{"title":"Wavelet soft-threshold method for determining an unknown source in a diffusion equation","authors":"Jinru Wang","doi":"10.1109/ICWAPR.2009.5207496","DOIUrl":null,"url":null,"abstract":"We consider the problem of determining an unknown source, which depends only on the spatial variable, in a diffusion equation. This is an ill-posed problem. For a reconstruction of the solution from indirect data, the dual least squares method generated by the family of Shannon wavelet subspaces is applied. Moreover, a certain simple nonlinear modification of the method based on local refinements of the wavelet expansion of the noisy data is investigated.","PeriodicalId":424264,"journal":{"name":"2009 International Conference on Wavelet Analysis and Pattern Recognition","volume":"7 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2009-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"2009 International Conference on Wavelet Analysis and Pattern Recognition","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ICWAPR.2009.5207496","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
We consider the problem of determining an unknown source, which depends only on the spatial variable, in a diffusion equation. This is an ill-posed problem. For a reconstruction of the solution from indirect data, the dual least squares method generated by the family of Shannon wavelet subspaces is applied. Moreover, a certain simple nonlinear modification of the method based on local refinements of the wavelet expansion of the noisy data is investigated.
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