an:01422891
Zbl 0939.92021
Katsevich, Alexander
On quasi-local inversion of spiral CT data
EN
Math. Methods Appl. Sci. 23, No. 3, 271-297 (2000).
0170-4214 1099-1476
2000
j
92C55 65R10 44A12
pseudo-differential operator
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.
Paninjukunnath Achuthan (Madras)