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Efficient implementation of ‘Optimal’ algorithms in computerized tomography
Author(s) -
Natterer F.,
Hadeler K. P.
Publication year - 1980
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670020415
Subject(s) - mathematics , algorithm , tikhonov regularization , convolution (computer science) , tomography , block (permutation group theory) , invariant (physics) , bayes' theorem , mathematical optimization , geometry , mathematical analysis , bayesian probability , computer science , inverse problem , artificial intelligence , statistics , physics , artificial neural network , optics , mathematical physics
We describe three optimal algorithms for the reconstruction of a function in R 2 from a finite number of line or strip integrals: Optimal recovery, Bayes estimate, Tikhonov‐Phillips method. In the case of a rotationally invariant scanning geometry we show that the resulting linear system is a block‐cyclic convolution. This observation leads to algorithms which are roughly as efficient as filtered backprojection which is one of the standard methods. The algorithms can be applied to the case of hollow and truncated projections. Numerical examples are given.