数信系列讲座(四):Inversion of the spherical Radon transform by means of Gabor and Wavelet frames with applications in diffraction tomography

来源单位及审核人:编辑:审核发布:数学与信息学院 发布时间:2023-04-06浏览次数:137

报告人:Uwe Kaehler教授(阿威罗大学)
题目:Inversion of the spherical Radon transform by means of Gabor and Wavelet frames with applications in diffraction tomography
日期:2023年4月28日
时间:14:00-16:00 (北京时间)
腾讯会议ID:293-205-499,Pin:1234
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https://meeting.tencent.com/dm/wsgxTtq9CDgY
摘要:There is a wide range of applications for function systems on the three-sphere , among them X-Ray diffraction tomography whose mathematical model is given by the spherical X-ray transform. Here, one needs to reconstruct the so-called orientation density function which is well-localized funcctionon the three-sphere . To approximate such a function we discuss the construction of Wavelet and Gabor frames on the three-sphere. In both cases we use the representation of the corresponding group (Lorentz group in the case of the wavelet transform and Euclidean group in the case of the Gabor transform). While this provides us with the continuous transforms in reality we need a discrete version. To this end we will use co-orbit space theory to construct wavelet and Gabor frames. Here we will show the difference in the construction of both cases. To illustrate the applicability of our frames we present an algorithm for the inversion of the spherical X-Ray transform .   

Uwe Kaehler教授简介:葡萄牙Aveiro大学数学系教授。1998/09于德国Chemnitz University of Technology数学系获得博士学位;2006/01于葡萄牙Aveiro大学数学系获得Habilitation高级学术资格(欧洲国家第二阶段博士)。研究领域为:Clifford分析及应用、PDE、算子理论、逼近论、离散函数论、调和分析。担任六个国际杂志编委(Complex Anal. and Operator Th., Applied Math. and Comp., Central European J. of Math., Open Math., Advances in Applied Clifford Algebras, IJWMIP),共发表论文102篇。 现任ISSAC主席。  

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