[电气工程与系统科学] 无字典MRI Perk：参数估计的回归方法 核仁 [推广有奖]

摘要翻译：
本文介绍了一种快速、通用的基于核回归(PERK)的定量磁共振成像(QMRI)无字典参数估计方法。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将这些参数-测量对作为标记训练点，并利用核函数和凸优化从它们中学习非线性回归函数。PERK提供了一个简单的实现，即对MRI测量值进行逐体素非线性提升，然后进行线性最小均方误差回归。我们演示了$T_1和T_2$estimation的PERK，这是一个研究得很好的应用程序，在这里比较PERK估计值和基于字典的网格搜索估计值很简单。数值模拟以及单层体模和活体实验表明，PERK和网格搜索在白质和灰质中产生了可比的$T_1和T_2$估计，但PERK的估计速度一致至少为$23倍。对于涉及每个体素更多潜在参数的全体积QMRI估计问题，该加速因子将增加几个数量级。
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英文标题：
《Dictionary-Free MRI PERK: Parameter Estimation via Regression with
  Kernels》
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作者：
Gopal Nataraj, Jon-Fredrik Nielsen, Clayton Scott, and Jeffrey A.
  Fessler
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最新提交年份：
2017
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分类信息：

一级分类：Statistics        统计学
二级分类：Machine Learning        机器学习
分类描述：Covers machine learning papers (supervised, unsupervised, semi-supervised learning, graphical models, reinforcement learning, bandits, high dimensional inference, etc.) with a statistical or theoretical grounding
覆盖机器学习论文（监督，无监督，半监督学习，图形模型，强化学习，强盗，高维推理等）与统计或理论基础
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一级分类：Electrical Engineering and Systems Science        电气工程与系统科学
二级分类：Signal Processing        信号处理
分类描述：Theory, algorithms, performance analysis and applications of signal and data analysis, including physical modeling, processing, detection and parameter estimation, learning, mining, retrieval, and information extraction. The term "signal" includes speech, audio, sonar, radar, geophysical, physiological, (bio-) medical, image, video, and multimodal natural and man-made signals, including communication signals and data. Topics of interest include: statistical signal processing, spectral estimation and system identification; filter design, adaptive filtering / stochastic learning; (compressive) sampling, sensing, and transform-domain methods including fast algorithms; signal processing for machine learning and machine learning for signal processing applications; in-network and graph signal processing; convex and nonconvex optimization methods for signal processing applications; radar, sonar, and sensor array beamforming and direction finding; communications signal processing; low power, multi-core and system-on-chip signal processing; sensing, communication, analysis and optimization for cyber-physical systems such as power grids and the Internet of Things.
信号和数据分析的理论、算法、性能分析和应用，包括物理建模、处理、检测和参数估计、学习、挖掘、检索和信息提取。“信号”一词包括语音、音频、声纳、雷达、地球物理、生理、（生物）医学、图像、视频和多模态自然和人为信号，包括通信信号和数据。感兴趣的主题包括：统计信号处理、谱估计和系统辨识；滤波器设计；自适应滤波/随机学习；（压缩）采样、传感和变换域方法，包括快速算法；用于机器学习的信号处理和用于信号处理应用的机器学习；网络与图形信号处理；信号处理中的凸和非凸优化方法；雷达、声纳和传感器阵列波束形成和测向；通信信号处理；低功耗、多核、片上系统信号处理；信息物理系统的传感、通信、分析和优化，如电网和物联网。
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一级分类：Physics        物理学
二级分类：Medical Physics        医学物理学
分类描述：Radiation therapy. Radiation dosimetry. Biomedical imaging modelling.  Reconstruction, processing, and analysis. Biomedical system modelling and analysis. Health physics. New imaging or therapy modalities.
放射治疗。辐射剂量学。生物医学成像建模。重建、处理和分析。生物医学系统建模与分析。健康物理学。新的成像或治疗方式。
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英文摘要：
  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.
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PDF链接：
https://arxiv.org/pdf/1710.02441