Table of Contents
ISRN Applied Mathematics
Volume 2011, Article ID 164564, 11 pages
http://dx.doi.org/10.5402/2011/164564
Research Article

Numerical Differentiation of Noisy, Nonsmooth Data

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

Received 8 March 2011; Accepted 4 April 2011

Academic Editors: L. Marin and D. Xiao

Copyright © 2011 Rick Chartrand. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.