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November  2008, 2(4): 427-454. doi: 10.3934/ipi.2008.2.427

Stability estimates in stationary inverse transport

Guillaume Bal 1, and  Alexandre Jollivet 2,

1. 

Department of Applied Physics and Applied Mathematics, Columbia University, New York NY, 10027
2. 

Department of Applied Physics and Applied Mathematics, Columbia University, New York, NY 10027, United States

Received  April 2008 Revised  September 2008 Published  November 2008

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 [2, 3] and partial stability estimates were obtained in [12] for spatially independent scattering coefficients. We generalize these results and prove an $L^1$-stability estimate for spatially dependent scattering coefficients.
Keywords: Inverse transport problem, stability estimates, albedo operator.
Mathematics Subject Classification: 35R30, 45Q05, 82C70.
Citation: Guillaume Bal, Alexandre Jollivet. Stability estimates in stationary inverse transport. Inverse Problems and Imaging, 2008, 2 (4) : 427-454. doi: 10.3934/ipi.2008.2.427
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