On Equivalence of l1 Norm Based Basic Sparse Representation Problems

被引：0

作者：

Jiang, Rui ^{[1
]}

Qiao, Hong ^{[1
]}

Zhang, Bo ^{[2
,3
]}

机构：

[1] Chinese Acad Sci, Inst Automat, Beijing, Peoples R China

[2] Chinese Acad Sci, AMSS, LSEC, Beijing, Peoples R China

[3] Chinese Acad Sci, AMSS, Inst Appl Math, Beijing, Peoples R China

来源：

2015 IEEE INTERNATIONAL CONFERENCE ON SIGNAL PROCESSING, COMMUNICATIONS AND COMPUTING (ICSPCC) | 2015年

关键词：

Equivalence; l(1) norm regularization problem; l(1) norm minimization problem; l(1) norm constraint problem; THRESHOLDING ALGORITHM;

D O I：

暂无

中图分类号：

TM [电工技术]; TN [电子技术、通信技术];

学科分类号：

0808 ; 0809 ;

摘要：

The l1 norm regularization problem, the l1 norm minimization problem and the l1 norm constraint problem are known collectively as the l1 norm based Basic Sparse Representation Problems (BSRPs), and have been popular basic models in the field of signal processing and machine learning. The equivalence of the above three problems is one of the crucial bases for the corresponding algorithms design. However, to the best our knowledge, this equivalence issue has not been addressed appropriately in the existing literature. In this paper, we will give a rigorous proof of the equivalence of the three l1 norm based BSRPs in the case when the dictionary is an overcomplete and row full rank matrix.

引用

页码：818 / 823

页数：6

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