The DOI matches its Crossref record; 28 of the 28 references it cites were found in a registry or an index.
Constrained restoration and the recovery of discontinuities
Abstract
The linear image restoration problem is to recover an original brightness distribution X/sup 0/ given the blurred and noisy observations Y=KX/sup 0/+B, where K and B represent the point spread function and measurement error, respectively. This problem is typical of ill-conditioned inverse problems that frequently arise in low-level computer vision. A conventional method to stabilize the problem is to introduce a priori constraints on X/sup 0/ and design a cost functional H(X) over images X, which is a weighted average of the prior constraints (regularization term) and posterior constraints (data term); the reconstruction is then the image X, which minimizes H. A prominent weakness in this approach, especially with quadratic-type stabilizers, is the difficulty in recovering discontinuities. The authors therefore examine prior smoothness constraints of a different form, which permit the recovery of discontinuities without introducing auxiliary variables for marking the location of jumps and suspending the constraints in their vicinity. In this sense, discontinuities are addressed implicitly rather than explicitly.>
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
Stochastic relaxation, gibbs distributions, and the bayesian restoration of images.
Geman, S., & Geman, D. (1984) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.1984.4767596 · Cited by 17,949
Self-citationOn the Statistical Analysis of Dirty Pictures
Besag, J. (1986) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.2517-6161.1986.tb01412.x · Cited by 4,191
Robust Statistics: The Approach Based on Influence Functions
Ruppert, D. (1987) · Technometrics · doi:10.2307/1269782 · Cited by 3,880
Jacob, M. (1989) · Health Education Journal · doi:10.1177/001789698904800401 · Cited by 3,090
Blake, A., & Zisserman, A. (1987) · The MIT Press eBooks · doi:10.7551/mitpress/7132.001.0001 · Cited by 2,105
Robust Statistics: The Approach Based on Influence Functions.
Jennison, C., Hampel, F. R., Ronchetti, E. M., Rousseeuw, P. J., & Stahel, W. A. (1987) · Journal of the Royal Statistical Society. Series A (General) · doi:10.2307/2981480 · Cited by 1,753
Computational vision and regularization theory
Poggio, T., Torre, V., & Koch, C. (1985) · Nature · doi:10.1038/317314a0 · Cited by 1,412
Bayesian reconstructions from emission tomography data using a modified EM algorithm
Green, P. J. (1990) · IEEE Transactions on Medical Imaging · doi:10.1109/42.52985 · Cited by 1,241
Percival, D. B. (1989) · Technometrics · doi:10.1080/00401706.1989.10488494 · Cited by 1,234
Modeling and Segmentation of Noisy and Textured Images Using Gibbs Random Fields
Derin, H., & Elliott, H. (1987) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.1987.4767871 · Cited by 977
Cited by
A sparse signal reconstruction perspective for source localization with sensor arrays
Malioutov, D., Cetin, M., & Willsky, A. S. (2005) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2005.850882 · Cited by 2,638
A New Alternating Minimization Algorithm for Total Variation Image Reconstruction
Wang, Y., Yang, J., Yin, W., & Zhang, Y. (2008) · SIAM Journal on Imaging Sciences · doi:10.1137/080724265 · Cited by 1,975
Majorization-Minimization Algorithms in Signal Processing, Communications, and Machine Learning
Sun, Y., Babu, P., & Palomar, D. P. (2017) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2016.2601299 · Cited by 1,820
Nonlinear image recovery with half-quadratic regularization
Geman, D., & Yang, C. (1995) · IEEE Transactions on Image Processing · doi:10.1109/83.392335 · Cited by 1,000
Self-citationRoth, S., & Black, M. J. (2009) · International Journal of Computer Vision · doi:10.1007/s11263-008-0197-6 · Cited by 847
Metadata
- Authors
- Geman, D., & Reynolds, G.
- Venue
- IEEE Transactions on Pattern Analysis and Machine Intelligence
- Published
- 1992-03
- Volume
- 14
- Issue
- 3
- Pages
- 367-383
- ISSN
- 0162-8828 (ISSN-L)
- OpenAlex
- W2080744942
- Cited by
- 1,085
- References
- 28
- FWCI
- 23.83
- 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: Constrained restoration and the recovery of discontinuities. https://app.cochat.ai/papers/10.1109/34.120331
- The paper
- Geman, D., & Reynolds, G. (1992). Constrained restoration and the recovery of discontinuities. IEEE Transactions on Pattern Analysis and Machine Intelligence. https://doi.org/10.1109/34.120331
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.
