龚荣芳 教授 (17 Jul. 2022, 14:00-17:00).pdf

应用数学讲座 Научный Семинар по Прикладной Математике Research Seminar on Applied Mathematics 应用数学报告（44） 报告人 / Докладчик / Speaker: 龚荣芳 教授 题目 / Название / Title: Study of bioluminescence tomography based on a new time-dependent coupled diffusion equation 时间 / Время / Time：17 Jul. 2022, 14:00-17:00 地点 / Место / Venue: 主楼 336 摘要 / Аннотация / Abstract: In this talk, we consider inverse source problems arising in bioluminescence tomography (BLT). Mathematically, BLT is an under-determined inverse source problem which leads to no solution uniqueness. Particularly, one cannot distinguish between a strong source over a small region and a weak source over a large region. Therefore, it is particularly important to know the support $\Omega_s$ of the underlining light source $p_*$ so that its strength could be reconstructed accurately. In the literature, $\Omega_s$ is assumed to be given. Practically, we only get an approximation $\Omega_a$ of it, known from some a priori information. The accuracy of $\Omega_a$ affects largely the one in approximate solutions of $p_*$. Therefore, in this talk, a new time-dependent coupled model is proposed motivated by the solution uniqueness. Some theoretical and numerical results are reported for the verification of the new model and methods. 龚荣芳教授简介： 龚荣芳教授，南京航空航天大学理学院，教授，博士生导师。研究方向为医学成像、 图像处理、参数识别和最优控制等数学物理反问题的正则化理论与数值方法。先后主 持完成国家自然科学基金、国家博士后基金、江苏省自然科学基金等 7 项，当前主持 国 家 自 然科 学 基金 面上 项 目 1 项 ， 参与 国 家 自 然科 学 基金 面上 项 目 1 项 。 在 Numerische Mathematik 、 Inverse Problems 、 Inverse problems and Imaging 、 Communications in Computational Physics 等期刊上发表 SCI 论文近 30 篇。 访问学者以及需要做报告的学者请联系 张晔 教授 / Всем желающим выступить с докладами на семинаре просьба обращаться к Чжану Е ye.zhang@smbu.edu.cn