Abstract
The inverse source problem for the radiative transfer equation is considered, with partial data. Here we demonstrate numerical computation of the normal operator $X_{V}^{*}X_{V}$, where $X_{V}$ is the partial data solution operator to the radiative transfer equation. The numerical scheme is based in part on a forward solver designed by Monard and Bal [J. Comput. Phys., 229 (2010), pp. 4952--4979]. We will see that one can detect quite well the visible singularities of an internal optical source $f$ for generic anisotropic $k$ and $\sigma$, with or without noise added to the accessible data $X_{V}f$. In particular, we use a truncated Neumann series to estimate $X_{V}$ and $X_{V}^{*}$, which provides a good approximation of $X_{V}^{*}X_{V}$ with an error of higher Sobolev regularity. This paper provides a visual demonstration of the author's previous work [M. Hubenthal, Inverse Problems, 27 (2011), 125009] in recovering the microlocally visible singularities of an unknown source from partial data. We also g...
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