This talk is concerned with the inverse scattering for a random source/potential, where the source/potential is assumed to be microlocally isotropic generalized Gaussian random field such that its covariance operator is a classical pseudo-differential operator. For such a distributional source/potential, we show that the direct scattering problem admits a unique solution in the sense of distribution. For the inverse scattering problem, we demonstrate that the principle symbol of the covariance operator can be uniquely determined with probability one by the high frequency limit of the averaged near-field or far-field data obtained form a single path of the random source/potential.

李建樑，2009年6月本科毕业于中国农业大学理学院，2014年7月获中国科学院大学理学博士学位。2017年11月－2018年11月受国家留学基金委资助赴美国普渡大学数学系访问一年。主要研究领域为反散射问题的理论与数值方法、随机反散射问题的理论研究。主持国家自然科学面上项目1项，青年项目1项，湖南省教育厅优秀青年项目1项，一般项目1项。在《Inverse Problems in Science and Engineering》、《Applicable Analysis》、《Computers and Mathematics with applications》、《SIAM Journal on Imaging Sciences》、《SIAM Journal on Mathematical Analysis》、《Communications in Partial Differential Equations》、《Inverse Problems and Imaging》发表论文9篇。