Synthesized algorithm of three-dimensional tomography

New algorithm of few view three-dimensional tomography combined of both the algorithms based on the exact inversion formulae and the Fourier methods is proposed. Two modifications FBPFS3D and FBP0FS3D are considered. The numerical simulation has been carried out. Both modifications can compete with the iterative algebraic algorithms when the projection number is 10–30 and FBPFS3D is preferable for large projection number. In the numerical simulation the projection number grows up to 361, FBPFS3D appear to have considerable advantage in the reconstruction accuracy over the algorithm FBP3D constructed from the exact inversion formula for P-transform. The reconstructionfrom the distorted projections shows the resistance to the accidental noise for both modifications. It can be improved by the regularization methods.