Numerical Differentiation of Noisy, Nonsmooth Data

Chartrand, Rick

doi:10.5402/2011/164564

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:

Chartrand, Rick ^[1]

Theoretical Division, MS B284, Los Alamos National Laboratory, Los Alamos, NM 87545, USA

Publication Date:: Wed May 11 00:00:00 EDT 2011

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.

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                    Chartrand, Rick. Numerical Differentiation of Noisy, Nonsmooth Data.  Country unknown/Code not available.  https://doi.org/10.5402/2011/164564

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                    Chartrand, Rick. Wed .  
"Numerical Differentiation of Noisy, Nonsmooth Data".  Country unknown/Code not available.  https://doi.org/10.5402/2011/164564.

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@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         = {Wed May 11 00:00:00 EDT 2011},

  month        = {Wed May 11 00:00:00 EDT 2011}

}

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Works referenced in this record:

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journal, January 1996

Vogel, C. R.; Oman, M. E.
SIAM Journal on Scientific Computing, Vol. 17, Issue 1
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A variational method for numerical differentiation
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Knowles, Ian; Wallace, Robert
Numerische Mathematik, Vol. 70, Issue 1
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Total variation regularisation of images corrupted by non-Gaussian noise using a quasi-Newton method
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Chartrand, R.; Staneva, V.
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A new approach for flow-through respirometry measurements in humans
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Melanson, Edward L.; Ingebrigtsen, Jan P.; Bergouignan, Audrey
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Abel inversion using total-variation regularization
journal, October 2005

Asaki, T. J.; Chartrand, R.; Vixie, K. R.
Inverse Problems, Vol. 21, Issue 6
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Abel inversion using total variation regularization: applications
journal, December 2006

Asaki, Thomas J.; Campbell, Patrick R.; Chartrand, Rick
Inverse Problems in Science and Engineering, Vol. 14, Issue 8
DOI: 10.1080/17415970600882549

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Dobson, David C.; Vogel, Curtis R.
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A Variational Approach to Reconstructing Images Corrupted by Poisson Noise
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Le, Triet; Chartrand, Rick; Asaki, Thomas J.
Journal of Mathematical Imaging and Vision, Vol. 27, Issue 3
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Inverse Problems Light: Numerical Differentiation
journal, June 2001

Hanke, Martin; Scherzer, Otmar
The American Mathematical Monthly, Vol. 108, Issue 6
DOI: 10.2307/2695705

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Title: Numerical Differentiation of Noisy, Nonsmooth Data

Abstract

Citation Formats

Iterative Methods for Total Variation Denoising journal, January 1996

A variational method for numerical differentiation journal, March 1995

Total variation regularisation of images corrupted by non-Gaussian noise using a quasi-Newton method journal, January 2008

A new approach for flow-through respirometry measurements in humans journal, June 2010

Abel inversion using total-variation regularization journal, October 2005

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Convergence of an Iterative Method for Total Variation Denoising journal, October 1997

Spline Functions and the Problem of Graduation journal, October 1964

Smoothing by spline functions journal, October 1967

Numerical Differentiation and Regularization journal, June 1971

A Variational Approach to Reconstructing Images Corrupted by Poisson Noise journal, March 2007

Inverse Problems Light: Numerical Differentiation journal, June 2001

Iterative Methods for Total Variation Denoising
journal, January 1996

A variational method for numerical differentiation
journal, March 1995

Total variation regularisation of images corrupted by non-Gaussian noise using a quasi-Newton method
journal, January 2008

A new approach for flow-through respirometry measurements in humans
journal, June 2010

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journal, October 2005

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journal, December 2006

Convergence of an Iterative Method for Total Variation Denoising
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Numerical Differentiation and Regularization
journal, June 1971

A Variational Approach to Reconstructing Images Corrupted by Poisson Noise
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journal, June 2001