{"title":"优于总变异正则化。","authors":"Gengsheng L Zeng","doi":"","DOIUrl":null,"url":null,"abstract":"<p><p>The total variation (TV) regularization is popular in iterative image reconstruction when the piecewise-constant nature of the image is encouraged. As a matter of fact, the TV regularization is not strong enough to enforce the piecewise-constant appearance. This paper suggests a different regularization function that is able to discourage some smooth transitions in the image and to encourage the piecewise-constant behavior. This new regularization function involves a Gaussian function. We use the limited-angle tomography problem to illustrate the effectiveness of this new regularization function. The limited-angle tomography situation considered in this paper uses a scanning angular range of <math><mrow><mn>40</mn></mrow> <mrow><mo>°</mo></mrow> </math> . For two-dimensional parallel-beam imaging, the required angular range is supposed to be <math><mrow><mn>180</mn></mrow> <mrow><mo>°</mo></mrow> </math> .</p>","PeriodicalId":520232,"journal":{"name":"International journal of biomedical research & practice","volume":"4 2","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11423893/pdf/","citationCount":"0","resultStr":"{\"title\":\"Better than the Total Variation Regularization.\",\"authors\":\"Gengsheng L Zeng\",\"doi\":\"\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p><p>The total variation (TV) regularization is popular in iterative image reconstruction when the piecewise-constant nature of the image is encouraged. As a matter of fact, the TV regularization is not strong enough to enforce the piecewise-constant appearance. This paper suggests a different regularization function that is able to discourage some smooth transitions in the image and to encourage the piecewise-constant behavior. This new regularization function involves a Gaussian function. We use the limited-angle tomography problem to illustrate the effectiveness of this new regularization function. The limited-angle tomography situation considered in this paper uses a scanning angular range of <math><mrow><mn>40</mn></mrow> <mrow><mo>°</mo></mrow> </math> . For two-dimensional parallel-beam imaging, the required angular range is supposed to be <math><mrow><mn>180</mn></mrow> <mrow><mo>°</mo></mrow> </math> .</p>\",\"PeriodicalId\":520232,\"journal\":{\"name\":\"International journal of biomedical research & practice\",\"volume\":\"4 2\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11423893/pdf/\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International journal of biomedical research & practice\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"2024/6/21 0:00:00\",\"PubModel\":\"Epub\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International journal of biomedical research & practice","FirstCategoryId":"1085","ListUrlMain":"","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2024/6/21 0:00:00","PubModel":"Epub","JCR":"","JCRName":"","Score":null,"Total":0}
The total variation (TV) regularization is popular in iterative image reconstruction when the piecewise-constant nature of the image is encouraged. As a matter of fact, the TV regularization is not strong enough to enforce the piecewise-constant appearance. This paper suggests a different regularization function that is able to discourage some smooth transitions in the image and to encourage the piecewise-constant behavior. This new regularization function involves a Gaussian function. We use the limited-angle tomography problem to illustrate the effectiveness of this new regularization function. The limited-angle tomography situation considered in this paper uses a scanning angular range of . For two-dimensional parallel-beam imaging, the required angular range is supposed to be .