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Nonparametric estimation of the singularities of a signal from noisy measurements

Authors: A. I. Katsevich and A. G. Ramm
Journal: Proc. Amer. Math. Soc. 121 (1994), 1221-1234
MSC: Primary 62G05
MathSciNet review: 1227518
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Abstract: We study a problem of locating and estimating singularities of a signal measured with noise on a discrete set of points (fixed-design model). The signal consists of a smooth part with bounded first derivative and of finite number of singularities of the type $ (x - {t_i})_ \pm ^p{d_i},0 \leq p \leq \frac{1}{2}$. The case $ p = 0$ corresponds to a piecewise continuous function. The algorithm is based on convolving the data with a kernel having compact support. Optimal bandwidth of the kernel is calculated, the consistency of the algorithm is proved. The results of testing the proposed algorithm on model examples are presented.

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Keywords: Noisy data, singularity localization, kernel estimation
Article copyright: © Copyright 1994 American Mathematical Society

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