摘要翻译：
补丁先验信息已成为图像复原的重要组成部分。在这类恢复算法中，一个强大的方法是流行的期望补丁对数似然(EPLL)算法。EPLL使用一种在干净的图像斑块上学习到的高斯混合模型(GMM)作为一种正则化退化斑块的方法。在本文中，我们证明了广义高斯混合模型(GGMM)比GMM更好地捕捉了斑块的底层分布。尽管GGMM是与EPLL相结合的一种强大的先验方法，但其分量的非高斯性给应用于计算密集型的图像恢复过程带来了重大挑战。具体来说，每个贴片都要经历贴片分类步骤和收缩步骤。这两个步骤可以用GMM先验有效地解决，但在使用GGMM先验时在计算上是不切实际的。本文给出了这两个步骤的近似值和计算公式，使得EPLL可以在含有数万个以上的片的图像上嵌入GGMM先验。我们的主要贡献是在深入的理论分析的基础上分析了我们的近似的准确性。我们的评估表明，GGMM先验算法始终是一个更好的拟合图像斑块分布的模型，并且在图像去噪任务中平均表现更好。
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英文标题：
《Image denoising with generalized Gaussian mixture model patch priors》
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作者：
Charles-Alban Deledalle (IMB, UCSD), Shibin Parameswaran (UCSD),
  Truong Q. Nguyen (UCSD)
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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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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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一级分类：Mathematics        数学
二级分类：Statistics Theory        统计理论
分类描述：Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计：例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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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：Statistics        统计学
二级分类：Statistics Theory        统计理论
分类描述：stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近，贝叶斯推论，决策理论，估计，基础，推论，检验。
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英文摘要：
  Patch priors have become an important component of image restoration. A powerful approach in this category of restoration algorithms is the popular Expected Patch Log-Likelihood (EPLL) algorithm. EPLL uses a Gaussian mixture model (GMM) prior learned on clean image patches as a way to regularize degraded patches. In this paper, we show that a generalized Gaussian mixture model (GGMM) captures the underlying distribution of patches better than a GMM. Even though GGMM is a powerful prior to combine with EPLL, the non-Gaussianity of its components presents major challenges to be applied to a computationally intensive process of image restoration. Specifically, each patch has to undergo a patch classification step and a shrinkage step. These two steps can be efficiently solved with a GMM prior but are computationally impractical when using a GGMM prior. In this paper, we provide approximations and computational recipes for fast evaluation of these two steps, so that EPLL can embed a GGMM prior on an image with more than tens of thousands of patches. Our main contribution is to analyze the accuracy of our approximations based on thorough theoretical analysis. Our evaluations indicate that the GGMM prior is consistently a better fit formodeling image patch distribution and performs better on average in image denoising task.
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PDF链接：
https://arxiv.org/pdf/1802.01458