The DOI matches its Crossref record; 9 of the 9 references it cites were found in a registry or an index.
Dictionaries for Sparse Representation Modeling
Abstract
Sparse and redundant representation modeling of data assumes an ability to describe signals as linear combinations of a few atoms from a pre-specified dictionary. As such, the choice of the dictionary that sparsifies the signals is crucial for the success of this model. In general, the choice of a proper dictionary can be done using one of two ways: i) building a sparsifying dictionary based on a mathematical model of the data, or ii) learning a dictionary to perform best on a training set. In this paper we describe the evolution of these two paradigms. As manifestations of the first approach, we cover topics such as wavelets, wavelet packets, contourlets, and curvelets, all aiming to exploit 1-D and 2-D mathematical models for constructing effective dictionaries for signals and images. Dictionary learning takes a different route, attaching the dictionary to a set of examples it is supposed to serve. From the seminal work of Field and Olshausen, through the MOD, the K-SVD, the Generalized PCA and others, this paper surveys the various options such training has to offer, up to the most recent contributions and structures.
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Cites
Daubechies, I. (1992) · doi:10.1137/1.9781611970104 · Cited by 15,979
An algorithm for the machine calculation of complex Fourier series
Cooley, J. W., & Tukey, J. W. (1965) · Mathematics of Computation · doi:10.1090/s0025-5718-1965-0178586-1 · Cited by 13,154
Huber, P. J. (1981) · Wiley Series in Probability and Statistics · doi:10.1002/0471725250 · Cited by 7,066
The wavelet transform, time-frequency localization and signal analysis
Daubechies, I. (1990) · IEEE Transactions on Information Theory · doi:10.1109/18.57199 · Cited by 6,483
The Laplacian pyramid as a compact image code
Burt, P., & Adelson, E. (1983) · IEEE Transactions on Communications · doi:10.1109/tcom.1983.1095851 · Cited by 6,077
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
Daugman, J. G. (1985) · Journal of the Optical Society of America A · doi:10.1364/josaa.2.001160 · Cited by 3,219
Fast Discrete Curvelet Transforms
Candès, E., Demanet, L., Donoho, D., & Ying, L. (2006) · Multiscale Modeling & Simulation · doi:10.1137/05064182x · Cited by 2,573
Wedgelets: nearly minimax estimation of edges
Donoho, D. L. (1999) · The Annals of Statistics · doi:10.1214/aos/1018031261 · Cited by 638
Cited by
Shuman, D. I., Narang, S. K., Frossard, P., Ortega, A., & Vandergheynst, P. (2013) · IEEE Signal Processing Magazine · doi:10.1109/msp.2012.2235192 · Cited by 4,421
Nonlocally Centralized Sparse Representation for Image Restoration
Dong, W., Zhang, L., Shi, G., & Li, X. (2013) · IEEE Transactions on Image Processing · doi:10.1109/tip.2012.2235847 · Cited by 1,505
Standard Plane Localization in Fetal Ultrasound via Domain Transferred Deep Neural Networks
Chen, H., Ni, D., Qin, J., Li, S., Yang, X., Wang, T., & Heng, P. A. (2015) · IEEE Journal of Biomedical and Health Informatics · doi:10.1109/jbhi.2015.2425041 · Cited by 379
Vertex-frequency analysis on graphs
Shuman, D. I., Ricaud, B., & Vandergheynst, P. (2016) · Applied and Computational Harmonic Analysis · doi:10.1016/j.acha.2015.02.005 · Cited by 349
Xu, S., Ji, L., Wang, Z., Li, P., Sun, K., Zhang, C., & Zhang, J. (2020) · IEEE Transactions on Computational Imaging · doi:10.1109/tci.2020.3039564 · Cited by 47
Sparse dictionary learning recovers pleiotropy from human cell fitness screens
Pan, J., Kwon, J. J., Talamas, J. A., Borah, A. A., Vazquez, F., Boehm, J. S., Tsherniak, A., Zitnik, M., McFarland, J. M., & Hahn, W. C. (2022) · Cell Systems · doi:10.1016/j.cels.2021.12.005 · Cited by 37
Sparsity-Aware Learning and Compressed Sensing: An Overview
Theodoridis, S., Kopsinis, Y., & Slavakis, K. (2014) · Academic Press Library in Signal Processing · doi:10.1016/b978-0-12-396502-8.00023-1 · Cited by 14
Learning a Class-specific and Shared Dictionary for Classifying Surface Defects of Steel Sheet
Zhou, S., Chen, Y., Zhang, D., Xie, J., & Zhou, Y. (2017) · ISIJ International · doi:10.2355/isijinternational.isijint-2016-478 · Cited by 9
Metadata
- Authors
- Rubinstein, R., Bruckstein, A. M., & Elad, M.
- Venue
- Proceedings of the IEEE
- Published
- 2010-06
- Volume
- 98
- Issue
- 6
- Pages
- 1045-1057
- ISSN
- 0018-9219 (ISSN-L)
- 1558-2256
- OpenAlex
- W2163398148
- Cited by
- 1,306
- References
- 9
- FWCI
- 60.64
- Type
- journal article
- Language
- en
- Open access
- closed
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