N. Temirgaliyev, Sh. K. Abikenova, Sh. U. Azhgaliev, Y. Y. Nurmoldin, G. E. Taugynbayeva, A. Zhubanysheva
{"title":"计算（数值）直径方案中计算断层扫描问题与有限卷积恢复函数问题的等价性","authors":"N. Temirgaliyev, Sh. K. Abikenova, Sh. U. Azhgaliev, Y. Y. Nurmoldin, G. E. Taugynbayeva, A. Zhubanysheva","doi":"10.26907/0021-3446-2023-12-95-102","DOIUrl":null,"url":null,"abstract":"The equivalence of the norms of deviations of the desired density of a body from operators such as finite density transformation with specially constructed elements and the Radon transformation from it is stated. It is shown how Computer Science, previously established in the theory of Computational (Numerical) diameter, immediately leads to non-trivial results in Computed Tomography.","PeriodicalId":507800,"journal":{"name":"Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika","volume":"323 3","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2023-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Equivalence of computed tomography problem with the problem of recovery of functions by finite convolutions in a scheme of computational (numerical) diameter\",\"authors\":\"N. Temirgaliyev, Sh. K. Abikenova, Sh. U. Azhgaliev, Y. Y. Nurmoldin, G. E. Taugynbayeva, A. Zhubanysheva\",\"doi\":\"10.26907/0021-3446-2023-12-95-102\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The equivalence of the norms of deviations of the desired density of a body from operators such as finite density transformation with specially constructed elements and the Radon transformation from it is stated. It is shown how Computer Science, previously established in the theory of Computational (Numerical) diameter, immediately leads to non-trivial results in Computed Tomography.\",\"PeriodicalId\":507800,\"journal\":{\"name\":\"Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika\",\"volume\":\"323 3\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-12-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.26907/0021-3446-2023-12-95-102\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.26907/0021-3446-2023-12-95-102","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Equivalence of computed tomography problem with the problem of recovery of functions by finite convolutions in a scheme of computational (numerical) diameter
The equivalence of the norms of deviations of the desired density of a body from operators such as finite density transformation with specially constructed elements and the Radon transformation from it is stated. It is shown how Computer Science, previously established in the theory of Computational (Numerical) diameter, immediately leads to non-trivial results in Computed Tomography.
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