Learning Compact q -Space Representations for Multi-Shell Diffusion-Weighted MRI.

Area of Science:

• Medical Imaging
• Neuroimaging
• Biophysics

Background:

• Diffusion-weighted MRI (DW-MRI) analyzes local diffusion in voxels via q-space signal.
• Recent advances highlight the importance of radial b-value dependence for microstructure imaging.
• Effective motion correction and outlier rejection necessitate compact, linear signal representations across radial and angular domains.

Purpose of the Study:

• Introduce SHARD (Spherical Harmonics And Radial Decomposition), a novel data-driven q-space signal representation.
• Provide a complete, orthogonal signal basis tailored to q-space geometry and specific data.
• Evaluate SHARD's performance against model-based methods and assess joint radial-spherical vs. single-shell representations.

Main Methods:

• Developed SHARD, a representation using spherical harmonics and radial decomposition into orthonormal components.
• Applied rank-reduced decomposition to human brain DW-MRI data.
• Utilized outlier robust regression for motion correction and outlier rejection applications.

Main Results:

• Rank-reduced SHARD outperformed model-based alternatives in human brain data.
• SHARD faithfully captured micro- and meso-structural information.
• Joint radial-spherical representations showed potential compared to single-shell methods.

Conclusions:

• SHARD offers a data-driven, compact linear representation of the q-space signal.
• The method is optimally suited for applications requiring low-rank signal predictions like motion correction and outlier rejection.
• SHARD demonstrates effective application in robust regression for outlier identification.