New methods for localizing discontinuities of a noisy function

Antonova, T. V.

doi:10.1134/s1995423910040026

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2017

2024

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Cited by 4 publications

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“…Alternative algorithms designed for noisy data have been proposed and discussed in other papers, such as [7]. However, these methods rely on prior knowledge of the function, on finding a type of function, called an averaging function, and on regularization parameters.…”

Section: Introductionmentioning

confidence: 99%

Approximating a Function with a Jump Discontinuity—The High-Noise Case

Muzaffar,

Levin,

Werman

2024

AppliedMath

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This paper presents a novel deep-learning network designed to detect intervals of jump discontinuities in single-variable piecewise smooth functions from their noisy samples. Enhancing the accuracy of jump discontinuity estimations can be used to find a more precise overall approximation of the function, as traditional approximation methods often produce significant errors near discontinuities. Detecting intervals of discontinuities is relatively straightforward when working with exact function data, as finite differences in the data can serve as indicators of smoothness. However, these smoothness indicators become unreliable when dealing with highly noisy data. In this paper, we propose a deep-learning network to pinpoint the location of a jump discontinuity even in the presence of substantial noise.

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Section: Introductionmentioning

confidence: 99%