Improved Myelin Water Fraction Estimation and Uncertainty Mapping in Multicomponent T2 Relaxometry via NNLS Bootstrap Aggregation

Abstract

Estimating the myelin water fraction (MWF) from multicomponent T2 relaxometry requires solving an ill-conditioned inverse problem, making estimates sensitive to noise. Regularization can improve stability but may introduce bias. Conventional NNLS-based methods also provide point estimates without directly quantifying voxelwise variability. To address these limitations, we propose the non-negative least squares Bootstrap Barycenter (NNLS-BB), combining residual resampling with repeated NNLS reconstruction. We average spectra and derived parameters across bootstrap replicates and use their standard deviations to characterize sensitivity to signal perturbations. The method requires neither an explicit spectral regularization penalty nor a training dataset. NNLS-BB was evaluated on 40,000 simulated voxels with signal-to-noise ratios of 50-1000, against conventional NNLS, two regularized NNLS methods, and a model-informed machine-learning (MIML) method. Scan-rescan repeatability was assessed across 20 white-matter regions in two independent cohorts comprising 13 healthy participants. NNLS-BB achieved the lowest MWF mean absolute error and root mean squared error in all simulated noise regimes. Mean absolute error decreased by 36-41% relative to conventional NNLS, alongside lower error dispersion. Compared with Bayes-Reg-$D^{-1}$ and MIML, NNLS-BB achieved comparable dispersion but substantially lower bias, although MIML reconstructed the full spectrum more accurately. In vivo, NNLS-BB yielded the lowest regional scan-rescan dispersion and highest mean correlation in both cohorts. Bootstrap standard-deviation maps provided complementary information about parameter variability. These results support residual-bootstrap aggregation for improving MWF estimation while providing voxelwise variability maps from a single acquisition.

arXiv comment22 pages, 5 figures, 3 tables