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Development of algorithms in computerized tomography. (English) Zbl 1100.65118
Ólafsson, Gestur (ed.) et al., The Radon transform, inverse problems, and tomography. American Mathematical Society short course, Atlanta, GA, USA, January 3–4, 2005. Providence, RI: American Mathematical Society (AMS) (ISBN 0-8218-3930-6/hbk). Proc. Symp. Appl. Math. 63, 25-42 (2006).
The author applies the method of approximate inverse for approximating the solution of the equation \(Ax = g\), where \(A\) is a compact integral operator in a Hilbert space. The method gives the reconstruction kernel of the inverse operator. This technique is applied for the inversion of the Radon transform in 2 and 3 dimensions, using the special form of the mollifier. The reconstruction algorithms in this case are of filtered backprojection type. In the case of real tomography data the reconstruction algorithm is not complete.
For the entire collection see [Zbl 1085.44001].

65R10 Numerical methods for integral transforms
65R32 Numerical methods for inverse problems for integral equations
44A12 Radon transform
92C55 Biomedical imaging and signal processing