时间分数阶方程正反问题系列报告（九）：GFTG prior and Optimal transport for Bayesian inverse problems

发布时间：2023-09-15 作者：浏览次数：

Speaker:	郑光辉	DateTime:	2023年9月24日（周日）上午10：50-11：35
Brief Introduction to Speaker: 郑光辉，湖南大学数学学院，副教授，硕士生导师。2012年博士毕业于兰州大学数学与统计学院，2015年3月--2016年3月访问巴黎高师数学系。主要从事偏微分方程反问题的理论及算法、贝叶斯统计反演与推断、等离子共振及超分辨成像等方面的研究。相关研究成果发表在《Inverse Problems》、《SIAM Journal on Numerical Analysis》、《 J. Differential Equations》、《Advances in Computational Mathematics》等多个SCI杂志上。主持国家自然科学青年基金1项和湖南省面上项目1项。		Place:	6号楼2楼报告厅
Abstract:The Bayesian inference is widely used in many scientific an engineering problems, especially in the inverse problems in infinite dimensional setting where the unknowns are functions.In this talk, we discuss the imaging inverse problem by employing an infinite dimensional Bayesian inference method with a general fractional total variation-Gaussian (GFTG) prior andoptimal transport technology. This novel hybrid prior is a development for the total variation-Gaussian (TG) prior, which is a combination of the Gaussian prior and a general fractional total variation regularization term, which contains a wide class of fractional derivative. Compared to the TG prior,the GFTG prior can effectively reduce the staircase effect, enhance the texture details of the images and also provide a complete theoretical analysis in the infinite dimensional limit similarly to TG prior. We give the well-posedness and infinite-dimensional approximation of the posterior measure of the Bayesian inverse problem...

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