**Abstract: **Imaging problems with electromagnetic waves and fields are of great interest due to non-intrusive inspection enabled by such imaging methods. In this talk, two major imaging methods in two different frequency bands will mainly be discussed, eddy current imaging at low frequency and microwave imaging at resonant frequency regime. As these two types of problems are nonlinear and unstable, from mathematical perspectives, one will show, in each, how these difficulties are specifically handled.

In the first part, the physical mechanism of eddy current inspection will be discussed, followed by a full description of an inspection system. An imaging method that could work with the measured eddy current signals will then be proposed. It includes a forward model for eddy current interactions with defects, an experimental signal calibration model, a defect model for inversion, and an optimization scheme. It will be shown how these bricks work together to provide imaging results from phaseless eddy current signals.

In the second part, the highly nonlinear inverse scattering problems (ISPs) will be shown how to be efficiently tackled by the recently proposed contraction integral equation for inversion (CIE-I), in both three-dimensional (3-D) problems and 2-D problems with phaseless data. With the CIE-I, the non-linearity of ISPs is largely remedied by suppressing multiple scattering effects within the inversions, without compromising the physical model accuracy. This is very important when handling the computationally costly 3-D ISPs, since each iteration of inversion might cost many computational resources. Compared to conventional imaging methods with the well-known Lippmann-Schwinger integral equation (LSIE), this new imaging method with CIE-I shows much better performance when tackling both 3-D ISPs and 2-D ones with phaseless data, w.r.t. resolvability against non-linearity and convergence speed.

**Biography: **Yu Zhong received the B.E. and M.E. degrees in electronic engineering from Zhejiang University, Hangzhou, China, in 2003 and 2006, respectively, and the Ph.D. degree in electrical and computer engineering from the National University of Singapore, Singapore, in 2010. He was a Research Engineer and a Fellow with the National University of Singapore, from 2009 to 2013, then involved in a French-Singaporean MERLION Cooperative Program. Since 2014, he has been a Scientist with the Institute of High Performance Computing (IHPC), Agency for Science, Technology and Research, Singapore. He has been regularly invited to the Laboratoire des Signaux et Systèmes (L2S), Gif-sur-Yvette, France, as Senior Scientific Expert once per year since 2012. He was invited as a Visiting Professor to University of Trento, Italy, in June 2018. His current research interests include numerical methods for inverse problems associated with waves and fields, electromagnetic and acoustic modeling with complex materials, and non-destructive testing.