Dictionary-Free MRI PERK: Parameter Estimation via Regression with Kernels

This paper introduces a fast, general method for dictionary-free parameter estimation in quantitative magnetic resonance imaging (QMRI) parameter estimation via regression with kernels (PERK). PERK first uses prior distributions and the nonlinear MR signal model to simulate many parameter-measurement pairs. Inspired by machine learning, PERK then takes these parameter-measurement pairs as labeled training points and learns from them a nonlinear regression function using kernel functions and convex optimization. PERK admits a simple implementation as per-voxel nonlinear lifting of MRI measurements followed by linear minimum mean-squared error regression. We demonstrate PERK for T-1, T-2 estimation, a well-studied application where it is simple to compare PERK estimates against dictionary-based grid search estimates and iterative optimization estimates. Numerical simulations as well as single-slice phantom and in vivo experiments demonstrate that PERK and other tested methods produce comparable T-1, T-2 estimates in white and gray matter, but PERK is consistently at least 140 x faster. This acceleration factor may increase by several orders of magnitude for full-volume QMRI estimation problems involving more latent parameters per voxel.