DictionaryFree MRI PERK: Parameter Estimation via Regression with Kernels
Abstract
This paper introduces a fast, general method for dictionaryfree parameter estimation in quantitative magnetic resonance imaging (QMRI) via regression with kernels (PERK). PERK first uses prior distributions and the nonlinear MR signal model to simulate many parametermeasurement pairs. Inspired by machine learning, PERK then takes these parametermeasurement 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 pervoxel nonlinear lifting of MRI measurements followed by linear minimum meansquared error regression. We demonstrate PERK for $T_1,T_2$ estimation, a wellstudied application where it is simple to compare PERK estimates against dictionarybased grid search estimates. Numerical simulations as well as singleslice phantom and in vivo experiments demonstrate that PERK and grid search produce comparable $T_1,T_2$ estimates in white and gray matter, but PERK is consistently at least $23\times$ faster. This acceleration factor will increase by several orders of magnitude for fullvolume QMRI estimation problems involving more latent parameters per voxel.
 Publication:

arXiv eprints
 Pub Date:
 October 2017
 arXiv:
 arXiv:1710.02441
 Bibcode:
 2017arXiv171002441N
 Keywords:

 Statistics  Machine Learning;
 Electrical Engineering and Systems Science  Signal Processing;
 Physics  Medical Physics
 EPrint:
 submitted to IEEE Transactions on Medical Imaging