Tomographic Image Reconstruction Based on Generalized Projections

The method of tomographic reconstruction of inhomogeneities in 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 backprojection results for different orientation diagrams. An iterative procedure for constructing sequential approximations to the desired solution is proposed.