AM Seminar: Enhanced Resolution Imaging in Strongly Scattering Media
Presenter: Chrysoula Tsogka, Professor, Applied Mathematics, UC Merced
Description: In a strongly scattering medium, waves undergo multiple scattering that is usually seen as an obstacle to imaging. Time-reversal experiments show the opposite: waves re-emitted into the medium refocus on their source more sharply than in a homogeneous medium, because scattering makes the array appear larger than it is. This effect, known as super-resolution, is not available to conventional imaging. Since the medium through which the waves travelled is unknown, conventional methods back-propagate the data in an approximation of the true background. In this talk I will show how super-resolution can be achieved in imaging when abundant array data are available. The key idea is to learn the Green’s functions of the unknown random medium directly from the data using sparse dictionary learning. The Green’s functions are recovered as unordered columns of the sensing matrix. To associate each column with its location in the imaging window, we build a graph from cross-correlations of the recovered columns and apply multidimensional scaling to the resulting proxy distances. The learned Green’s functions are then used to form images by back-propagation or by $\ell_2$ and $\ell_1$ methods, with resolution beyond the homogeneous medium limit. I will also discuss recent extensions: a new dictionary learning algorithm that starts from a random initialization, imaging on unstructured grids, and imaging through changing random media. Joint work with M. Moscoso, A. Novikov, G. Papanicolaou, A. Christie, M. Leibovich and J. Zheng.
About the speaker: Chrysoula Tsogka is a Professor of Applied Mathematics at the University of California, Merced, where she also serves as Chair of the Applied Mathematics Graduate Group. She received her Ph.D. in Applied Mathematics from the University Paris IX Dauphine and was a Postdoctoral Fellow at Stanford University. Before joining UC Merced in 2019, she was a tenured CNRS researcher at LMA in Marseille, an Assistant Professor at the University of Chicago, and a Professor at the University of Crete. Her research focuses on numerical methods for direct and inverse wave propagation problems and on imaging in complex media. Her recent work includes quantitative synthetic aperture radar (SAR) imaging for the detection and classification of buried landmines, and data-driven methods, such as dictionary learning, for super-resolution imaging in strongly scattering media. She serves on the editorial boards of Inverse Problems, the Journal of Computational Physics and the Journal of Mathematical Imaging and Vision.