Optical tomography on graphs. (5th April 2017)

• Record Type: Journal Article
• Authors: Chung, Francis J; Gilbert, Anna C; Hoskins, Jeremy G; Schotland, John C
• Is Part Of: Inverse problems. Volume 33:Number 5(2017:May)
• Publication Date: 2017-04-05
• Subjects: optical tomograpy -- spectral graph theory -- inverse Born series; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/aa66d1
• Languages: English
• ISSNs: 0266-5611

Abstract

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.