报告人：郑光辉副教授

报告题目：A general fractional total variation-Gaussian (GFTG) prior for Bayesian inverse problems

报告摘要：

(1) The Bayesian inference is widely used in many scientific and 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. This novel hybrid prior is a development for the total variation-Gaussian (TG) prior and the non-local total variation-Gaussian (NLTG) 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.

(2) 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 based on the GFTG prior, and then the samples are extracted from the posterior distribution by using the preconditioned Crank-Nicolson (pCN) algorithm. Finally, we give several numerical examples of image reconstruction under liner and nonlinear models to illustrate the advantages of the proposed improved prior.

报告时间：2022年11月5日，上午11:00-14:00

报告形式：腾讯会议；会议号：667-278-134

获取会议密码请发邮件至：xcwang@hit.edu.cn

报告人简介：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，曾先后访问巴黎高师数学系，香港浸会大学数学系进行科研合作。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》、《J.Math.PuresAppl.》、《SIAM J. Numer. Anal.》、《J. Differential Equations》、《Adv. Comput. Math.》、《ESAIM: Math. Model. Numer. Anal.》等多个SCI杂志上。