Optical tomography on graphs. (5th April 2017) - Chung, Francis J; Gilbert, Anna C; Hoskins, Jeremy G; Schotland, John C
Abstract: We present an algorithm for solving inverse problems on graphs analogous to those arising in diffuse optical tomography for continuous media. In particular, we formulate and analyze a discrete version of the inverse Born series, proving estimates characterizing the domain of convergence, approximation errors, and stability of our approach. We also present a modification which allows additional information on the structure of the potential to be incorporated, facilitating recovery for a broader class of problems.