Convolutional Dictionary Learning with Huber Error and l1 Regularization Terms

Satoshi Yoda, Hironori Kawazoe, Y. Kuroki
{"title":"Convolutional Dictionary Learning with Huber Error and l1 Regularization Terms","authors":"Satoshi Yoda, Hironori Kawazoe, Y. Kuroki","doi":"10.1109/ISPACS51563.2021.9651025","DOIUrl":null,"url":null,"abstract":"This paper addresses a robust convolutional dictionary learning method against outliers. Convolutional dictionary learning approximates a signal with the sum of dictionary filters and corresponding coefficients, and its cost function consists of the weighted sum of the two terms: error and regularization terms. Many studies employ the l2 and the l1 norms for the former and the latter respectively, and to increase the robustness, the l1 norm is substituted for the error term. For such optimization problems with the sum of the two convex terms, the proximal gradient method is a powerful solver; however, it is not applicable for the two l1 terms, of which gradient is not continuous at any point. This paper tries to apply the Moreau envelope for the l1 error term, and the l1 error is expressed as Huber error function, which is differentiable and Lipschitz continuous. Experimental results show that dictionaries generated with the proposed method are robuster than those with the l2 error term.","PeriodicalId":359822,"journal":{"name":"2021 International Symposium on Intelligent Signal Processing and Communication Systems (ISPACS)","volume":"40 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2021-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"2021 International Symposium on Intelligent Signal Processing and Communication Systems (ISPACS)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ISPACS51563.2021.9651025","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0

Abstract

This paper addresses a robust convolutional dictionary learning method against outliers. Convolutional dictionary learning approximates a signal with the sum of dictionary filters and corresponding coefficients, and its cost function consists of the weighted sum of the two terms: error and regularization terms. Many studies employ the l2 and the l1 norms for the former and the latter respectively, and to increase the robustness, the l1 norm is substituted for the error term. For such optimization problems with the sum of the two convex terms, the proximal gradient method is a powerful solver; however, it is not applicable for the two l1 terms, of which gradient is not continuous at any point. This paper tries to apply the Moreau envelope for the l1 error term, and the l1 error is expressed as Huber error function, which is differentiable and Lipschitz continuous. Experimental results show that dictionaries generated with the proposed method are robuster than those with the l2 error term.
基于Huber误差和l1正则化项的卷积字典学习
本文提出了一种针对异常值的鲁棒卷积字典学习方法。卷积字典学习用字典滤波器和相应系数的和逼近信号,其代价函数由误差项和正则化项两项的加权和组成。许多研究分别对前者和后者采用l2范数和l1范数,为了提高鲁棒性,用l1范数代替误差项。对于这类具有两个凸项和的优化问题,近端梯度法是一种有效的求解方法;但是对于两个l1项不适用,因为l1项的梯度在任何一点都不是连续的。本文尝试对l1误差项采用莫罗包络,并将l1误差表示为可微且Lipschitz连续的Huber误差函数。实验结果表明,使用该方法生成的字典比使用l2错误项生成的字典具有更好的鲁棒性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 求助全文
来源期刊
自引率
0.00%
发文量
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:604180095
Book学术官方微信