Geodesic
On the localization of fractal discontinuity lines from noisy data
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 9 (2023), pp. 27-44

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We consider the ill-posed problem of localizing (finding the position of) the discontinuity lines of a function of two variables: the function is smooth outside the discontinuity lines, and at each point on the line it has a discontinuity of the first kind. We construct averaging procedures and study global discrete regularizing algorithms for approximating discontinuity lines. Lipschitz conditions are imposed on the discontinuity lines. A parametric family of fractal lines is constructed, for which all conditions can be checked analytically. A fractal is indicated that has a large fractal dimension, for which the efficiency of the constructed methods can be guaranteed.
Keywords: ill-posed problems, regularization method, discontinuity lines, global localization, discretization, Lipschitz condition.
Mots-clés : fractal 
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     author = {A. L. Ageev and T. V. Antonova},
     title = {On the localization of fractal discontinuity lines from noisy data},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {27--44},
     publisher = {mathdoc},
     number = {9},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2023_9_a2/}
}
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A. L. Ageev; T. V. Antonova. On the localization of fractal discontinuity lines from noisy data. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 9 (2023), pp. 27-44. http://geodesic.mathdoc.fr/item/IVM_2023_9_a2/