Tensorial Spherical Polar Fourier Diffusion MRI with Optimal Dictionary Learning

Area of Science:

• Neuroimaging
• Diffusion MRI
• Computational Neuroscience

Background:

• High Angular Resolution Diffusion Imaging (HARDI) provides superior white matter microstructure characterization compared to Diffusion Tensor Imaging (DTI) by avoiding Gaussian diffusion assumptions.
• Traditional HARDI methods require extensive signal measurements and long scan times, limiting clinical applicability.
• Compressed Sensing (CS) enables signal reconstruction from fewer samples, reducing scan time, but relies on effective signal sparsification via a suitable dictionary.

Purpose of the Study:

• To introduce Tensorial Spherical Polar Fourier Imaging (TSPFI) for continuous diffusion signal and propagator recovery using an orthonormal TSPF basis.
• To develop Dictionary Learning TSPFI (DL-TSPFI) for learning a sparser dictionary from Gaussian mixture signals, enhancing CS reconstruction.
• To evaluate DL-TSPFI's performance against existing methods in terms of signal sparsity and reconstruction accuracy.

Main Methods:

• Proposed TSPFI method representing diffusion signals with an orthonormal TSPF basis, generalizing DTI and SPFI.
• Developed DL-TSPFI to learn a sparse dictionary from Gaussian mixture signals via efficient subspace learning and adaptive tensor setting.
• Applied the learned DL-TSPF dictionary using DTI and weighted LASSO for Compressed Sensing reconstruction in different voxels.

Main Results:

• The learned DL-TSPF dictionary demonstrated a sparser signal representation compared to the original SPF basis and DL-SPF dictionary.
• DL-TSPFI achieved a lower Root-Mean-Squared-Error (RMSE) in reconstruction compared to existing methods.
• The method proved effective for adaptive dictionary application across different voxels.

Conclusions:

• DL-TSPFI offers a significant advancement in HARDI by enabling faster, more accurate brain microstructure imaging through sparse signal representation and CS.
• The proposed method generalizes existing techniques and provides a more robust dictionary for diffusion MRI reconstruction.
• DL-TSPFI holds promise for enhancing the clinical utility of advanced diffusion imaging techniques.