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.
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This work was supported in part by the National Science Foundation grants DMS- 1115574, DMS-1108969 and DMS-1619907 to JCS, and National Science Foundation grants CCF-1161233 and CIF-0910765 to ACG.
Chung, Francis J.; Gilbert, Anna C.; Hoskins, Jeremy G.; and Schotland, John C., "Optical Tomography on Graphs" (2017). Mathematics Faculty Publications. 39.