New method of image reconstruction from projections

The paired transform-based method for solving the continuous model of image reconstruction by projections is described. The method is based on the tensor and paired forms of representation of the two-dimension (2-D) image with respect to the discrete Fourier transform (DFT). Basis functions of the paired transformation are defined completely by parallel projections. The paired representation yields an algorithm of image reconstruction by minimum number of attenuation measurements in certain projections. The inverse formula for image reconstruction in continuous model is derived. The minimum number of directions along which the projection data are needed for image reconstruction is given.