@Ying_AHU 有什么好的低秩稀疏方面的综述论文吗

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http://www.weibo.com/2439005813/BpQZWbf0i

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概念

http://en.wikipedia.org/wiki/Low-rank_approximation In mathematics, low-rank approximation is a minimization problem, in which the cost function measures the fit between a given matrix (the data) and an approximating matrix (the optimization variable), subject to a constraint that the approximating matrix has reduced rank. The problem is used for mathematical modeling and data compression.

http://en.wikipedia.org/wiki/Sparse_approximation Sparse approximation (also referred to as sparse decomposition) is the problem of estimating a sparse multi-dimensional vector, satisfying a linear system of equations given high-dimensional observed data and a design matrix. Sparse approximation techniques have found wide use in applications such as image processing, audio processing, biology, and document analysis.

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http://www.bfcat.com/index.php/2012/10/background-subtraction-using-low-rank-and-group-sparsity-constraints/ 读论文：ECCV'12 Background Subtraction Using Low Rank and Group Sparsity Constraints 2012年10月14日 ⁄ 视觉会议, 阅读笔记 ⁄ 评论数 1 ⁄ 被围观 3,949 views+

“最近很火的一个话题，低秩和稀疏的矩阵分解。这次ECCV也有人把它用到视频前景背景分割里面了”

http://www.research.rutgers.edu/~shaoting/paper/ECCV12-background.pdf

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http://web.stanford.edu/~emileric/pdfs/SPLR.pdf Estimation of Simultaneously Sparse and Low Rank Matrices ICML2012

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私信

看这里： https://github.com/memect/hao/issues/272 确认了一下几个相关概念， 加了几篇相关文章，但还没找到综述，恐怕只能按引用链来查论文了。

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http://users.cms.caltech.edu/~venkatc/cspw_slr_sysid09.pdf Sparse and Low-Rank Matrix Decompositions (2009) Venkat Chandrasekaran, Sujay Sanghavi, Pablo A. Parrilo, Alan S. Willsky

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http://icml.cc/2012/papers/674.pdf Estimation of Simultaneously Sparse and Low Rank Matrices

Emile Richard, Pierre-Andre Savalle, Nicolas Vayatis ICML'12

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http://www.icml-2011.org/papers/41_icmlpaper.pdf Estimation of Simultaneously Sparse and Low Rank Matrices

Tianyi Zhou,Tianyi Zhou
ICML'11

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http://statweb.stanford.edu/~candes/papers/L+S-MRI.pdf Low-Rank and Sparse Matrix Decomposition for Accelerated Dynamic MRI with Separation of Background and Dynamic Components

Ricardo Otazo, Emmanuel Candès, Daniel K. Sodickson

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http://web.stanford.edu/~boyd/papers/prox_algs.html

http://www.stanford.edu/~boyd/papers/pdf/prox_algs.pdf Proximal Algorithms Parikh and S. Boyd Foundations and Trends in Optimization Vol. 1, No. 3 (2013) 123–231

This monograph is about a class of optimization algorithms called proximal algorithms. Much like Newton's method is a standard tool for solving unconstrained smooth optimization problems of modest size, proximal algorithms can be viewed as an analogous tool for nonsmooth, constrained, large-scale, or distributed versions of these problems. They are very generally applicable, but are especially well-suited to problems of substantial recent interest involving large or high-dimensional datasets. Proximal methods sit at a higher level of abstraction than classical algorithms like Newton's method: the base operation is evaluating the proximal operator of a function, which itself involves solving a small convex optimization problem. These subproblems, which generalize the problem of projecting a point into a convex set, often admit closed-form solutions or can be solved very quickly with standard or simple specialized methods. Here, we discuss the many different interpretations of proximal operators and algorithms, describe their connections to many other topics in optimization and applied mathematics, survey some popular algorithms, and provide a large number of examples of proximal operators that commonly arise in practice.

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http://arxiv.org/pdf/0906.2220.pdf RANK-SPARSITY INCOHERENCE FOR MATRIX DECOMPOSITION

VENKAT CHANDRASEKARAN, SUJAY SANGHAVI, PABLO A. PARRILO, AND ALAN S. WILLSKY

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http://onlinelibrary.wiley.com/doi/10.1002/gamm.201310004/pdf

A literature survey of low-rank tensor approximation techniques Lars Grasedyck1, Daniel Kressner2,* and Christine Tobler Article first published online: 13 AUG 2013 DOI: 10.1002/gamm.201310004

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http://perception.csl.illinois.edu/matrix-rank/rasl.html

RASL: Robust Alignment by Sparse and Low-rank Decomposition for Linearly Correlated Images, Yigang Peng, Arvind Ganesh, John Wright, Wenli Xu, and Yi Ma. Submitted to IEEE Transactions on Pattern Analysis and Machine Intelligence (PAMI), July 2010.

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又找到一些相关的论文，都有不错的引用率。 你能不能看看然后选一两篇你喜欢的，顺路把你的体会分享给小伙伴？ 谢谢！