science:

• Neuroscience
• Medical Imaging
• Computational Mathematics

Background:

• Neuroimaging research aims to understand human brain organization in health and disease.
• Averaging brain imaging data across individuals is challenging due to data size, complex geometry, and inter-subject variability.
• Current methods often involve data smoothing before linear group averaging, which can obscure fine details.

Purpose of the Study:

• To develop an efficient algorithm for averaging non-normalized neuroimaging data defined on arbitrary discrete domains.
• To address the challenge of inter-subject variability in group-level brain imaging analysis.
• To leverage transportation metrics and entropic smoothing for robust group averaging.

Main Methods:

• Proposed a novel algorithm based on Kantorovich's ideas for efficient averaging of non-normalized data.
• Linked Kantorovich means to Wasserstein barycenters, enabling entropic smoothing.
• Formulated the problem as a smooth convex optimization problem with strong convergence guarantees.

Main Results:

• Demonstrated an efficient method for averaging functional MRI and magnetoencephalography (MEG) source estimates.
• Successfully applied the algorithm to data defined on both voxel grids and triangulations of the cortical surface.
• The approach handles complex brain geometry and inter-subject variability effectively.

Conclusions:

• The developed algorithm provides a versatile tool for group-level analysis in neuroimaging.
• This method enhances the ability to study brain anatomy and function across populations.
• The approach offers improved accuracy and robustness in averaging complex, high-dimensional neuroimaging datasets.