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Numerical Differentiation of Noisy, Nonsmooth Data

Journal Article · · ISRN Applied Mathematics
DOI:https://doi.org/10.5402/2011/164564· OSTI ID:1198314
 [1]
  1. Theoretical Division, MS B284, Los Alamos National Laboratory, Los Alamos, NM 87545, USA
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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.

Sponsoring Organization:
USDOE
OSTI ID:
1198314
Journal Information:
ISRN Applied Mathematics, Journal Name: ISRN Applied Mathematics Vol. 2011; ISSN 2090-5564
Publisher:
Hindawi (International Scholarly Research Network)Copyright Statement
Country of Publication:
Country unknown/Code not available
Language:
English

References (12)

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A Variational Approach to Reconstructing Images Corrupted by Poisson Noise journal March 2007
Total variation regularisation of images corrupted by non-Gaussian noise using a quasi-Newton method journal January 2008
Spline Functions and the Problem of Graduation journal October 1964
Abel inversion using total variation regularization: applications journal December 2006
Abel inversion using total-variation regularization journal October 2005
Numerical Differentiation and Regularization journal June 1971
Iterative Methods for Total Variation Denoising journal January 1996
Convergence of an Iterative Method for Total Variation Denoising journal October 1997
A new approach for flow-through respirometry measurements in humans journal June 2010
Inverse Problems Light: Numerical Differentiation journal June 2001

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