摘要翻译：
本文讨论了一个从压缩测量数据中恢复彩色图像的不适定问题。与现有的基于一维向量的方法不同，我们利用了图像中固有的非局部相似性，将彩色图像的每个斑块视为一个三维张量，不仅包括水平和垂直维，还包括光谱维。一组非局部相似片构成一个四维张量，通过高阶奇异值分解，得到一个非局部高阶字典。高阶字典中包含了多个子字典，在相应的维度上解相关组，从而帮助更好地重建彩色图像的细节。此外，我们利用一个基于权张量的稀疏正则化来提高最终解的稀疏性。该算法能够在优化中区分由高阶字典生成的稀疏表示中期望具有较大量级的系数。因此，在迭代求解中，它就像一个加权过程，通过逼近最小均方误差滤波器来设计，以获得更好的恢复效果。实验结果表明，该方法比现有的方法有较大的改进。
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英文标题：
《Compressive Sensing of Color Images Using Nonlocal Higher Order
  Dictionary》
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作者：
Khanh Quoc Dinh, Thuong Nguyen Canh, and Byeungwoo Jeon
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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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一级分类：Computer Science        计算机科学
二级分类：Computer Vision and Pattern Recognition        计算机视觉与模式识别
分类描述：Covers image processing, computer vision, pattern recognition, and scene understanding. Roughly includes material in ACM Subject Classes I.2.10, I.4, and I.5.
涵盖图像处理、计算机视觉、模式识别和场景理解。大致包括ACM课程I.2.10、I.4和I.5中的材料。
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英文摘要：
  This paper addresses an ill-posed problem of recovering a color image from its compressively sensed measurement data. Differently from the typical 1D vector-based approach of the state-of-the-art methods, we exploit the nonlocal similarities inherently existing in images by treating each patch of a color image as a 3D tensor consisting of not only horizontal and vertical but also spectral dimensions. A group of nonlocal similar patches form a 4D tensor for which a nonlocal higher order dictionary is learned via higher order singular value decomposition. The multiple sub-dictionaries contained in the higher order dictionary decorrelate the group in each corresponding dimension, thus help the detail of color images to be reconstructed better. Furthermore, we promote sparsity of the final solution using a sparsity regularization based on a weight tensor. It can distinguish those coefficients of the sparse representation generated by the higher order dictionary which are expected to have large magnitude from the others in the optimization. Accordingly, in the iterative solution, it acts like a weighting process which is designed by approximating the minimum mean squared error filter for more faithful recovery. Experimental results confirm improvement by the proposed method over the state-of-the-art ones.
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PDF链接：
https://arxiv.org/pdf/1711.09375