摘要翻译：
在高维磁共振成像应用中，在空间频域($k$-space)中耗时、顺序的数据采样通常可以通过在线性重建中考虑沿空间以外的成像维度的依赖性来加速，其代价是依赖于采样模式的噪声放大。例如支持约束、并行和动态MRI，$K$-空间采样策略主要由图像域度量驱动，对于任意采样模式，计算代价很高。在给定对象所限制的子空间的情况下，提供系统的、计算高效的任意多维笛卡尔采样模式的自动设计以减轻噪声放大仍然具有挑战性。为了解决这个问题，本工作引入了一个理论框架，它描述了采样模式的局部几何性质，并将这些性质与由其前两个谱矩描述的信息矩阵的特征值扩展的度量联系起来。这种新的准则用于复杂多维采样模式的非常有效的优化，不需要重建图像或显式映射噪声放大。用活体数据进行的实验表明，该标准与传统的、综合的图像域和基于K空间的度量之间有很强的一致性，表明该方法在计算高效（动态）、自动和自适应设计采样模式方面的潜力。
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英文标题：
《On-the-fly Adaptive $k$-Space Sampling for Linear MRI Reconstruction
  Using Moment-Based Spectral Analysis》
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作者：
Evan Levine and Brian Hargreaves
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最新提交年份：
2017
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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：Image and Video Processing        图像和视频处理
分类描述：Theory, algorithms, and architectures for the formation, capture, processing, communication, analysis, and display of images, video, and multidimensional signals in a wide variety of applications. Topics of interest include: mathematical, statistical, and perceptual image and video modeling and representation; linear and nonlinear filtering, de-blurring, enhancement, restoration, and reconstruction from degraded, low-resolution or tomographic data; lossless and lossy compression and coding; segmentation, alignment, and recognition; image rendering, visualization, and printing; computational imaging, including ultrasound, tomographic and magnetic resonance imaging; and image and video analysis, synthesis, storage, search and retrieval.
用于图像、视频和多维信号的形成、捕获、处理、通信、分析和显示的理论、算法和体系结构。感兴趣的主题包括：数学，统计，和感知图像和视频建模和表示；线性和非线性滤波、去模糊、增强、恢复和重建退化、低分辨率或层析数据；无损和有损压缩编码；分割、对齐和识别；图像渲染、可视化和打印；计算成像，包括超声、断层和磁共振成像；以及图像和视频的分析、合成、存储、搜索和检索。
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英文摘要：
  In high-dimensional magnetic resonance imaging applications, time-consuming, sequential acquisition of data samples in the spatial frequency domain ($k$-space) can often be accelerated by accounting for dependencies along imaging dimensions other than space in linear reconstruction, at the cost of noise amplification that depends on the sampling pattern. Examples are support-constrained, parallel, and dynamic MRI, and $k$-space sampling strategies are primarily driven by image-domain metrics that are expensive to compute for arbitrary sampling patterns. It remains challenging to provide systematic and computationally efficient automatic designs of arbitrary multidimensional Cartesian sampling patterns that mitigate noise amplification, given the subspace to which the object is confined. To address this problem, this work introduces a theoretical framework that describes local geometric properties of the sampling pattern and relates these properties to a measure of the spread in the eigenvalues of the information matrix described by its first two spectral moments. This new criterion is then used for very efficient optimization of complex multidimensional sampling patterns that does not require reconstructing images or explicitly mapping noise amplification. Experiments with in vivo data show strong agreement between this criterion and traditional, comprehensive image-domain- and $k$-space-based metrics, indicating the potential of the approach for computationally efficient (on-the-fly), automatic, and adaptive design of sampling patterns.
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PDF链接：
https://arxiv.org/pdf/1710.07837