MAPL1: q-space reconstruction using -regularized mean apparent propagator.

Area of Science:

• Diffusion Magnetic Resonance Imaging (dMRI)
• Computational Neuroscience
• Medical Imaging Analysis

Background:

• Accurate reconstruction of the mean apparent propagator (MAP) is crucial for diffusion MRI.
• Limited q-space sampling in dMRI compromises reconstruction quality.
• Existing methods like MAP and MAPL have limitations in handling undersampled data.

Purpose of the Study:

• To enhance the quality of MAP reconstruction from limited q-space samples.
• To introduce and evaluate an L1-regularized MAP (MAPL1) method.
• To compare MAPL1 against traditional MAP and Laplacian-regularized MAP (MAPL) techniques.

Main Methods:

• Implementation of L1-regularized MAP (MAPL1) to incorporate higher-order basis functions.
• Comparison of MAPL1 with non-negativity constrained least-squares (MAP) and Laplacian-regularized MAP (MAPL).
• Evaluation using simulations of crossing fibers, calculating normalized mean squared error (NMSE) and Pearson's correlation coefficient.
• Assessment of coefficient-based diffusion indices in both simulated and in vivo data.

Main Results:

• MAPL1 demonstrated a 1-3% improvement in NMSE compared to MAP and MAPL under high undersampling.
• MAPL1 achieved more reproducible and accurate reconstructions across all sampling rates when sparsity criteria were met.
• Improved reconstructions using MAPL1 led to enhanced coefficient-based diffusion indices in in vivo data.

Conclusions:

• Incorporating an L1 regularizer into MAP reconstruction enables the use of more basis functions for improved fitting without increasing sampling.
• This advancement allows for complete diffusion spectrum reconstruction from acquisition times comparable to diffusion tensor imaging (DTI) protocols.
• MAPL1 offers a promising approach to obtain richer diffusion information efficiently.