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Inverse radiative transfer problems in two-dimensional participating media

In the present work inverse radiative transfer problems in two-dimensional heterogeneous participating media are considered. An implicit formulation is used in which the cost functional of the squared residues between calculated and measured exit radiation intensities is minimized. The Levenberg–Marquardt method, a gradient-based minimization algorithm, is used, and therefore at every iteration of the iterative procedure the solution of the direct problem is required. For the solution of the direct problem, which is modeled by the linearized Boltzmann equation, the discrete-ordinates method with a finite difference approximation for the spatial derivatives is used. The inverse problems considered are related to the estimation of the absorption and anisotropic scattering coefficients, as well as the estimation of source terms.