The DOI matches its Crossref record; 1 of the 1 references it cites were found in a registry or an index.
Comparing Measures of Sparsity
Abstract
Sparsity of representations of signals has been shown to be a key concept of fundamental importance in fields such as blind source separation, compression, sampling and signal analysis. The aim of this paper is to compare several commonly-used sparsity measures based on intuitive attributes. Intuitively, a sparse representation is one in which a small number of coefficients contain a large proportion of the energy. In this paper, six properties are discussed: (Robin Hood, Scaling, Rising Tide, Cloning, Bill Gates, and Babies), each of which a sparsity measure should have. The main contributions of this paper are the proofs and the associated summary table which classify commonly-used sparsity measures based on whether or not they satisfy these six propositions. Only two of these measures satisfy all six: the pq-mean with p les 1, q > 1 and the Gini index.
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Cites
Sparse Representation for Color Image Restoration
Mairal, J., Elad, M., & Sapiro, G. (2008) · IEEE Transactions on Image Processing · doi:10.1109/tip.2007.911828 · Cited by 1,716
Cited by
Blind deconvolution using a normalized sparsity measure
Krishnan, D., Tay, T., & Fergus, R. (2011) · CVPR 2011 · doi:10.1109/cvpr.2011.5995521 · Cited by 1,119
Erion, G., Janizek, J. D., Sturmfels, P., Lundberg, S. M., & Lee, S.-I. (2021) · Nature Machine Intelligence · doi:10.1038/s42256-021-00343-w · Cited by 300
Improvement of kurtosis-guided-grams via Gini index for bearing fault feature identification
Miao, Y., Zhao, M., & Lin, J. (2017) · Measurement Science and Technology · doi:10.1088/1361-6501/aa8a57 · Cited by 282
Wirth, S., Baraduc, P., Planté, A., Pinède, S., & Duhamel, J.-R. (2017) · PLOS Biology · doi:10.1371/journal.pbio.2001045 · Cited by 129
Condran, S., Bewong, M., Islam, M. Z., Maphosa, L., & Zheng, L. (2022) · IEEE Access · doi:10.1109/access.2022.3188649 · Cited by 99
Metadata
- Authors
- Hurley, N., & Rickard, S.
- Venue
- IEEE Transactions on Information Theory
- Published
- 2009-10
- Volume
- 55
- Issue
- 10
- Pages
- 4723-4741
- ISSN
- 0018-9448 (ISSN-L)
- 1557-9654
- OpenAlex
- W2111854888
- Cited by
- 757
- References
- 1
- FWCI
- 13.49
- Type
- journal article
- Language
- en
- Open access
- closed
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