UDC 519.6
1 Karpenko Physico-Mechanical Institute, National Academy of Sciences of Ukraine, Lviv, Ukraine
 lozynskyy.a@gmail.com
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2 Karpenko Physico-Mechanical Institute, National Academy of Sciences of Ukraine, Lviv, Ukraine
romanyshyn@ipm.lviv.ua
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3 Karpenko Physico-Mechanical Institute, National Academy of Sciences of Ukraine, Lviv, Ukraine
rusyn@ipm.lviv.ua
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TOMOGRAPHIC RESTORATION OF IMAGES BASED ON GENERALIZED PROJECTIONS
Abstract. The method of tomographic reconstruction of inhomogeneities in the case of an arbitrary directional diagram
and scanning along one coordinate is described. It is shown that in this case registered data (projections) are represented
as the sum of the line-by-line convolutions of the lines of the directional diagram and the corresponding line of the reconstructed distribution.
The features of projection data, backprojections are analyzed. It is proposed to construct a cumulative image as an additive
or conjunctive combination of the back projection results for different orientation diagrams.
An iterative procedure for constructing sequential approximations to the desired solution is proposed.
Keywords: tomographic restoration, spatial distribution, directional diagram, convolution, backprojection, total image.
FULL TEXT
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