The DOI matches its Crossref record; 10 of the 10 references it cites were found in a registry or an index.
Numerical Differentiation of Noisy, Nonsmooth Data
Open accessAbstract
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.
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Cites
Nonlinear total variation based noise removal algorithms
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Iterative Methods for Total Variation Denoising
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REGULARIZATION OF INCORRECTLY POSED PROBLEMS
Tikhonov, A. N. (1963) · Cited by 867
SPLINE FUNCTIONS AND THE PROBLEM OF GRADUATION
Schoenberg, I. J. (1964) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.52.4.947 · Cited by 439
A Variational Approach to Reconstructing Images Corrupted by Poisson Noise
Le, T., Chartrand, R., & Asaki, T. J. (2007) · Journal of Mathematical Imaging and Vision · doi:10.1007/s10851-007-0652-y · Cited by 412
Self-citationA new approach for flow-through respirometry measurements in humans
Melanson, E. L., Ingebrigtsen, J. P., Bergouignan, A., Ohkawara, K., Kohrt, W. M., & Lighton, J. R. B. (2010) · American Journal of Physiology-Regulatory, Integrative and Comparative Physiology · doi:10.1152/ajpregu.00055.2010 · Cited by 69
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Discovering governing equations from data by sparse identification of nonlinear dynamical systems
Brunton, S. L., Proctor, J. L., & Kutz, J. N. (2016) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1517384113 · Cited by 4,796
Data-driven discovery of coordinates and governing equations
Champion, K., Lusch, B., Kutz, J. N., & Brunton, S. L. (2019) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1906995116 · Cited by 909
Inferring biological networks by sparse identification of nonlinear dynamics
Mangan, N. M., Brunton, S. L., Proctor, J. L., & Kutz, J. N. (2016) · IEEE Transactions on Molecular, Biological and Multi-Scale Communications · doi:10.1109/tmbmc.2016.2633265 · Cited by 436
Discovery of nonlinear multiscale systems: Sampling strategies and embeddings
Champion, K. P., Brunton, S. L., & Kutz, J. N. (2019) · SIAM Journal on Applied Dynamical Systems · doi:10.1137/18m1188227 · Cited by 171
Sparse identification of nonlinear dynamics for rapid model recovery
Quade, M., Abel, M., Nathan Kutz, J., & Brunton, S. L. (2018) · Chaos: An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/1.5027470 · Cited by 163
Metadata
- Authors
- Chartrand, R.
- Venue
- ISRN Applied Mathematics
- Publisher
- Wiley
- Published
- 2011-05-11
- Volume
- 2011
- Pages
- 1-11
- ISSN
- 2090-5564 (ISSN-L)
- 2090-5572
- OpenAlex
- W1978060721
- Cited by
- 444
- References
- 10
- FWCI
- 11.27
- Type
- journal article
- Language
- en
- Open access
- diamond
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Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
