Stability estimates in stationary inverse transport

Details Stability estimates in stationary inverse transport Stability estimates in stationary inverse transport

2008-04-08

arxiv.org/abs/0804.1320v1

Inverse Problems and Imaging 2, 4 (2008) 427-454

Physics

Mathematical Physics

Scientific paper

We study the stability of the reconstruction of the scattering and absorption coefficients in a stationary linear transport equation from knowledge of the full albedo operator in dimension $n\geq3$. The albedo operator is defined as the mapping from the incoming boundary conditions to the outgoing transport solution at the boundary of a compact and convex domain. The uniqueness of the reconstruction was proved in [M. Choulli-P. Stefanov, 1996 and 1999] and partial stability estimates were obtained in [J.-N. Wang, 1999] for spatially independent scattering coefficients. We generalize these results and prove an $L^1$-stability estimate for spatially dependent scattering coefficients.

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