IEEE Trans Med Imaging. 2018 Sep;37(9):2103-2114. doi: 10.1109/TMI.2018.2817547. Epub 2018 Mar 20.
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 $ {\textit {T}{1}}, {\textit {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 $ {\textit {T}{1}}, {\textit {T}{2}}$ estimates in white and gray matter, but PERK is consistently at least $140\times $ faster. This acceleration factor may increase by several orders of magnitude for full-volume QMRI estimation problems involving more latent parameters per voxel.
本文介绍了一种快速、通用的方法，用于通过核回归（PERK）进行定量磁共振成像（QMRI）参数估计中的无字典参数估计。PERK 首先使用先验分布和非线性 MR 信号模型来模拟许多参数-测量对。受机器学习的启发，PERK 然后将这些参数-测量对作为带标签的训练点，并使用核函数和凸优化从它们中学习非线性回归函数。PERK 作为 MRI 测量的逐体素非线性提升，然后是线性最小均方误差回归，具有简单的实现。我们演示了 PERK 在 $ {\textit {T}{1}}, {\textit {T}{2}}$ 估计中的应用，这是一个研究得很好的应用，很容易将 PERK 估计与基于字典的网格搜索估计和迭代优化估计进行比较。数值模拟以及单切片体模和体内实验表明，PERK 和其他测试方法在白质和灰质中产生可比的 $ {\textit {T}{1}}, {\textit {T}{2}}$ 估计，但 PERK 的速度始终至少快 $140\times$。对于每个体素涉及更多潜在参数的全容积 QMRI 估计问题，这个加速因子可能会增加几个数量级。
