On quasi-local inversion of spiral CT data.

*(English)*Zbl 0939.92021Efficient 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.

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.

Reviewer: Paninjukunnath Achuthan (Madras)

##### MSC:

92C55 | Biomedical imaging and signal processing |

65R10 | Numerical methods for integral transforms |

44A12 | Radon transform |

##### Keywords:

pseudo-differential operator
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\textit{A. Katsevich}, Math. Methods Appl. Sci. 23, No. 3, 271--297 (2000; Zbl 0939.92021)

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##### References:

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