计算数学
       首页 |  期刊介绍 |  编委会 |  投稿指南 |  期刊订阅 |  下载中心 |  留言板 |  联系我们 |  重点论文 |  在线办公 | 
计算数学  2018, Vol. 40 Issue (4): 450-469    DOI:
论文 最新目录 | 下期目录 | 过刊浏览 | 高级检索 Previous Articles  |  Next Articles  
组模偏正则化及其应用
邱安东, 杨娇娇, 冯涵, 杨周旺
中国科学技术大学 数学科学学院, 合肥 230026
GROUP PARTIAL REGULARIZATION AND ITS APPLICATIONS
Qiu Andong, Yang Jiaojiao, Feng Han, Yang Zhouwang
School of Mathematical Sciences, University of Science and Technology of China, Hefei 230026, China
 全文: PDF (613 KB)   HTML (1 KB)   输出: BibTeX | EndNote (RIS)      背景资料
摘要 本文研究组模下偏正则最小化问题,证明了解的存在性,稀疏性.研究了零空间性质对最优解的刻画.仔细探讨了解的一种单调性,并应用这种单调性说明最优化问题的求解可以分解到各组中.最后给出了一个所证定理在地震反演的应用.
服务
把本文推荐给朋友
加入我的书架
加入引用管理器
E-mail Alert
RSS
作者相关文章
关键词偏正则化   稀疏恢复   零空间性质   分离性质   地震反演     
Abstract: By introducing the group norm, the paper proves the existence and sparsity theorems concerning minimization with partial regularization. Null space properties are considered to characterize optimal solutions. Monotone properties are discussed in depth, which justifies the approach that solving the minimization problem can be done separately in each group. The results are applied to an example of seismic inversion.
Key wordspartial regularization   sparse recovery   null space property   separation property   seismic inversion   
收稿日期: 2017-12-20;
基金资助:

国家自然科学基金(10371130)和中国国家重点基础研究发展计划(2004CB318000)资助项目.

引用本文:   
. 组模偏正则化及其应用[J]. 计算数学, 2018, 40(4): 450-469.
. GROUP PARTIAL REGULARIZATION AND ITS APPLICATIONS[J]. Mathematica Numerica Sinica, 2018, 40(4): 450-469.
 
[1] Lu Z, Li X. Sparse recovery via partial regularization:Models, theory and algorithms[J]. arXiv preprint arXiv:1511.07293, 2015.
[2] Ben-Israel A, Greville T N E. Generalized inverses:theory and applications[M]. Springer Science & Business Media, 2003.
[3] Clarke F H. Optimization and nonsmooth analysis[M]. Society for Industrial and Applied Mathematics, 1990.
[4] Clarke F H. Generalized gradients and applications[J]. Transactions of the American Mathematical Society, 1975, 205:247-262.
[5] Candes E J, Tao T. Decoding by linear programming[J]. IEEE transactions on information theory, 2005, 51(12):4203-4215.
[6] Chen S S, Donoho D L, Saunders M A. Atomic decomposition by basis pursuit[J]. SIAM review, 2001, 43(1):129-159.
[7] Tibshirani R. Regression shrinkage and selection via the lasso[J]. Journal of the Royal Statistical Society. Series B (Methodological), 1996, 267-288.
[8] Frank L L E, Friedman J H. A statistical view of some chemometrics regression tools[J]. Technometrics, 1993, 35(2):109-135.
[9] Fu W J. Penalized regressions:the bridge versus the lasso[J]. Journal of computational and graphical statistics, 1998, 7(3):397-416.
[10] Candes E J, Wakin M B, Boyd S P. Enhancing sparsity by reweighted l1 minimization[J]. Journal of Fourier analysis and applications, 2008, 14(5-6):877-905.
[11] Weston J, Elisseeff A, Schölkopf B, et al. Use of the zero-norm with linear models and kernel methods[J]. Journal of machine learning research, 2003, 3(Mar):1439-1461.
[1] 施章磊, 李维国. 矩阵广义逆硬阈值追踪算法与稀疏恢复问题[J]. 计算数学, 2017, 39(2): 189-199.

Copyright 2008 计算数学 版权所有
中国科学院数学与系统科学研究院 《计算数学》编辑部
北京2719信箱 (100190) Email: gxy@lsec.cc.ac.cn
本系统由北京玛格泰克科技发展有限公司设计开发
技术支持: 010-62662699 E-mail:support@magtech.com.cn
京ICP备05002806号-10