A novel filter design technique in 2D computerized tomography

The approximate inverse is a method to precompute inversion operators for linear and some special nonlinear problems. In this paper this technique is applied to derive inversion formulae for the parallel geometry in x-ray computerized tomography. The structure of reconstruction formulae is given, and for the case of a finite number of data convolution filters are computed leading to methods of filtered backprojection type. The technique can be extended to treat other scanning geometries. The main advantage is the possibility to precompute the reconstruction kernel independently of the data so that a fast reconstruction is possible.