The DOI matches its Crossref record; 16 of the 16 references it cites were found in a registry or an index.
Total Generalized Variation
Abstract
The novel concept of total generalized variation of a function u is introduced, and some of its essential properties are proved. Differently from the bounded variation seminorm, the new concept involves higher-order derivatives of u. Numerical examples illustrate the high quality of this functional as a regularization term for mathematical imaging problems. In particular this functional selectively regularizes on different regularity levels and, as a side effect, does not lead to a staircasing effect.
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
Nonlinear total variation based noise removal algorithms
Rudin, L. I., Osher, S., & Fatemi, E. (1992) · Physica D: Nonlinear Phenomena · doi:10.1016/0167-2789(92)90242-f · Cited by 15,704
A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems
Beck, A., & Teboulle, M. (2009) · SIAM Journal on Imaging Sciences · doi:10.1137/080716542 · Cited by 11,952
Functions of Bounded Variation and Free Discontinuity Problems
Ambrosio, L., Fusco, N., & Pallara, D. (2000) · doi:10.1093/oso/9780198502456.001.0001 · Cited by 4,318
chambolle (2004) · doi:10.1023/b:jmiv.0000011321.19549.88 · Cited by 3,227
Image recovery via total variation minimization and related problems
Chambolle, A., & Lions, P.-L. (1997) · Numerische Mathematik · doi:10.1007/s002110050258 · Cited by 1,569
A Nonlinear Primal-Dual Method for Total Variation-Based Image Restoration
Chan, T. F., Golub, G. H., & Mulet, P. (1999) · SIAM Journal on Scientific Computing · doi:10.1137/s1064827596299767 · Cited by 840
Convex Analysis and Nonlinear Optimization
Borwein, J. M., & Lewis, A. S. (2006) · CMS books in mathematics · doi:10.1007/978-0-387-31256-9 · Cited by 780
High-Order Total Variation-Based Image Restoration
Chan, T., Marquina, A., & Mulet, P. (2000) · SIAM Journal on Scientific Computing · doi:10.1137/s1064827598344169 · Cited by 776
Image Sharpening by Flows Based on Triple Well Potentials
Gilboa, G., Sochen, N., & Zeevi, Y. Y. (2004) · Journal of Mathematical Imaging and Vision · doi:10.1023/b:jmiv.0000011320.81911.38 · Cited by 616
Variational Methods in Imaging
(2009) · Applied Mathematical Sciences · doi:10.1007/978-0-387-69277-7 · Cited by 462
Cited by
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
State of the Art on 3D Reconstruction with RGB‐D Cameras
Zollhöfer, M., Stotko, P., Görlitz, A., Theobalt, C., Nießner, M., Klein, R., & Kolb, A. (2018) · Computer Graphics Forum · doi:10.1111/cgf.13386 · Cited by 339
Okolie, C. J., & Smit, J. L. (2022) · ISPRS Journal of Photogrammetry and Remote Sensing · doi:10.1016/j.isprsjprs.2022.03.016 · Cited by 139
Representer Theorems for Sparsity-Promoting $\ell _{1}$ Regularization
Unser, M., Fageot, J., & Gupta, H. (2016) · IEEE Transactions on Information Theory · doi:10.1109/tit.2016.2590421 · Cited by 36
Metadata
- Authors
- Bredies, K., Kunisch, K., & Pock, T.
- Venue
- SIAM Journal on Imaging Sciences
- Published
- 2010-01
- Volume
- 3
- Issue
- 3
- Pages
- 492-526
- ISSN
- 1936-4954 (ISSN-L)
- OpenAlex
- W2000594266
- Cited by
- 1,535
- References
- 16
- FWCI
- 39.07
- 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: Total Generalized Variation. https://app.cochat.ai/papers/10.1137/090769521
- The paper
- Bredies, K., Kunisch, K., & Pock, T. (2010). Total Generalized Variation. SIAM Journal on Imaging Sciences. https://doi.org/10.1137/090769521
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.
