摘要翻译：
提出了一种自适应结构化低秩MR图像恢复算法，从欠采样Fourier系数中恢复MR图像。图像被建模为分段常数分量和分段线性分量的组合。每个分量的Fourier系数满足一个湮没关系，从而得到一个结构化的Toeplitz矩阵。利用矩阵的低秩性质，构造了一个能有效求解的组合正则化优化问题。数值实验表明，该算法比以前提出的算法具有更好的恢复性能。
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英文标题：
《Adaptive structured low rank algorithm for MR image recovery》
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作者：
Yue Hu, Xiaohan Liu, Mathews Jacob
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最新提交年份：
2018
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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：
  We introduce an adaptive structured low rank algorithm to recover MR images from their undersampled Fourier coefficients. The image is modeled as a combination of a piecewise constant component and a piecewise linear component. The Fourier coefficients of each component satisfy an annihilation relation, which results in a structured Toeplitz matrix. We exploit the low rank property of the matrices to formulate a combined regularized optimization problem, which can be solved efficiently. Numerical experiments indicate that the proposed algorithm provides improved recovery performance over the previously proposed algorithms.
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PDF链接：
https://arxiv.org/pdf/1805.05013