講座主題：The study of bioluminescence tomography based on several approximations of the radiative transport equation
專家姓名：龔榮芳
工作單位：南京航空航天大學數學學院
講座時間：2022年11月22日 14:00-15:00
講座地點：騰訊會議：206-776-299
主辦單位：煙臺大學數學與信息科學學院
內容摘要：
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.
主講人介紹：
龔榮芳，南京航空航天大學數學學院，教授、博士生導師，計算科學系主任。2009年博士畢業于浙江大學，隨后進入南京航空航天大學數學系工作，期間先后在美國Iowa大學、瑞典Orebro大學、澳大利亞國立大學進行學術訪問。龔榮芳博士的研究方向主要包括光學成像、色譜成像、Cauchy問題等應用反問題的建模、正則化理論與方法，已在《Numerische Mathematik》、《Inverse Problems》、《Computational Methods in Applied Mechanics and Engineering》等發表學術論文近30篇。主持完成國家自然科學基金青年項目、江蘇省自然科學基金等7項。目前主持國家自然科學基金面上項目1項，參與國家面上項目1項、“LJ”專項1項。
