Combined Tensor Fitting and TV Regularization in Diffusion Tensor Imaging Based on a Riemannian Manifold Approach

Area of Science:

• Medical Imaging
• Computational Neuroscience
• Differential Geometry

Background:

• Diffusion Tensor Imaging (DTI) is crucial for analyzing white matter structure.
• Traditional DTI analysis involves separate denoising and tensor fitting steps, which can introduce errors.
• Existing methods lack integrated approaches for simultaneous denoising and tensor fitting within a manifold framework.

Purpose of the Study:

• To develop a unified framework for combined Total Variation (TV) denoising and diffusion tensor fitting in DTI.
• To leverage the affine-invariant Riemannian metric for improved tensor fitting on the diffusion tensor manifold.
• To introduce a novel energy functional and associated algorithms for simultaneous DTI data processing.

Main Methods:

• Defined a TV-type energy functional incorporating measured Diffusion Weighted Images (DWIs) and manifold nearness of diffusion tensors.
• Developed generalized forward-backward splitting algorithms for optimizing the proposed functional.
• Validated the approach using synthetic and real 3D DTI datasets.

Main Results:

• Demonstrated effective combined denoising and diffusion tensor fitting.
• Showcased the performance of the generalized forward-backward splitting algorithms on DTI data.
• Presented the first TV regularization approach within a combined manifold and inverse problem setup for DTI.

Conclusions:

• The proposed method offers a significant advancement in DTI data processing by integrating denoising and tensor fitting.
• The use of manifold geometry and advanced splitting algorithms improves the accuracy and robustness of DTI analysis.
• This work lays the foundation for future developments in manifold-based DTI regularization techniques.