English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

We consider the inverse problem of reconstructing the scattering andabsorption coefficients using boundary measurements for a time dependentradiative transfer equation (RTE). As the measurement is mostly polluted byerrors, both experimental and computational, an important question is toquantify how the error is amplified in the process of reconstruction. In theforward setting, the solution to the RTE behaves differently in differentregimes, and the stability of the inverse problem vary accordingly. Inparticular, we consider two scalings in this paper. The first one concerns witha diffusive scaling whose macroscopic limit is a diffusion equation. In thiscase, we showed, following the similar approach as in [Chen, Li and Wang,arXiv:1703.00097], that the stability degrades when the limit is taken. Thesecond one considers a highly forward peaked scattering, wherein the scatteringoperator is approximated by a Fokker-Planck operator as a limit. In this case,we showed that a fully recover of the scattering coefficient is less possiblein the limit, whereas obtaining a rescaled version of the scatteringcoefficient becomes more practice friendly.

Stability of inverse transport equation in diffusion scaling and Fokker-Planck limit