By Kirkwood J.R.
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In this paper we present a general approach to derive inversion algorithms for tomographic applications, the so-called approximate inverse. Three different techniques for calculating a reconstruction kernel are shown and applied to invert the Radon transform, to compute approximations in the limited angle problem and to solve the 3D cone beam reconstruction problem. Reconstructions from real data in this case are presented. 1. Introduction In this paper we present some principles in designing inversion algorithms in tomography.
Rieder, Incomplete data problems in X-ray computerized tomography, ILTruncated projections and region-of-interest tomography. Numer. math. 56 (1989), 3 7 1 383. K. Louis, T. Schuster, A novel filter design technique in 2D computerized tomography. Inverse Problems 12 (1996) 685-696. [Maa87] P. Maass, The X-ray transform: singular value decomposition and resolution. Inverse Problems 3 (1987), 729-741. B. N. C. Lauterbur, On Two Approaches to 3D Reconstruction in NMR Zeugmatography in Herman, G. T.
In the case of exact inversion formula e 7 is the delta distribution, in the case of the approximate inversion formula it is an approximation of this distribution, see the method of approximate inverse. 5) ^ = -^TiMr>aTiD