Application of Atomic and R-functions in Numerical Methods for Inversion of the Radon Transform

Digital tomography widely applied in scientific and medical research. Quality improvement of tomographic images is an actual problem. In mathematical algorithms of digital tomography reconstruction of internal structure of the object according to projection data is implemented. The problem is reduced to inverse ill-posed problem of inversion of Radon transform. Due to the problem is ill-posed, regularization is required (for example Tikhonov regularization or iterative algorithms). In the paper ability of application atomic and R-functions in Fourier synthesis method and iterative reconstruction method is discussed. Atomic functions are solutions of functional-differential equations of special form. They are infinitely smooth and compactly supported. R-functions are used to describe geometric objects. R-function corresponding to the closed region is positive inside the region, negative outside the region and vanishes on its boundary.