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

arXiv: https://arxiv.org/abs/1710.02441 · HTML: https://mlsanity.com/paper/1710.02441/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Oct 2017.

## Built on by (most cited first, 1 of 1)

- [Cram'er-Rao bound-informed training of neural networks for quantitative MRI](https://mlsanity.com/paper/2109.10535/) (2021)

## Abstract (arXiv)

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 T1,T2 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 T1,T2 estimates in white and gray matter, but PERK is consistently at least 23× faster. This acceleration factor will increase by several orders of magnitude for full-volume QMRI estimation problems involving more latent parameters per voxel.