報告人：Uwe Kaehler教授(阿威羅大學(xué))
題目：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
時間：14:00-16:00 (北京時間)
騰訊會議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教授簡介：葡萄牙Aveiro大學(xué)數(shù)學(xué)系教授。1998/09于德國Chemnitz University of Technology數(shù)學(xué)系獲得博士學(xué)位；2006/01于葡萄牙Aveiro大學(xué)數(shù)學(xué)系獲得Habilitation高級學(xué)術(shù)資格(歐洲國家第二階段博士),。研究領(lǐng)域為：Clifford分析及應(yīng)用,、PDE,、算子理論,、逼近論、離散函數(shù)論,、調(diào)和分析,。擔(dān)任六個國際雜志編委(Complex Anal. and Operator Th., Applied Math. and Comp., Central European J. of Math., Open Math., Advances in Applied Clifford Algebras, IJWMIP),共發(fā)表論文102篇,。 現(xiàn)任ISSAC主席。  

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