Geodesic
Discretization of a new method for localizing discontinuity lines of a noisy two-variable function
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 22 (2016) no. 2, pp. 8-17

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We consider the ill-posed problem of localizing (finding the position of) lines of discontinuity of a noisy function of two variables. New regularizing methods of localization are constructed in a discrete form. In these methods, the averaging kernel is varying, which simplifies the implementation of the algorithms. We obtain estimates for the localization error of the methods and for their separability threshold, which is another important characteristic.
Keywords: ill-posed problem, localization of singularities, line of discontinuity, regularization, discretization. 
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     author = {A. L. Ageev and T. V. Antonova},
     title = {Discretization of a new method for localizing discontinuity lines of a noisy two-variable function},
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     url = {http://geodesic.mathdoc.fr/item/TIMM_2016_22_2_a1/}
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A. L. Ageev; T. V. Antonova. Discretization of a new method for localizing discontinuity lines of a noisy two-variable function. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 22 (2016) no. 2, pp. 8-17. http://geodesic.mathdoc.fr/item/TIMM_2016_22_2_a1/