The DOI matches its Crossref record; 3 of the 3 references it cites were found in a registry or an index.
Deblurring and Denoising of Images by Nonlocal Functionals
Abstract
This paper investigates the use of regularization functionals with nonlocal correlation terms for the problem of image denoising and image deblurring. These functionals are expressed as integrals over the Cartesian product of the pixel space. We show that the class of neighborhood filters can be described in this framework. Using these functionals we can consider the functional analytic properties of some of these neighborhood filters and show how they can be seen as regularization terms using a smoothed version of the Prokhorov metric. Moreover, we define a nonlocal variant of the well-known bounded variation regularization, which does not suffer from the staircase effect. We show existence of a minimizer of the corresponding regularization functional for the denoising and deblurring problem, and we present some numerical examples comparing the nonlocal version to the bounded variation regularization and the nonlocal mean filter.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
Bilateral Filtering for Gray and Color Images
Tomasi, C., & Manduchi, R. (2002) · Sixth International Conference on Computer Vision (IEEE Cat. No.98CH36271) · doi:10.1109/iccv.1998.710815 · Cited by 8,177 · cited 2×
“Such filters have originally been proposed by Yaroslavsky [26, 27], and further generalized in [23, 24].”
BackgroundHuber, P. J. (1981) · Wiley Series in Probability and Statistics · doi:10.1002/0471725250 · Cited by 7,066
SUSAN—a new approach to low level image processing
Smith, S. M., & Brady, J. M. (1997) · International Journal of Computer Vision · doi:10.1023/a:1007963824710 · Cited by 3,333
Cited by
Nonlocal Image and Movie Denoising
Buades, A., Coll, B., & Morel, J.-M. (2008) · International Journal of Computer Vision · doi:10.1007/s11263-007-0052-1 · Cited by 769
Bregmanized Nonlocal Regularization for Deconvolution and Sparse Reconstruction
Zhang, X., Burger, M., Bresson, X., & Osher, S. (2010) · SIAM Journal on Imaging Sciences · doi:10.1137/090746379 · Cited by 688
Self-citationNonlocal Discrete Regularization on Weighted Graphs: A Framework for Image and Manifold Processing
Elmoataz, A., Lezoray, O., & Bougleux, S. (2008) · IEEE Transactions on Image Processing · doi:10.1109/tip.2008.924284 · Cited by 466
Non-local Color Image Denoising with Convolutional Neural Networks
Lefkimmiatis, S. (2017) · 2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR) · doi:10.1109/cvpr.2017.623 · Cited by 363
Metadata
- Authors
- Kindermann, S., Osher, S., & Jones, P. W.
- Venue
- Multiscale Modeling & Simulation
- Published
- 2005-01
- Volume
- 4
- Issue
- 4
- Pages
- 1091-1115
- ISSN
- 1540-3459 (ISSN-L)
- 1540-3467
- OpenAlex
- W2038649727
- Cited by
- 369
- References
- 3
- FWCI
- 13.16
- Type
- journal article
- Language
- en
- Open access
- closed
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: Deblurring and Denoising of Images by Nonlocal Functionals. https://app.cochat.ai/papers/10.1137/050622249
- The paper
- Kindermann, S., Osher, S., & Jones, P. W. (2005). Deblurring and Denoising of Images by Nonlocal Functionals. Multiscale Modeling & Simulation. https://doi.org/10.1137/050622249
Data sources
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.
