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三元名家论坛:The study of bioluminescence tomography based on several approximations of the radiative transport equation
作者:     供图:     供图:     日期:2022-11-17     来源:    

讲座主题:The study of bioluminescence tomography based on several approximations of the radiative transport equation

专家姓名:龚荣芳

工作单位:南京航空航天大学数学学院

讲座时间:2022年11月22日 14:00-15:00

讲座地点:腾讯会议:206-776-299

主办单位:tyc1286太阳集团数学与信息科学学院

内容摘要:

In this talk, an inverse source problem arising from bioluminescence tomography (BLT) is considered. BLT is a kind of light imaging and has many advantages in such as sensitivity, cost-effectiveness, high signal-to noise ratios and non-destructivity etc., and thus has a promising prospect in many applications such as cancer diagnosis, drug discovery and development as well as gene therapies and so on. In the literature, BLT is extensively studied based on (stationary) diffusion approximation (DA) equation, where the distribution of peak sources is to reconstruct and no solution uniqueness is guaranteed without proper a priori information. In this work, motivated by solution uniqueness, a new dynamic coupled DA model is proposed. Theoretical analysis including the well-posedness of the forward problem and the solution uniqueness of the inverse problem are given. Based on the new model, the Tikhonov regularization framework is established followed by finite element discretization. Several numerical examples are implemented to validate the effectiveness of the new model and the proposed algorithm.

主讲人介绍:

龚荣芳,南京航空航天大学数学学院,教授、博士生导师,计算科学系主任。2009年博士毕业于浙江大学,随后进入南京航空航天大学数学系工作,期间先后在美国Iowa大学、瑞典Orebro大学、澳大利亚国立大学进行学术访问。龚荣芳博士的研究方向主要包括光学成像、色谱成像、Cauchy问题等应用反问题的建模、正则化理论与方法,已在《Numerische Mathematik》、《Inverse Problems》、《Computational Methods in Applied Mechanics and Engineering》等发表学术论文近30篇。主持完成国家自然科学基金青年项目、江苏省自然科学基金等7项。目前主持国家自然科学基金面上项目1项,参与国家面上项目1项、“LJ”专项1项。