The DOI matches its Crossref record; 32 of the 32 references it cites were found in a registry or an index.
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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Cites
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Daubechies, I. (1992) · doi:10.1137/1.9781611970104 · Cited by 15,979
Ideal Spatial Adaptation by Wavelet Shrinkage
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Adapting to Unknown Smoothness via Wavelet Shrinkage
Donoho, D. L., & Johnstone, I. M. (1995) · Journal of the American Statistical Association · doi:10.1080/01621459.1995.10476626 · Cited by 4,577
Adaptive wavelet thresholding for image denoising and compression
Chang, S.-F., Yu, B., & Vetterli, M. (2000) · IEEE Transactions on Image Processing · doi:10.1109/83.862633 · Cited by 2,927
Estimation of the Mean of a Multivariate Normal Distribution
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Digital Image Enhancement and Noise Filtering by Use of Local Statistics
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Ideal Spatial Adaptation by Wavelet Shrinkage
Donoho, D. L., & Johnstone, I. M. (1994) · Biometrika · doi:10.2307/2337118 · Cited by 2,506
Estimation with Quadratic Loss
James, W., & Stein, C. M. (1992) · Springer series in statistics · doi:10.1007/978-1-4612-0919-5_30 · Cited by 2,319
Image denoising using scale mixtures of gaussians in the wavelet domain
Portilla, J., Strela, V., Wainwright, M. J., & Simoncelli, E. P. (2003) · IEEE Transactions on Image Processing · doi:10.1109/tip.2003.818640 · Cited by 2,280
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No-Reference Image Quality Assessment in the Spatial Domain
Mittal, A., Moorthy, A. K., & Bovik, A. C. (2012) · IEEE Transactions on Image Processing · doi:10.1109/tip.2012.2214050 · Cited by 6,064
Deep Convolutional Neural Network for Inverse Problems in Imaging
Jin, K. H., McCann, M. T., Froustey, E., & Unser, M. (2017) · IEEE Transactions on Image Processing · doi:10.1109/tip.2017.2713099 · Cited by 2,529
“ct a 512 512 image on the GPU. I. INTRODUCTION Over the past decades, iterative reconstruction methods have become the dominant approach to solving inverse problems in imaging including denoising [1]–[4], deconvolution [5], [6], and interpolation [7], [8]. Thanks to robust regularizers such as total variation [1], [2]…”
MethodSelf-citationImage Denoising and Inpainting with Deep Neural Networks
Xie, J., Xu, L., & Chen, E. (2012) · Cited by 1,237
State of the Art in Defect Detection Based on Machine Vision
Ren, Z., Fang, F., Yan, N., & Wu, Y. (2021) · International Journal of Precision Engineering and Manufacturing-Green Technology · doi:10.1007/s40684-021-00343-6 · Cited by 896
A Tour of Modern Image Filtering: New Insights and Methods, Both Practical and Theoretical
Milanfar, P. (2012) · IEEE Signal Processing Magazine · doi:10.1109/msp.2011.2179329 · Cited by 606
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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