In this talk, we introduce a new sampling method for shape and location reconstruction in inverse acoustic scattering problems by using far field measurements. The key ingredient of this method is a novel indicator function. Only inner products are involved in the computation, which makes the method very easy and simple to implement. With the help of the factorization of the far field operator, we establish an inf-criterion for characterization of underlying scatters. This result is then used to give a lower bound of the proposed indicator function for sampling points inside the scatters. While for the sampling points outside the scatters, we show that the indicator function decays as the sampling point goes away from the boundary of the scatters. We also show that the proposed method is extremely stable with respect to errors in the data. Some numerical experiments are presented to demonstrate the feasibility and effectiveness of our method.

Dr. Xiaodong Liu received his PhD degree in applied mathematics from Graduate University of Chinese Academy of Sciences in 2010. He was a Humboldt Research Fellow in Karlsruhe Institute of Technology, Germany, from 2011 to 2013. In 2012, he joined Academy of Mathematics and Systems Science (AMSS), Chinese Academy of Sciences, Beijing, as a Assistant Professor, where he was promoted to Associate Professor in Applied Mathematics in 2015. His current research focus on the uniqueness and numerical methods in inverse scattering problems. In 2014, He was selected as a Chen Jingrun star of the future by the AMSS. In 2015, He was a co-recipient of the Inspur Youth Academic Award during International conference on inverse problems, imaging, and applications.