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

TL;DR

This paper presents PERK, a fast, dictionary-free method for MRI parameter estimation using kernel regression, achieving comparable accuracy to traditional methods but with significantly improved speed, especially for large-scale problems.

Contribution

Introduces PERK, a novel kernel-based regression approach for MRI parameter estimation that eliminates the need for dictionaries and accelerates computation.

Findings

PERK achieves at least 23x faster estimates than grid search.

PERK produces comparable T1, T2 estimates to traditional methods.

PERK's speed advantage increases with more parameters in full-volume QMRI.

Abstract

This paper introduces a fast, general method for dictionary-free 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 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. Numerical simulations as well as single-slice 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 full-volume QMRI estimation problems involving more latent parameters per voxel.