Strategies of reconstruction algorithms for computerized tomography

The purpose of this survey is to present the general mathematical frame and the fundamental assumptions of various strategies; Fourier methods approximate an explicit deterministic inversion formula for the Radon transform. Algebraic reconstruction techniques set up an a priori discrete model through a series expansion approach to the solution. The numerical system to be solved is huge when a fine grid of pixels is to be reconstructed; iterative solutions may then be found. Recently some least square procedures have been shown to be tractable which avoid the use of iterative methods. Finally the maximum likelihood approach incorporates accurately the Poisson nature of photon noise and is well adapted to emission computed tomography. (Auth.)