Optical tomography on graphs

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.

References in corpus (3)

• Convergence and Stability of the Inverse Scattering Series for Diffuse Waves
• On the Convergence of the Born Series in Optical Tomography with Diffuse Light
• Restarted inverse Born series for the Schrödinger problem with discrete internal measurements

Cited by in corpus (2)

• Stable recovery of piecewise constant conductance on spider networks
• Norm-dependent convergence and stability of the inverse scattering series for diffuse and scalar waves