Algorithm of reconstruction of three-dimensional images in X-ray computed tomography with a cone beam

An algorithm for reconstructing three-dimensional images for X-ray computed tomography with a cone beam of radiation is developed. The algorithm is based on an accurate analytical representation of the three-dimensional Radon transformation of the projection data. For this representation, an iteration-invariant point scattering function (FRT) is introduced. The proposed algorithm overcomes the main drawback of approximate algorithms-it provides a sufficiently high quality of the obtained images even at large angles of the radiation cone, which is manifested in a relatively small number of image artefacts. The quality of the reconstructed tomographic images was evaluated.