学术报告

题      目：Hybrid Projection Methods for Solution Decomposition in Large-scale Bayesian Inverse Problems

报  告  人：姜嘉骅  助理教授  (邀请人：钟柳强 )

                                    英国伯明翰大学

时      间：9月4日  11：00-12：00

地     点：数科院东楼401

报告人简介:

        姜嘉骅，英国伯明翰大学助理教授，主要从事模型降阶，不确定性量化，反问题在图像处理上的应用等方面的研究。在医疗成像方面，姜博士提出的混合投影成像技术和基于深度学习的直接采样法在荧光成像，扩散光层析成像，CT，核磁共振成像上有重要应用。姜博士获中国科学技术大学学士学位，麻省大学达特茅斯分校博士学位，之后赴弗吉尼亚理工大学展开博士后研究。中国国家青年基金和上海市扬帆计划获得者。在SISC，JSC，Inverse problems 等多个应用数学和工程领域的核心期刊上发表论文，同时还担任JSC，JCP，Inverse problems等多个国际重要学术期刊的审稿人。

摘      要：

       We develop hybrid projection methods for computing solutions to large-scale inverse problems, where the solution represents a sum of different stochastic components. Such scenarios arise in many imaging applications (e.g., anomaly detection in atmospheric emissions tomography) where the reconstructed solution can be represented as a combination of two or more components and each component contains different smoothness or stochastic properties. In a deterministic inversion or inverse modeling framework, these assumptions correspond to different regularization terms for each solution in the sum. Although various prior assumptions can be included in our framework, we focus on the scenario where the solution is a sum of a sparse solution and a smooth solution. For computing solution estimates, we develop hybrid projection methods for solution decomposition that are based on a combined flexible and generalized Golub-Kahan processes. This approach integrates techniques from the generalized Golub-Kahan bidiagonalization and the flexible Krylov methods. The benefits of the proposed methods are that the decomposition of the solution can be done iteratively, and the regularization terms and regularization parameters are adaptively chosen at each iteration. Numerical results from photoacoustic tomography and atmospheric inverse modeling demonstrate the potential for these methods to be used for anomaly detection.