The DOI matches its Crossref record; 81 of the 81 references it cites were found in a registry or an index.
Solving Inverse Problems With Piecewise Linear Estimators: From Gaussian Mixture Models to Structured Sparsity
Abstract
A general framework for solving image inverse problems with piecewise linear estimations is introduced in this paper. The approach is based on Gaussian mixture models, which are estimated via a maximum a posteriori expectation-maximization algorithm. A dual mathematical interpretation of the proposed framework with a structured sparse estimation is described, which shows that the resulting piecewise linear estimate stabilizes the estimation when compared with traditional sparse inverse problem techniques. We demonstrate that, in a number of image inverse problems, including interpolation, zooming, and deblurring of narrow kernels, the same simple and computationally efficient algorithm yields results in the same ballpark as that of the state of the art.
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
Boyd, S., & Vandenberghe, L. (2004) · doi:10.1017/cbo9780511804441 · Cited by 56,601
Regression shrinkage and selection via the lasso
Tibshirani, R. (1996) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.2517-6161.1996.tb02080.x · Cited by 51,482
Maximum Likelihood from Incomplete Data Via the EM Algorithm
Dempster, A. P., Laird, N. M., & Rubin, D. B. (1977) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.2517-6161.1977.tb01600.x · Cited by 50,444
Donoho, D. L. (2006) · IEEE Transactions on Information Theory · doi:10.1109/tit.2006.871582 · Cited by 23,994
Donoho, D. L. (2004) · Cited by 16,703
A Wavelet Tour of Signal Processing
(1999) · Elsevier eBooks · doi:10.1016/b978-0-12-466606-1.x5000-4 · Cited by 16,227
$rm K$-SVD: An Algorithm for Designing Overcomplete Dictionaries for Sparse Representation
Aharon, M., Elad, M., & Bruckstein, A. (2006) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2006.881199 · Cited by 9,451
Efron, B., Hastie, T., Johnstone, I., & Tibshirani, R. (2004) · The Annals of Statistics · doi:10.1214/009053604000000067 · Cited by 9,357
Image denoising by sparse 3-D transform-domain collaborative filtering
Dabov, K., Foi, A., Katkovnik, V., & Egiazarian, K. (2007) · IEEE Transactions on Image Processing · doi:10.1109/tip.2007.901238 · Cited by 9,283
Matching pursuits with time-frequency dictionaries
Mallat, S. G., & Zhang, Z. (1993) · IEEE Transactions on Signal Processing · doi:10.1109/78.258082 · Cited by 9,112
Self-citation
Cited by
The Little Engine That Could: Regularization by Denoising (RED)
Romano, Y., Elad, M., & Milanfar, P. (2017) · SIAM Journal on Imaging Sciences · doi:10.1137/16m1102884 · Cited by 934
Turning a denoiser into a super-resolver using plug and play priors
Brifman, A., Romano, Y., & Elad, M. (2016) · 2016 IEEE International Conference on Image Processing (ICIP) · doi:10.1109/icip.2016.7532589 · Cited by 91
Stochastic Image Denoising by Sampling from the Posterior Distribution
Kawar, B., Vaksman, G., & Elad, M. (2021) · 2021 IEEE/CVF International Conference on Computer Vision Workshops (ICCVW) · doi:10.1109/iccvw54120.2021.00213 · Cited by 42
Metadata
- Authors
- Yu, G., Sapiro, G., & Mallat, S.
- Venue
- IEEE Transactions on Image Processing
- Published
- 2012-05
- Volume
- 21
- Issue
- 5
- Pages
- 2481-2499
- ISSN
- 1057-7149 (ISSN-L)
- 1941-0042
- OpenAlex
- W2109320267
- Cited by
- 561
- References
- 81
- FWCI
- 35.89
- 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: Solving Inverse Problems With Piecewise Linear Estimators: From Gaussian Mixture Models to Structured Sparsity. https://app.cochat.ai/papers/10.1109/tip.2011.2176743
- The paper
- Yu, G., Sapiro, G., & Mallat, S. (2012). Solving Inverse Problems With Piecewise Linear Estimators: From Gaussian Mixture Models to Structured Sparsity. IEEE Transactions on Image Processing. https://doi.org/10.1109/tip.2011.2176743
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.
