摘要翻译：
本文提出了一种新的扩散MRI单壳和多壳采样方案。在弥散磁共振成像中，为了使扫描时间在临床环境中切实可行，样本数量尽可能少是最重要的。所提出的方案使用有效的测量数，因为样本数等于用于重建的正交基中的自由度。与标准正则化最小二乘法相比，提出了一种新的基于较小线性方程组的单壳和多壳采样方案的重构算法。这些新的重建算法中使用的较小矩阵被设计成良好的条件，导致提高重建精度。在新的重建算法中引入正则化，并使用Rician或非中心Chi噪声模型，实现了精确和鲁棒的重建。我们用标准的最小二乘重建方法对我们的单壳和多壳格式进行了定量的验证，表明当样本数等于基中的自由度时，它们能够更准确地重建。人脑数据也用于定性评价重建
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英文标题：
《Efficient sampling and robust 3D diffusion magnetic resonance imaging
  signal reconstruction》
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作者：
Alice P. Bates, Zubair Khalid, Jason D. McEwen, Rodney A. Kennedy,
  Alessandro Daducci and Erick J. Canales-Rodr\'iguez
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最新提交年份：
2019
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分类信息：

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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英文摘要：
  This paper presents novel single and multi-shell sampling schemes for diffusion MRI. In diffusion MRI, it is paramount that the number of samples is as small as possible in order that scan times are practical in a clinical setting. The proposed schemes use an efficient number of measurements in that the number of samples is equal to the degrees of freedom in the orthonormal bases used for reconstruction. Novel reconstruction algorithms based on smaller subsystems of linear equations, as compared to the standard regularized least-squares method, are developed for both single and multi-shells sampling schemes. The smaller matrices used in these novel reconstruction algorithms are designed to be well-conditioned, leading to improved reconstruction accuracy. Accurate and robust reconstruction is also achieved through incorporation of regularization into the novel reconstruction algorithms and using a Rician or non-central Chi noise model. We quantitatively validate our single and multi-shell schemes against standard least-squares reconstruction methods to show that they enable more accurate reconstruction when the number of samples is equal to the degrees of freedom in the basis. Human brain data is also used to qualitatively evaluate reconstruction
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PDF链接：
https://arxiv.org/pdf/1807.09637