New methods in computer tomography

Two new methods of block-cycling inversion so as classical one (block-toeplitz inversion) for Radon problem in computer tomography with rotating invariant scheme of scanning are presented. Blockcycling form of the Radon operator allows to apply it's direct block-cycling inversion generalizing the implicit formula of an inverse circulant (in the I method) and block-Greville method (in the II one) instead of a classical block-Toeplitz inversion based on the notion of Toeplitz rang. The time complexity of the new algorithms 6N times better by perfomance at the stage of preliminary inversion, so as on the flow taking into account the parallel processing and 4 times better by memory volume required but their main advantage- the simplicity of implementation. The new algorithms were numerically simulated with the space resolution up to $101\times 101$ with maximum – 15 min. for one variant of the model at the PC PENTIUM-166-32 (Fortran Powerstation). An important problem of Radon operator's almost singularity was discovered which is masked by compactness of the Radon operator so as averaging of cycling diagonal elements.