Speaker: Peijun Li (Purdue University)

Abstract: The inverse source problem, as an important research subject in the inverse scattering theory, has significant applications in diverse scientific and industrial areas such as antenna design and synthesis, medical imaging, and optical tomography. The inverse random source problem refers to the inverse source problem that involves uncertainties, which is substantially more challenging due to the additional difficulties of randomness and uncertainties. In this talk, our recent progress on inverse random source problems for the stochastic wave equations will be introduced. The random source under consideration is assumed to be a microlocally isotropic Gaussian random field such that its covariance operator is a classical pseudo-differential operator. Given the random source, the direct problem is to determine the wavefield; the inverse problem is to recover the unknown source that generates the prescribed radiated wave field. The well-posedness and regularity of the solution will be addressed for the direct problem. For the inverse problem, it is shown that the principal symbol of the covariance operator of the random source can be uniquely determined by the high frequency limit of the wavefield at a single realization. I will also highlight ongoing projects in potential and medium problems for stochastic wave equations.