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Quantitative inverse scattering via reduced order modeling

Banff International Research Station for Mathematical Innovation and Discovery

I will discuss an inverse problem for the wave equation, where a collection (array) of sensors probes an unknown heterogeneous medium with waves and measures the echoes.The goal is to determine scattering structures in the medium modeled by a reflectivity function. Much of the existing imaging methodology is based on a linear least squares data fit approach. However, the mapping between the reflectivity and the wave measured at the array is nonlinear and the resulting images have artifacts. I will show how to use a reduced order model (ROM) approach to solve the inverse scattering problem. The ROM is data driven i.e., it is constructed from the data, with no knowledge of the medium. It approximates the wave propagator, which is the operator that maps the wave from one time step to the next. I will show how to use the ROM to: (1) Remove the multiple scattering (nonlinear) effects from the data, which can then be used with any linearized inversion algorithm. (2) Obtain a well conditioned quantitative inversion algorithm for estimating the reflectivity.

Mathematics; Partial differential equations; Calculus of variations and optimal control; optimization; Women and early careers in math

video/mp4

Author affiliation: University of Michigan

2019-12-08

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/72594

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/