A New SURE Approach to Image Denoising: Interscale Orthonormal Wavelet Thresholding
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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
Daubechies, I. (1992) · doi:10.1137/1.9781611970104 · Cited by 15,979
Daubechies, I. C., & Heil, C. (1992) · Computers in Physics · doi:10.1063/1.4823127 · Cited by 15,729 · see citing works
Ideal Spatial Adaptation by Wavelet Shrinkage
Donoho, D. L., & Johnstone, I. M. (1994) · Biometrika · doi:10.1093/biomet/81.3.425 · Cited by 8,730 · see citing works
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 · see citing works
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 · see citing works
Estimation of the Mean of a Multivariate Normal Distribution
Stein, C. M. (1981) · The Annals of Statistics · doi:10.1214/aos/1176345632 · Cited by 2,795 · see citing works
Digital Image Enhancement and Noise Filtering by Use of Local Statistics
Lee, J.-S. (1980) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.1980.4766994 · Cited by 2,742 · see citing works
Ideal Spatial Adaptation by Wavelet Shrinkage
Donoho, D. L., & Johnstone, I. M. (1994) · Biometrika · doi:10.2307/2337118 · Cited by 2,506 · see citing works
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 · see citing works
The curvelet transform for image denoising
Starck, J., Candès, E. J., & Donoho, D. L. (2002) · IEEE Transactions on Image Processing · doi:10.1109/tip.2002.1014998 · Cited by 2,267 · see citing works
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 2,256 · see citing works
Complex Wavelets for Shift Invariant Analysis and Filtering of Signals
Kingsbury, N. (2001) · Applied and Computational Harmonic Analysis · doi:10.1006/acha.2000.0343 · Cited by 1,680 · see citing works
Adapting to Unknown Smoothness via Wavelet Shrinkage
Donoho, D. L., & Johnstone, I. M. (1995) · Journal of the American Statistical Association · doi:10.2307/2291512 · Cited by 1,664 · see citing works
Wavelet-based statistical signal processing using hidden Markov models
Crouse, M. S., Nowak, R. D., & Baraniuk, R. G. (1998) · IEEE Transactions on Signal Processing · doi:10.1109/78.668544 · Cited by 1,631 · see citing works
Better Subset Regression Using the Nonnegative Garrote
Breiman, L. (1995) · Technometrics · doi:10.2307/1269730 · Cited by 1,045 · see citing works
Bivariate shrinkage functions for wavelet-based denoising exploiting interscale dependency
Sendur, L., & Selesnick, I. (2002) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2002.804091 · Cited by 1,008 · see citing works
Spatially adaptive wavelet thresholding with context modeling for image denoising
Chang, S., Yu, B., & Vetterli, M. (2000) · IEEE Transactions on Image Processing · doi:10.1109/83.862630 · Cited by 887 · see citing works
Image processing with complex wavelets
Kingsbury, N. (1999) · Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering Sciences · doi:10.1098/rsta.1999.0447 · Cited by 816 · see citing works
Low-complexity image denoising based on statistical modeling of wavelet coefficients
Mıhçak, M. K., Kozintsev, I. V., Ramchandran, K., & Moulin, P. (1999) · IEEE Signal Processing Letters · doi:10.1109/97.803428 · Cited by 780 · see citing works
Statistical Modeling by Wavelets
Kettaneh, N. (2000) · Technometrics · doi:10.1080/00401706.2000.10486065 · Cited by 748 · see citing works
Statistical Modeling by Wavelets
Vidaković, B. (1999) · Wiley series in probability and statistics · doi:10.1002/9780470317020 · Cited by 631 · see citing works
Bivariate shrinkage with local variance estimation
Sendur, L., & Selesnick, I. (2002) · IEEE Signal Processing Letters · doi:10.1109/lsp.2002.806054 · Cited by 580 · see citing works
Wavelet Thresholding via A Bayesian Approach
Abramovich, F., Sapatinas, T., & Silverman, B. W. (1998) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/1467-9868.00151 · Cited by 548 · see citing works
Pižurica, A., & Philips, W. R. (2006) · IEEE Transactions on Image Processing · doi:10.1109/tip.2005.863698 · Cited by 400 · see citing works
Wavelet Shrinkage Denoising Using the Non-Negative Garrote
Gao, H. (1998) · Journal of Computational and Graphical Statistics · doi:10.1080/10618600.1998.10474789 · Cited by 365 · see citing works
WAVESHRINK WITH FIRM SHRINKAGE
Gao, H., & Bruce, A. G. (1997) · Cited by 277 · see citing works
Bayesian Denoising of Visual Images in the Wavelet Domain
Simoncelli, E. P. (1999) · Lecture notes in statistics · doi:10.1007/978-1-4612-0567-8_18 · Cited by 240 · see citing works
Adaptive denoising based on SURE risk
Zhang, X.-P. S., & Desai, M. D. (1998) · IEEE Signal Processing Letters · doi:10.1109/97.720560 · Cited by 227 · see citing works
Wavelet Shrinkage Denoising Using the Non-Negative Garrote
Gao, H. (1998) · Journal of Computational and Graphical Statistics · doi:10.2307/1390677 · Cited by 150 · see citing works
Building robust wavelet estimators for multicomponent images using Stein's principle
Benazza‐Benyahia, A., & Pesquet, J. (2005) · IEEE Transactions on Image Processing · doi:10.1109/tip.2005.857247 · Cited by 86 · see citing works
A new wavelet estimator for image denoising
Pesquet, J. (1997) · IEE International Conference on Image Processing and its Applications (IPA) · doi:10.1049/cp:19970893 · Cited by 31 · see citing works
WAVELET-CONSTRAINED IMAGE RESTORATION
Combettes, P. L., & Pesquet, J. (2004) · International Journal of Wavelets Multiresolution and Information Processing · doi:10.1142/s0219691304000688 · Cited by 30 · see citing works
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- E. P. Simoncelli, Bayesian Interference in Wavelet Based Models, ser. Lecture Notes in Statistics. New York: Springer-Verlag, Mar. 1999, vol. 141, ch. 18, pp. 291-308.
- Dr. Blu is the recipient of the 2003 best paper award (SP Theory and Methods) from the IEEE Signal Processing Society. He is currently an Associate Editor for the IEEE TRANSACTIONS ON IMAGE PROCESSING and, since 2006, for the IEEE TRANSACTIONS ON SIGNAL PROCESSING.
- Michael Unser (M'89-SM'94-F'99) received the M.S. (summa cum laude) and Ph.D. degrees in elec- trical engineering from the Swiss Federal Institute of Technology (EPFL), Lausanne, Switzerland, in 1981 and 1984, respectively. From 1985 to 1997, he was a Scientist with the Na- tional Institutes of Health, Bethesda, MD. He is now a Professor and Director of the Biomedical Imaging Group, EPFL. His main research topics are biomed- ical image processing, splines, and wavelets. He is the author of over 120 published journal papers in these areas.
- Dr. Unser has been actively involved with the IEEE TRANSACTIONS ON MEDICAL IMAGING, holding the positions of Associate Editor (1999-2002 and 2006-present), member of steering committee, and Associate Editor-in-Chief (2003-2005). He has acted as an Associate Editor or member of the edito- rial board for eight more international journals, including the IEEE Signal Processing Magazine, the IEEE TRANSACTIONS ON IMAGE PROCESSING (1992-1995), and the IEEE SIGNAL PROCESSING LETTERS (1994-1998). He organized the first IEEE International Symposium on Biomedical Imaging (ISBI 2002). He currently chairs the technical committee of the IEEE-SP Society on Bio Imaging and Signal Processing (BISP), and well as the ISBI steering committee. He is a recipient of three Best Paper Awards from the IEEE Signal Processing Society.
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Ong, F., Uecker, M., Tariq, U., Hsiao, A., Alley, M. T., Vasanawala, S. S., & Lustig, M. S. (2014) · Magnetic Resonance in Medicine · doi:10.1002/mrm.25176 · Cited by 60 · see citing works
Removal of Correlated Noise by Modeling the Signal of Interest in the Wavelet Domain
Goossens, B., Pižurica, A., & Philips, W. R. (2009) · IEEE Transactions on Image Processing · doi:10.1109/tip.2009.2017169 · Cited by 60 · see citing works
Non-Local Means Image Denoising With a Soft Threshold
Lu, L., Jin, W., & Wang, X. (2014) · IEEE Signal Processing Letters · doi:10.1109/lsp.2014.2371332 · Cited by 57 · see citing works
Bhandari, A. K., Kumar, D., Kumar, A., & Singh, A. K. (2015) · Neurocomputing · doi:10.1016/j.neucom.2015.09.079 · Cited by 56 · see citing works
LLSURE: Local Linear SURE-Based Edge-Preserving Image Filtering
Qiu, T., Wang, A., Yu, N., & Song, A. (2012) · IEEE Transactions on Image Processing · doi:10.1109/tip.2012.2214052 · Cited by 55 · see citing works
Rethinking Biased Estimation: Improving Maximum Likelihood and the Cramér–Rao Bound
Eldar, Y. C. (2007) · now publishers, Inc. eBooks · doi:10.1561/9781601981318 · Cited by 55 · see citing works
Image Denoising via Bandwise Adaptive Modeling and Regularization Exploiting Nonlocal Similarity
Xiong, R., Liu, H., Zhang, X., Zhang, J., Ma, S., Wu, F., & Gao, W. (2016) · IEEE Transactions on Image Processing · doi:10.1109/tip.2016.2614160 · Cited by 53 · see citing works
Wavelet-based denoising: A brief review
Chen, G., Xie, W., & Zhao, Y. (2013) · International Conference on Intelligent Control and Information Processing · doi:10.1109/icicip.2013.6568140 · Cited by 53 · see citing works
Yu, B., Li, S., Chen, C., Xu, J., Qiu, W., Wu, X., & Chen, R. (2017) · Chemometrics and Intelligent Laboratory Systems · doi:10.1016/j.chemolab.2017.05.009 · Cited by 52 · see citing works
Briggs, C., Hirasawa, M., & Semba, K. (2018) · Journal of Neuroscience · doi:10.1523/jneurosci.2179-17.2018 · Cited by 52 · see citing works
Terris, M., Dabbech, A., Tang, C., & Wiaux, Y. (2022) · Monthly Notices of the Royal Astronomical Society · doi:10.1093/mnras/stac2672 · Cited by 50 · see citing works
Novel Speed-Up Strategies for Non-Local Means Denoising With Patch and Edge Patch Based Dictionaries
Bhujle, H. V., & Chaudhuri, S. (2013) · IEEE Transactions on Image Processing · doi:10.1109/tip.2013.2290871 · Cited by 50 · see citing works
The Estimation of Laplace Random Vectors in Additive White Gaussian Noise
Selesnick, I. (2008) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2008.920488 · Cited by 50 · see citing works
Kriti, N. A., Virmani, J., & Agarwal, R. (2018) · Journal of Applied Biomedicine · doi:10.1016/j.bbe.2018.10.002 · Cited by 49 · see citing works
Image denoising using local Wiener filter and its method noise
Zhang, X. (2016) · Optik · doi:10.1016/j.ijleo.2016.05.002 · Cited by 47 · see citing works
Liang, Z., Xu, B., Chi, Z., & Feng, D. D. (2011) · Expert Systems with Applications · doi:10.1016/j.eswa.2011.09.114 · Cited by 46 · see citing works
Jumah, A. A. (2013) · Journal of Signal and Information Processing · doi:10.4236/jsip.2013.41004 · Cited by 46 · see citing works
Deep Denoising for Scientific Discovery: A Case Study in Electron Microscopy
Mohan, S., Manzorro, R., Vincent, J., Tang, B., Sheth, D. Y., Simoncelli, E. P., Matteson, D. S., Crozier, P. A., & Fernandez‐Granda, C. (2022) · IEEE Transactions on Computational Imaging · doi:10.1109/tci.2022.3176536 · Cited by 45 · see citing works
Dehnavi, A., Esmaeili, M., Rabbani, H., & Hajizadeh, F. (2016) · Journal of Medical Signals & Sensors · doi:10.4103/2228-7477.186878 · Cited by 44 · see citing works
Total variation with overlapping group sparsity for deblurring images under Cauchy noise
Ding, M., Huang, T., Wang, S., Mei, J.-J., & Zhao, X.-L. (2018) · Applied Mathematics and Computation · doi:10.1016/j.amc.2018.08.014 · Cited by 45 · see citing works
Sparse Representation Prior and Total Variation--Based Image Deblurring under Impulse Noise
Ma, L., Yu, J. Q., & Zeng, T. (2013) · SIAM Journal on Imaging Sciences · doi:10.1137/120866452 · Cited by 44 · see citing works
Covariance Estimation in Decomposable Gaussian Graphical Models
Wiesel, A., Eldar, Y. C., & Hero, A. O. (2009) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2009.2037350 · Cited by 44 · see citing works
A weighted bio-signal denoising approach using empirical mode decomposition
Lahmiri, S., & Boukadoum, M. (2015) · Biomedical Engineering Letters · doi:10.1007/s13534-015-0182-2 · Cited by 44 · see citing works
- 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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