NSF Award
2308200
This project involves the development of new methods for determining internal material parameters from external measurements, with a focus on radar applications, medical imaging, and optical design. In the new algorithms, a key innovation lies in using the data itself to generate a compact model for wave propagation, resulting in highly efficient image reconstruction. The applicability of these algorithms will be expanded to handle large and noisy data sets, complex media, and scenarios where sources and receivers are not collocated—a significant limitation in existing reduced model approaches. Furthermore, novel methodologies will be developed for the reconstruction of materials exhibiting nonlinear wave propagation characteristics. By reducing computational costs, the methods developed in this project will enable improved imaging in large-scale situations. Several students will be trained over the course of this research, and plans to promote diversity and inclusion in research are integrated into student recruitment.<br/><br/>This research will overcome challenges to image reconstruction by improving some of the most promising direct methods for inversion. This includes (i) expanding data driven reduced order model imaging methods to very general classes of data sets, models with nonlocal operators and transmission problems, while at the same time establishing a rigorous foundation, (ii) developing novel inversion methods for coefficient determination when the underlying forward model is nonlinear and (iii) imaging general linear and nonlinear anisotropy in the hybrid method Magnetoacoustic Tomography with Magnetic Induction. The novel reduced order model approaches will be developed to handle large and noisy data sets, problems in which source and receiver are not collocated, and imaging problems with dispersion. The inverse Born series will be adapted to handle inversion where the forward problem is nonlinear, and its application will rely on the description of the forward series and will involve a convergence analysis. The well-posedness of the system of transport equations for Magnetoacoustic Tomography with Magnetic Induction imaging of general anisotropy will be established using carefully defined inflow boundary conditions.<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.
