Revisiting the T₂ spectrum imaging inverse problem: Bayesian regularized non-negative least squares.

Area of Science:

• Neuroimaging
• Biophysics
• Computational Neuroscience

Background:

• Multi-echo T2 magnetic resonance imaging (MRI) allows estimation of brain tissue properties like myelin water fraction (MWF).
• Non-parametric T2 spectral estimation using regularized non-negative least squares (NNLS) is crucial but faces challenges with ill-conditioning, noise sensitivity, and regularization weight impact.
• Standard and alternative regularization forms in NNLS can yield different solutions, necessitating performance assessment.

Purpose of the Study:

• To highlight the impact of different regularization parameterizations on inverse problem solutions in T2 spectral estimation.
• To evaluate the performance of standard versus alternative regularization forms.
• To introduce and validate a novel Bayesian regularized NNLS method (BayesReg) for improved T2 distribution and MWF estimation.

Main Methods:

• Developed and implemented the Bayesian regularized NNLS (BayesReg) method.
• Compared BayesReg against conventional L-curve and Chi-square (X2) fitting methods using both standard and alternative regularization forms.
• Validated methods using synthetic data, in vivo human brain scan-rescan analysis, and ex vivo data correlated with histology.

Main Results:

• BayesReg demonstrated accurate MWF estimates with superior stability across various signal-to-noise ratios on synthetic data.
• The alternative regularization form consistently yielded better results than the standard form across tested methods.
• Human brain data showed higher reproducibility for L-curve and BayesReg maps, with BayesReg producing T2 spectra less affected by over-smoothing.

Conclusions:

• BayesReg presents a robust alternative for estimating T2 distributions and myelin water fraction (MWF) maps from multi-echo MRI data.
• The choice of regularization form significantly influences estimation outcomes, with the alternative form showing advantages.
• Improved accuracy and stability of MWF estimation can enhance the understanding of brain tissue properties.