Stability estimates in stationary inverse transport

Guillaume Bal; Alexandre Jollivet

doi:10.3934/ipi.2008.2.427

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2008, Volume 2, Issue 4: 427-454. Doi: 10.3934/ipi.2008.2.427

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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

Received: March 31, 2008

Revised: August 31, 2008

Published: October 2008

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Abstract

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.

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Mathematics Subject Classification: 35R30, 45Q05, 82C70.

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