Approximate stability estimates in inverse transport theory

The theory of inverse transport consists of reconstructing optical properties of a domain of interest from measurements performed at the boundary of the domain. Using the decomposition of the measurement operator into singular components (ballistic part, single scattering part, multiple scattering part), several stability estimates have been obtained that show what may stably be reconstructed from available measurements. Such stability estimates typically assume that the measurements are in the range of the functional mapping the optical parameters to the measurement operator. In practice, available measurements are rarely in the latter range, which renders the stability estimates of lesser interest. In this paper, we generalize the derivation of the stability estimates to account for general physical noise models. The resulting approximate stability estimates provide a quantitative description of the type of information that may be obtained on the optical parameters.