稀疏性與L1範數

摘自:http://blog.sina.com.cn/s/blog_49b5f5080100b62j.html


Sparse大家並不陌生,是個經典話題了。而此時sparse已經捲土重來,雖然還是那一鍋湯,但是藥已經換了。以L1-minimization爲核心的算法,近幾年飛速進展,Compressive Sensing (Compressive Sampling) 已然成爲數學領域和信號處理最前沿最熱門的方向。最近一年多這種新形式的算法快速蔓延到模式識別界應用,論文質量高、算法效果好、而且算法一般都非常簡單而這僅僅是個開始,所以我一直有這個想法專開一貼,供大家一起討論、共同進步,今天付諸與行動,希望大家支持。在這個地方(第一個帖),我會陸續更新提供一些這方面的材料,供大家瞭解。如果大家提供了有趣的材料,我也儘量加進來。當然,此貼重點還是放在理論應用和模式識別上。大家踊躍發言啊!


Compressive Sensing資源主頁
Compressive Sensing Resources (最權威最全面的Compressive Sensing資源主頁,幾乎什麼都能找的到);
Compressive Sensing (和上面的差不多);
Compressive Sensing Listing; 馬毅的課程主頁
Compressive Sensing VideosCompressed Sensing Codes (還有Compressive Sensing Resources 的Software一欄中);
Nuit BlancheCompressive Sensing: The Big PictureTerence Tao's What's new;



理論方面的代表人物
David DonohoEmmanuel 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 (介紹性的資料和視頻


理論方面的代表文獻
Donoho 和 Candes 的文章幾乎都是經典


模式識別領域的應用(包括機器視覺):
大家可以去Compressive Sensing Resources 看 Statistical Signal Processing, Machine Learning, Bayesian Methods, Applications of Compressive Sensing 等欄目
馬毅的一系列論文
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.

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