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Title: Numerical Differentiation of Noisy, Nonsmooth Data

Abstract

We consider the problem of differentiating a function specified by noisy data. Regularizing the differentiation process avoids the noise amplification of finite-difference methods. We use total-variation regularization, which allows for discontinuous solutions. The resulting simple algorithm accurately differentiates noisy functions, including those which have a discontinuous derivative.

Authors:
 [1]
  1. Theoretical Division, MS B284, Los Alamos National Laboratory, Los Alamos, NM 87545, USA
Publication Date:
Sponsoring Org.:
USDOE
OSTI Identifier:
1198314
Resource Type:
Published Article
Journal Name:
ISRN Applied Mathematics
Additional Journal Information:
Journal Name: ISRN Applied Mathematics Journal Volume: 2011; Journal ID: ISSN 2090-5564
Publisher:
Hindawi (International Scholarly Research Network)
Country of Publication:
Country unknown/Code not available
Language:
English

Citation Formats

Chartrand, Rick. Numerical Differentiation of Noisy, Nonsmooth Data. Country unknown/Code not available: N. p., 2011. Web. doi:10.5402/2011/164564.
Chartrand, Rick. Numerical Differentiation of Noisy, Nonsmooth Data. Country unknown/Code not available. doi:10.5402/2011/164564.
Chartrand, Rick. Sat . "Numerical Differentiation of Noisy, Nonsmooth Data". Country unknown/Code not available. doi:10.5402/2011/164564.
@article{osti_1198314,
title = {Numerical Differentiation of Noisy, Nonsmooth Data},
author = {Chartrand, Rick},
abstractNote = {We consider the problem of differentiating a function specified by noisy data. Regularizing the differentiation process avoids the noise amplification of finite-difference methods. We use total-variation regularization, which allows for discontinuous solutions. The resulting simple algorithm accurately differentiates noisy functions, including those which have a discontinuous derivative.},
doi = {10.5402/2011/164564},
journal = {ISRN Applied Mathematics},
number = ,
volume = 2011,
place = {Country unknown/Code not available},
year = {2011},
month = {1}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
DOI: 10.5402/2011/164564

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Works referenced in this record:

Iterative Methods for Total Variation Denoising
journal, January 1996

  • Vogel, C. R.; Oman, M. E.
  • SIAM Journal on Scientific Computing, Vol. 17, Issue 1
  • DOI: 10.1137/0917016

Smoothing by spline functions
journal, October 1967