稀疏性与L1范数

转自prfans：

Sparse, L1-minimization, Compressive Sensing 集中讨论帖（第一页常更新）

Sparse大家并不陌生，是个经典话题了。而此时sparse已经卷土重来，虽然还是那一锅汤，但是药已经换了。以L1-minimization为核心的算法，近几年飞速进展，Compressive Sensing (Compressive Sampling) 已然成为数学领域和信号处理最前沿最热门的方向。最近一年多这种新形式的算法快速蔓延到模式识别界应用，论文质量高、算法效果好、而且算法一般都非常简单。而这仅仅是个开始，所以我一直有这个想法专开一贴，供大家一起讨论、共同进步，今天付诸与行动，希望大家支持。在这个地方（第一个帖），我会陆续更新提供一些这方面的材料，供大家了解。如果大家提供了有趣的材料，我也尽量加进来。当然，此贴重点还是放在理论应用和模式识别上。大家踊跃发言啊！


Compressive Sensing资源主页：
Compressive Sensing Resources （最权威最全面的Compressive Sensing资源主页，几乎什么都能找的到）；
Compressive Sensing （和上面的差不多）；
Compressive Sensing Listing； 马毅的课程主页
Compressive Sensing Videos；Compressed Sensing Codes （还有Compressive Sensing Resources 的Software一栏中）；
Nuit Blanche；Compressive Sensing: The Big Picture；Terence Tao's What's new;



理论方面的代表人物：
David Donoho; Emmanuel Candes;


Tutorials
Emmanuel Candès, Compressive sampling. (Int. Congress of Mathematics, 3, pp. 1433-1452, Madrid, Spain, 2006)
Richard Baraniuk, Compressive sensing. (IEEE Signal Processing Magazine, 24(4), pp. 118-121, July 2007)
Emmanuel Candès and Michael Wakin, An introduction to compressive sampling. (IEEE Signal Processing Magazine, 25(2), pp. 21 - 30, March 2008)
Justin Romberg, Imaging via compressive sampling. (IEEE Signal Processing Magazine, 25(2), pp. 14 - 20, March 2008)

Conferences and Symposiums
Short Course: Sparse Representations and High Dimensional Geometry, May 30 - June 1, 2007
New Directions Short Course: Compressive Sampling and Frontiers in Signal Processing, June 4 - 15, 2007 （介绍性的资料和视频）


理论方面的代表文献：
Donoho 和 Candes 的文章几乎都是经典


模式识别领域的应用（包括机器视觉）：
大家可以去Compressive Sensing Resources 看 Statistical Signal Processing, Machine Learning, Bayesian Methods, Applications of Compressive Sensing 等栏目
马毅的一系列论文
John Wright, Allen Yang, Arvind Ganesh, Shankar Shastry, and Yi Ma, Robust face recognition via sparse representation. (To appear in IEEE Trans. on Pattern Analysis and Machine Intelligence) , 2008
Allen Yang, John Wright, Yi Ma, and Shankar Sastry, Feature selection in face recognition: A sparse representation perspective. (Preprint, 2007)
Kwak, N., Principal Component Analysis Based on L1-Norm Maximization, IEEE Transactions on Pattern Analysis and Machine Intelligence, 2008.
Bhusnurmath, Arvind; Taylor, Camillo J., Graph Cuts via $ell_1$ Norm Minimization, IEEE Transactions on Pattern Analysis and Machine Intelligence, 2008.
Jianchao Yang, John Wright, Thomas Huang, and Yi Ma, Image Super-Resolution as Sparse Representation of Raw Image Patches, IEEE Conference on Computer Vision and Pattern Recognition (CVPR), June 2008.
Arvind Ganesh, Zihan Zhou, and Yi Ma, Separation of A Subspace-Sparse Signal: Algorithms and Conditions, ICASSP 2009.