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On quasi-local inversion of spiral CT data. (English) Zbl 0939.92021
Efficient mathematical methods are of immense use in applied sciences. Here is an explicit example for how one can deal with a medical imaging situation involving spiral computed tomography (CT) and the selected handling of data. The author has presented a quasi-local algorithm for computing an approximation $$f_0$$ of a well-defined function $$f$$ which retains all the sharp properties of $$f$$. An in-depth study of the algorithm is discussed together with results of numerical testing on simulated data.
After constructing the function of $$f_0$$, a proof is provided asserting that the map $$f\to f_0$$ is a pseudo-differential operator (PDO). Then stability simplification and computation of $$f_0$$ are discussed. Some refinements on the choice of components, sampling of spirals and selection of parameters of the computational scheme adopted are also described at length. A numerical experiment is performed in order to test the proposed algorithm and the emerging data have been displayed in 6 figures. There are altogether 9 sections, 113 equations, 8 theorems including one lemma and 25 references.
##### MSC:
 92C55 Biomedical imaging and signal processing 65R10 Numerical methods for integral transforms 44A12 Radon transform
##### Keywords:
pseudo-differential operator
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##### References:
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