The DOI matches its Crossref record; 43 of the 43 references it cites were found in a registry or an index.
Image Denoising Using the Higher Order Singular Value Decomposition
Abstract
In this paper, we propose a very simple and elegant patch-based, machine learning technique for image denoising using the higher order singular value decomposition (HOSVD). The technique simply groups together similar patches from a noisy image (with similarity defined by a statistically motivated criterion) into a 3D stack, computes the HOSVD coefficients of this stack, manipulates these coefficients by hard thresholding, and inverts the HOSVD transform to produce the final filtered image. Our technique chooses all required parameters in a principled way, relating them to the noise model. We also discuss our motivation for adopting the HOSVD as an appropriate transform for image denoising. We experimentally demonstrate the excellent performance of the technique on grayscale as well as color images. On color images, our method produces state-of-the-art results, outperforming other color image denoising algorithms at moderately high noise levels. A criterion for optimal patch-size selection and noise variance estimation from the residual images (after denoising) is also presented.
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
Scale-space and edge detection using anisotropic diffusion
Perona, P., & Malik, J. (1990) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/34.56205 · Cited by 12,119
Mean shift: a robust approach toward feature space analysis
Comaniciu, D., & Meer, P. (2002) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/34.1000236 · Cited by 11,305
$rm K$-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
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
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
Bilateral Filtering for Gray and Color Images
Tomasi, C., & Manduchi, R. (2002) · Sixth International Conference on Computer Vision (IEEE Cat. No.98CH36271) · doi:10.1109/iccv.1998.710815 · Cited by 8,177
Multiscale structural similarity for image quality assessment
Wang, Z., Simoncelli, E. P., & Bovik, A. C. (2004) · The Thrity-Seventh Asilomar Conference on Signals, Systems & Computers, 2003 · doi:10.1109/acssc.2003.1292216 · Cited by 6,253
Emergence of simple-cell receptive field properties by learning a sparse code for natural images
Olshausen, B. A., & Field, D. J. (1996) · Nature · doi:10.1038/381607a0 · Cited by 5,694
(1982) · Elsevier eBooks · doi:10.1016/c2009-0-21955-6 · Cited by 4,596
A Review of Image Denoising Algorithms, with a New One
Buades, A., Coll, B., & Morel, J. M. (2005) · Multiscale Modeling & Simulation · doi:10.1137/040616024 · Cited by 4,083
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 2,255
Anisotropic diffusion in image processing
Weickert, J. (1998) · Cited by 2,225
Translation-Invariant De-Noising
Coifman, R. R., & Donoho, D. L. (1995) · Lecture Notes in Statistics · doi:10.1007/978-1-4612-2544-7_9 · Cited by 1,914
Non-local sparse models for image restoration
Mairal, J., Bach, F., Ponce, J., Sapiro, G., & Zisserman, A. (2009) · 2009 IEEE 12th International Conference on Computer Vision · doi:10.1109/iccv.2009.5459452 · Cited by 1,666
From learning models of natural image patches to whole image restoration
Zoran, D., & Weiss, Y. (2011) · 2011 International Conference on Computer Vision · doi:10.1109/iccv.2011.6126278 · Cited by 1,522
Kernel Regression for Image Processing and Reconstruction
Takeda, H., Farsiu, S., & Milanfar, P. (2007) · IEEE Transactions on Image Processing · doi:10.1109/tip.2006.888330 · Cited by 1,340
Learning Overcomplete Representations
Lewicki, M. S., & Sejnowski, T. J. (2000) · Neural Computation · doi:10.1162/089976600300015826 · Cited by 1,129
Bivariate shrinkage functions for wavelet-based denoising exploiting interscale dependency
Sendur, L., & Selesnick, I. W. (2002) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2002.804091 · Cited by 1,014
Multilinear Analysis of Image Ensembles: TensorFaces
Vasilescu, M. A. O., & Terzopoulos, D. (2002) · Lecture Notes in Computer Science · doi:10.1007/3-540-47969-4_30 · Cited by 836
Fourth-order partial differential equations for noise removal
You, Y.-L., & Kaveh, M. (2000) · IEEE Transactions on Image Processing · doi:10.1109/83.869184 · Cited by 826
Total variation based image restoration with free local constraints
Rudin, L. I., & Osher, S. (2002) · Proceedings of 1st International Conference on Image Processing · doi:10.1109/icip.1994.413269 · Cited by 673
Vector-valued image regularization with PDEs: a common framework for different applications
Tschumperle, D., & Deriche, R. (2005) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2005.87 · Cited by 671
Two-stage image denoising by principal component analysis with local pixel grouping
Zhang, L., Dong, W., Zhang, D., & Shi, G. (2010) · Pattern Recognition · doi:10.1016/j.patcog.2009.09.023 · Cited by 651
Yu, G.-S., Sapiro, G., & Mallat, S. (2010) · IEEE Transactions on Image Processing · doi:10.21236/ada540722 · Cited by 625
Yu, G., Sapiro, G., & Mallat, S. (2012) · IEEE Transactions on Image Processing · doi:10.1109/tip.2011.2176743 · Cited by 561
Learning Multiscale Sparse Representations for Image and Video Restoration
Mairal, J., Sapiro, G., & Elad, M. (2008) · Multiscale Modeling & Simulation · doi:10.1137/070697653 · Cited by 460
Generalized Low Rank Approximations of Matrices
Ye, J. (2005) · Machine Learning · doi:10.1007/s10994-005-3561-6 · Cited by 428
Nonparametric Bayesian Dictionary Learning for Analysis of Noisy and Incomplete Images
Zhou, M., Chen, H., Paisley, J., Ren, L., Li, L., Xing, Z., Dunson, D., Sapiro, G., & Carin, L. (2012) · IEEE Transactions on Image Processing · doi:10.1109/tip.2011.2160072 · Cited by 378
BM3D Image Denoising with Shape-Adaptive Principal Component Analysis
Dabov, K., Foi, A., Katkovnik, V. Y., & Egiazarian, K. (2009) · Cited by 377
Singular value decompositions and digital image processing
Andrews, H., & Patterson, C. L. (1976) · IEEE Transactions on Acoustics Speech and Signal Processing · doi:10.1109/tassp.1976.1162766 · Cited by 372
Signal Processing based on Multilinear Algebra
Lathauwer, L. D. (1997) · OpenGrey (Institut de l'Information Scientifique et Technique) · Cited by 360
Clustering-Based Denoising With Locally Learned Dictionaries
Chatterjee, P., & Milanfar, P. (2009) · IEEE Transactions on Image Processing · doi:10.1109/tip.2009.2018575 · Cited by 280
Unsupervised, information-theoretic, adaptive image filtering for image restoration
Awate, S. P., & Whitaker, R. T. (2006) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2006.64 · Cited by 268
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 236
Adaptive principal components and image denoising
Muresan, D. D., & Parks, T. W. (2004) · Proceedings 2003 International Conference on Image Processing (Cat. No.03CH37429) · doi:10.1109/icip.2003.1246908 · Cited by 235
Neighborhood filters and PDE’s
Buades, A., Coll, B., & Morel, J. (2006) · Numerische Mathematik · doi:10.1007/s00211-006-0029-y · Cited by 156
Cluster-based probability model and its application to image and texture processing
Popat, K., & Picard, R. W. (1997) · IEEE Transactions on Image Processing · doi:10.1109/83.551697 · Cited by 116
Transform domain image restoration methods: review, comparison, and interpretation
Yaroslavsky, L., Egiazarian, K., & Astola, J. T. (2001) · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · doi:10.1117/12.424970 · Cited by 83
Image information restoration based on long-range correlation
Zhang, D. D., & Wang, Z. (2002) · IEEE Transactions on Circuits and Systems for Video Technology · doi:10.1109/tcsvt.2002.1003472 · Cited by 81
2-Dimensional Singular Value Decomposition for 2D Maps and Images
Ding, C. H. Q., & Ye, J. (2005) · doi:10.1137/1.9781611972757.4 · Cited by 75
Dependent Hierarchical Beta Process for Image Interpolation and Denoising
Zhou, M., Yang, H., Sapiro, G., Dunson, D., & Carin, L. (2011) · Cited by 59
Gurumoorthy, K. S., Rajwade, A. V., Banerjee, A., & Rangarajan, A. (2009) · IEEE Transactions on Image Processing · doi:10.1109/tip.2009.2034991 · Cited by 37
Self-citationFeature Preserving Image Smoothing Using a Continuous Mixture of Tensors
Subakan, Ö. N., Jian, B., Vemuri, B. C., & Vallejos, C. E. (2007) · IEEE/CVF International Conference on Computer Vision (ICCV) · doi:10.1109/iccv.2007.4408918 · Cited by 19
Research works printed but not linked: 5
- Coifman, 1995, Translation-Invariant Denoising
- 10.2307/2337118 · DOI
- 10.1109/9780470544976.ch15 · doi:10.1109/9780470544976.ch15
- 10.1109/LSP.2007.916045 · doi:10.1109/lsp.2007.916045
- 10.1007/3-540-44745-8_11 · doi:10.1007/3-540-44745-8_11
Cited by
Learning Deep CNN Denoiser Prior for Image Restoration
Zhang, K., Zuo, W., Gu, S., & Zhang, L. (2017) · 2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR) · doi:10.1109/cvpr.2017.300 · Cited by 2,116
Chen, Y., & Pock, T. (2017) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2016.2596743 · Cited by 1,344
Fast Hyperspectral Image Denoising and Inpainting Based on Low-Rank and Sparse Representations
Zhuang, L., & Bioucas-Dias, J. M. (2018) · IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing · doi:10.1109/jstars.2018.2796570 · Cited by 363
A review on medical image denoising algorithms
Mohd Sagheer, S. V., & George, S. N. (2020) · Biomedical Signal Processing and Control · doi:10.1016/j.bspc.2020.102036 · Cited by 316
Bearing fault diagnosis based on SVD feature extraction and transfer learning classification
Shen, F., Chen, C., Yan, R., & Gao, R. X. (2015) · 2015 Prognostics and System Health Management Conference (PHM) · doi:10.1109/phm.2015.7380088 · Cited by 119
Metadata
- Authors
- Rajwade, A., Rangarajan, A., & Banerjee, A.
- Venue
- IEEE Transactions on Pattern Analysis and Machine Intelligence
- Published
- 2013-04
- Volume
- 35
- Issue
- 4
- Pages
- 849-862
- ISSN
- 0162-8828 (ISSN-L)
- 2160-9292
- OpenAlex
- W2154011501
- Cited by
- 375
- References
- 43
- FWCI
- 21.97
- 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
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.
