Multi-exponential Relaxometry using $$$\ell_1$$$-regularized Iterative NNLS (MERLIN) for Accurate and Robust Myelin Water Fraction Imaging

A new parameter estimation algorithm, MERLIN, is presented for accurate and robust multi-exponential relaxometry using MRI. Multi-exponential relaxometry is fundamentally ill-conditioned, and as such, is extremely sensitive to noise. MERLIN is a fully automated, multi-voxel approach that incorporates $$$\ell_1$$$-regularization to enforce sparsity and spatial consistency of the estimated distributions. The proposed method is compared to the conventional $$$\ell_2$$$-regularized NNLS (rNNLS) in simulations and in vivo experiments, using a multi-echo gradient-echo (MEGE) sequence at 3T. The estimated water fraction maps from MERLIN are spatially more consistent, more precise, and more accurate, reducing the root-mean-squared-error by up to 90 percent in simulations.