The DOI matches its Crossref record; 8 of the 8 references it cites were found in a registry or an index.
Noise reduction using an undecimated discrete wavelet transform
Abstract
A new nonlinear noise reduction method is presented that uses the discrete wavelet transform. Similar to Donoho (1995) and Donohoe and Johnstone (1994, 1995), the authors employ thresholding in the wavelet transform domain but, following a suggestion by Coifman, they use an undecimated, shift-invariant, nonorthogonal wavelet transform instead of the usual orthogonal one. This new approach can be interpreted as a repeated application of the original Donoho and Johnstone method for different shifts. The main feature of the new algorithm is a significantly improved noise reduction compared to the original wavelet based approach. This holds for a large class of signals, both visually and in the l/sub 2/ sense, and is shown theoretically as well as by experimental results.
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
Daubechies, I. (1992) · doi:10.1137/1.9781611970104 · Cited by 15,979
Daubechies, I., & Heil, C. (1992) · Computers in Physics · doi:10.1063/1.4823127 · Cited by 15,631
De-noising by soft-thresholding
Donoho, D. L. (1995) · IEEE Transactions on Information Theory · doi:10.1109/18.382009 · Cited by 9,619
Ideal spatial adaptation by wavelet shrinkage
Donoho, D. L., & Johnstone, I. M. (1994) · Biometrika · doi:10.1093/biomet/81.3.425 · Cited by 8,760
Wavelet Shrinkage: Asymptopia?
Donoho, D. L., Johnstone, I. M., Kerkyacharian, G., & Picard, D. (1995) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.2517-6161.1995.tb02032.x · Cited by 1,749
The Stationary Wavelet Transform and some Statistical Applications
Nason, G. P., & Silverman, B. W. (1995) · Lecture Notes in Statistics · doi:10.1007/978-1-4612-2544-7_17 · Cited by 1,122
Zero-crossings of a wavelet transform
Mallat, S. (1991) · IEEE Transactions on Information Theory · doi:10.1109/18.86995 · Cited by 704
Time-invariant orthonormal wavelet representations
Pesquet, J.-C., Krim, H., & Carfantan, H. (1996) · IEEE Transactions on Signal Processing · doi:10.1109/78.533717 · Cited by 407
Cited by
Fast Image Recovery Using Variable Splitting and Constrained Optimization
Afonso, M. V., Bioucas-Dias, J. M., & Figueiredo, M. A. T. (2010) · IEEE Transactions on Image Processing · doi:10.1109/tip.2010.2047910 · Cited by 1,223
Afonso, M. V., Bioucas-Dias, J. M., & Figueiredo, M. A. T. (2011) · IEEE Transactions on Image Processing · doi:10.1109/tip.2010.2076294 · Cited by 938
Single-shot compressive spectral imaging with a dual-disperser architecture
Gehm, M. E., John, R., Brady, D. J., Willett, R. M., & Schulz, T. J. (2007) · Optics Express · doi:10.1364/oe.15.014013 · Cited by 787
Majorization–Minimization Algorithms for Wavelet-Based Image Restoration
Figueiredo, M. A. T., Bioucas-Dias, J. M., & Nowak, R. D. (2007) · IEEE Transactions on Image Processing · doi:10.1109/tip.2007.909318 · Cited by 548
Bayesian tree-structured image modeling using wavelet-domain hidden Markov models
Romberg, J. K., Choi, H., & Baraniuk, R. G. (2001) · IEEE Transactions on Image Processing · doi:10.1109/83.931100 · Cited by 503
Metadata
- Authors
- Lang, M., Guo, H., Odegard, J. E., Burrus, C. S., & Wells, R. O.
- Venue
- IEEE Signal Processing Letters
- Published
- 1996-01
- Volume
- 3
- Issue
- 1
- Pages
- 10-12
- ISSN
- 1070-9908 (ISSN-L)
- 1558-2361
- OpenAlex
- W2022905067
- Cited by
- 484
- References
- 8
- FWCI
- 14.49
- 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: Noise reduction using an undecimated discrete wavelet transform. https://app.cochat.ai/papers/10.1109/97.475823
- The paper
- Lang, M., Guo, H., Odegard, J. E., Burrus, C. S., & Wells, R. O. (1996). Noise reduction using an undecimated discrete wavelet transform. IEEE Signal Processing Letters. https://doi.org/10.1109/97.475823
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.
