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A New SURE Approach to Image Denoising: Interscale Orthonormal Wavelet Thresholding
Open accessAbstract
This paper introduces a new approach to orthonormal wavelet image denoising. Instead of postulating a statistical model for the wavelet coefficients, we directly parametrize the denoising process as a sum of elementary nonlinear processes with unknown weights. We then minimize an estimate of the mean square error between the clean image and the denoised one. The key point is that we have at our disposal a very accurate, statistically unbiased, MSE estimate--Stein's unbiased risk estimate--that depends on the noisy image alone, not on the clean one. Like the MSE, this estimate is quadratic in the unknown weights, and its minimization amounts to solving a linear system of equations. The existence of this a priori estimate makes it unnecessary to devise a specific statistical model for the wavelet coefficients. Instead, and contrary to the custom in the literature, these coefficients are not considered random anymore. We describe an interscale orthonormal wavelet thresholding algorithm based on this new approach and show its near-optimal performance--both regarding quality and CPU requirement--by comparing it with the results of three state-of-the-art nonredundant denoising algorithms on a large set of test images. An interesting fallout of this study is the development of a new, group-delay-based, parent-child prediction in a wavelet dyadic tree.
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Metadata
- Authors
- Luisier, F., Blu, T., & Unser, M.
- Affiliations
- École Polytechnique Fédérale de Lausanne (CH)
- Venue
- IEEE Transactions on Image Processing
- Published
- 2007-03
- Volume
- 16
- Issue
- 3
- Pages
- 593-606
- ISSN
- 1057-7149 (ISSN-L)
- OpenAlex
- W2007203285
- Cited by
- 623
- References
- 30
- Citations by year
- 2026: 5 · 2025: 11 · 2024: 14 · 2023: 16 · 2022: 21 · 2021: 17 · 2020: 26 · 2019: 39 · 2018: 39 · 2017: 45 · 2016: 45 · 2015: 49 · 2014: 63 · 2013: 38 · 2012: 47
- FWCI
- 51.60
- Type
- journal article
- Language
- en
- Open access
- green
- bigwww.epfl.ch
- Locations
- IEEE Transactions on Image Processing (publishedVersion)
- PubMed (publishedVersion)
- Infoscience (Ecole Polytechnique Fédérale de Lausanne) (submittedVersion, cc-by-nc-nd)
- Infoscience (Ecole Polytechnique Fédérale de Lausanne) (submittedVersion)
- Funders
- National Science Foundation (200020)
- École Polytechnique Fédérale de Lausanne
- Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung (109415, 200020)
- Centre d'Imagerie BioMédicale
- Topics
- Physical Sciences › Computer Science › Computer Vision and Pattern Recognition › Image and Signal Denoising Methods
- Physical Sciences › Computer Science › Computer Vision and Pattern Recognition › Image Enhancement Techniques
- Physical Sciences › Computer Science › Computer Vision and Pattern Recognition › Advanced Data Compression Techniques
- Keywords
- image denoising, Stein's unbiased risk estimate, mean squared error estimation, wavelet coefficient modeling
- MeSH terms
- Algorithms, Artificial Intelligence, Image Enhancement, Image Interpretation, Computer-Assisted, Sensitivity and Specificity, Reproducibility of Results, Information Storage and Retrieval, Artifacts
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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 ›
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