Multi-Exponential Relaxometry Using $\ell_{{1}}$ -Regularized Iterative NNLS (MERLIN) With Application to Myelin Water Fraction Imaging

A new parameter estimation algorithm, MERLIN, is presented for accurate and robust multi-exponential relaxometry using magnetic resonance imaging, a tool that can provide valuable insight into the tissue microstructure of the brain. Multi-exponential relaxometry is used to analyze the myelin water fraction and can help to detect related diseases. However, the underlying problem is ill-conditioned, and as such, is extremely sensitive to noise and measurement imperfections, which can lead to less precise and more biased parameter estimates. MERLIN is a fully automated, multi-voxel approach that incorporates state-of-the-art
$\ell _{1}$
-regularization to enforce sparsity and spatial consistency of the estimated distributions. The proposed method is validated in simulations and
in vivo
experiments, using a multi-echo gradient-echo (MEGE) sequence at 3 T. MERLIN is compared to the conventional single-voxel
$\ell _{2}$
-regularized NNLS (rNNLS) and a multi-voxel extension with spatial priors (rNNLS + SP), where it consistently showed lower root mean squared errors of up to 70 percent for all parameters of interest in these simulations.