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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Nonparametric estimation of the singularities of a signal from noisy measurements
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by A. I. Katsevich and A. G. Ramm PDF
Proc. Amer. Math. Soc. 121 (1994), 1221-1234 Request permission

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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Additional Information
  • © Copyright 1994 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 121 (1994), 1221-1234
  • MSC: Primary 62G05
  • DOI: https://doi.org/10.1090/S0002-9939-1994-1227518-3
  • MathSciNet review: 1227518