Tomography problems for media with low refraction.

The tomogram deformation method, previously proposed by the author for fan-beam tomography problems, has been extended here to a number of simple curved rays that allow one-to-one transitions to parallel straight lines. The transition from straight lines to curvilinear lines expands the range of possible statements of problems of tomographic diagnostics of objects, in particular, for cases of weak refraction in the medium under study, when it is possible to analytically describe the equation of the ray path in a first approximation. The software implementation of the algorithm is performed using the example of a family of trajectories described by a sinusoid with a controlled period and amplitude. A numerical simulation on a number of mathematical models showed the possibility of geometric implementation of the Generalized Radon Transform inversion based on the direct and inverse tomogram deformation procedures. In the two- dimensional statement of the problem, it is shown that artifacts of fan-beam and wave few-view tomography largely repeat the form of the trajectories themselves: for fan-beam tomography, the image of artifacts is close to weak hyperbolic disturbances, for wave tomography, characteristic wave structures appear in the polar coordinate system - in radius and in angle. These artifacts arise at the stage of backprojection, during the transition from rectilinear projections to projections along the initial trajectories, with the inverse deformation being carried out. [ABSTRACT FROM AUTHOR]