Abstract
We consider the modeling of an integral geometry problem on a family of broken lines with a given weight function. One of the main problems in solving the problem of integral geometry is to construct an analytical formula that is expressed in terms of given integral data. In the general case, this process requires the creation of special computational algorithms based on the general theory of ill-posed problems. In this regard, it is advisable to use the regularization method to build stable algorithms for solving the problem.
In this paper, we obtained an analytic representation of the solution of the considered problem of integral geometry in the class of smooth finite functions. Considering when noisy integral data are always present during measurements, a stable algorithm is constructed based on the idea of Tikhonov’s regularization for the numerical solution of the problem of integral geometry on a family of broken lines. The conducted numerical experiment shows that the developed algorithm effectively restores the image of the internal structure of the studied objects with sufficient accuracy.
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Uteuliev, N.U., Djaykov, G.M., Pirimbetov, A.O. (2023). Modeling the Problem of Integral Geometry on the Family of Broken Lines Based on Tikhonov Regularization. In: Zaynidinov, H., Singh, M., Tiwary, U.S., Singh, D. (eds) Intelligent Human Computer Interaction. IHCI 2022. Lecture Notes in Computer Science, vol 13741. Springer, Cham. https://doi.org/10.1007/978-3-031-27199-1_41
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