Equivariant Spherical Deconvolution: Learning Sparse Orientation Distribution Functions from Spherical Data.

Area of Science:

• Medical Imaging
• Neuroimaging
• Machine Learning

Background:

• Diffusion MRI (dMRI) data contains complex signals in each voxel due to anisotropic tissue structures like white matter.
• Current linear spherical deconvolution methods struggle to accurately resolve crossing-fiber configurations and estimate partial volume fractions in dMRI.
• Accurate reconstruction of white matter fiber directions is crucial for understanding brain structure and function.

Purpose of the Study:

• To introduce a novel rotation-equivariant self-supervised learning framework for sparse deconvolution of spherical signals in dMRI.
• To improve the nonlinear estimation of white matter fiber structures by addressing limitations of existing linear methods.
• To enhance the accuracy of fiber tractography and partial volume estimation in dMRI.

Main Methods:

• Developed a self-supervised spherical convolutional neural network with guaranteed rotation equivariance.
• Applied the framework to the sparse deconvolution of non-negative scalar fields on the unit sphere.
• Validated the method using single and multi-shell synthetic dMRI datasets and a human subject dataset.

Main Results:

• The proposed method demonstrated competitive performance against common baseline methods on synthetic benchmarks.
• Achieved improved downstream performance on fiber tractography measures using the Tractometer benchmark dataset.
• Showed enhanced tractography and partial volume estimation on a multi-shell dataset from human subjects.

Conclusions:

• The rotation-equivariant self-supervised learning framework offers a promising nonlinear approach for dMRI spherical deconvolution.
• This method improves the resolution of complex white matter structures, including crossing fibers.
• The framework has the potential to advance neuroimaging analysis and clinical applications of dMRI.