Regularized spherical polar fourier diffusion MRI with optimal dictionary learning.

Area of Science:

• Medical Imaging
• Signal Processing
• Computational Neuroscience

Background:

• Compressed Sensing (CS) enables robust signal reconstruction from limited measurements by leveraging signal sparsity.
• Diffusion MRI (dMRI) signal and Ensemble Average Propagator (EAP) reconstruction often rely on CS with Dictionary Learning (DL).
• Existing DL methods in dMRI, such as Discrete Representation DL (DR-DL) and Continuous Representation DL (CR-DL), face challenges like numerical inaccuracy and lack of adaptivity.

Purpose of the Study:

• To propose a novel Continuous Representation DL (CR-DL) method, termed Dictionary Learning - Spherical Polar Fourier Imaging (DL-SPFI), for enhanced dMRI signal and EAP reconstruction.
• To develop a DL approach that learns an optimal dictionary from continuous Gaussian diffusion signals.
• To introduce a voxel-adaptive dictionary learning framework for robust and accurate dMRI data recovery.

Main Methods:

• Implemented DL-SPFI, a CR-DL approach that learns a dictionary from continuous Gaussian diffusion signals.
• Employed a weighted LASSO framework for adaptive application of the learned dictionary across different voxels.
• Optimized the reconstruction process within a reduced subspace of Spherical Polar Fourier (SPF) coefficients.

Main Results:

• The learned dictionary in DL-SPFI was demonstrated to be optimal for Gaussian diffusion signals.
• DL-SPFI achieved significantly lower reconstruction error compared to state-of-the-art DR-DL and CR-DL methods.
• Experimental results on synthetic and real dMRI data showed sparser coefficients and improved reconstruction accuracy using DL-SPFI.

Conclusions:

• DL-SPFI provides a superior method for compressed-sensing reconstruction of dMRI diffusion-weighted signals and EAP.
• The proposed voxel-adaptive dictionary learning significantly enhances reconstruction robustness and accuracy.
• DL-SPFI overcomes limitations of previous methods, offering a more precise and efficient approach for dMRI analysis.