{"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.