{"title":"确定扩散方程中未知源的小波软阈值法","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":"{\"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}","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}
Wavelet soft-threshold method for determining an unknown source in a diffusion equation
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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