A method of multiple-shot scatter correction in transmission tomography systems is considered. It is assumed that the scattering is confined within a cone of relatively small angles, and the propagation is governed by a standard parabolic wave equation. An approximate directed-wave propagator may then be obtained, which relates a set of diffraction patterns measured for a multitude of point sources, to a linogram of the object. Introducing a specially designed coordinate transformation, we rewrite this propagator in a separable form as a paired Fresnel transform. Further, a corresponding inverse operator is applied to extract emulated projections (constituting jointly a sinogram) of the object from the measured data. Apart from the original algorithm, which suffers essentially from truncation errors, its improved, considerably more robust version is also constructed. The estimated sinograms may be inverted by any of the existing methods including a filtered back-projection or algebraic reconstruction techniques. The results of simulations show an essential reduction of diffraction/scattering artifacts and improved resolution of reconstructed images. At the same time it is found that scatter correction may cause object-dependent ring artifacts observed in the tomograms.
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