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This work develops new numerical methods for the solution of the tomographyproblem in domains with reflecting obstacles. We compare the solution'sperformance for Lambertian reflection, for classical tomography with ubrokenrays and for specular reflection. Our numerical method using Lambertianreflection improves the solution's accuracy by an order of magnitude comparedto classical tomography with ubroken rays and for tomography in the presence ofa specularly reflecting obstacle the numerical method improves the solution'saccuracy approximately by a factor of three times. We present efficient newalgorithms for the solution's software implementation and analyze thesolution's performance and effectiveness.

Mathematical Modeling and Solution of the Tomography Problem in Domains with Reflecting Obstacles