Abstract
The K-COD (K-Complete Orthogonal Decomposition) algorithm for generating adaptive dictionary for signals sparse representation in the framework of K-means clustering is proposed in this paper, in which rank one approximation for components assembling signals based on COD and K-means clustering based on chaotic random search are well utilized. The results of synthetic test and empirical experiment for the real data show that the proposed algorithm outperforms recently reported alternatives: K-Singular Value Decomposition (K-SVD) algorithm and Method of Optimal Directions (MOD) algorithm.
Similar content being viewed by others
References
D. L. Donoho, M. Elad, and V. N. Temlyakov, Stable recovery of sparse overcomplete representations in the presence of noise. IEEE Transactions on Information Theory, 52(2006)1, 6–18.
J. Chen and X. M. Huo. Theoretical results on sparse representations of multiple-measurement vectors. IEEE Transactions on Signal Processing, 54(2006)12, 4634–4643.
M. Akcakaya and V. Tarokh. A frame construction and a universal distortion bound for sparse representations. IEEE Transactions on Signal Processing, 56(2008)6, 2443–2450.
S. G. Mallat and Z. F. Zhang. Matching pursuits with time-frequency dictionaries. IEEE Transactions on Signal Processing, 41(1993)12, 3397–3415.
J. A. Tropp. Greed is Good: algorithmic results for sparse approximation. IEEE Transactions on Information Theory, 50(2004)10, 2231–2242.
M. S. Lewicki and T. J. Sejnowski. Learning overcomplete representations. Neural Computation, 12 (2000), 337–365.
D. L. Donoho and X. M. Huo, Uncertainty principles and ideal atomic decomposition. IEEE Transactions on Information Theory, 47(2001)7, 2845–2862.
M. Akcakaya and V. Tarokh. Performance of sparse representation algorithms using randomly generated frames. IEEE Signal Processing Letters, 14(2007)11, 777–780.
K. Engan, S. O. Aase, and J. H. Husey. Method of optimal directions for frame design. Proceedings of IEEE International Conference on Acoustics, Speech, Signal Processing, Phoenix, AZ, USA, Mar. 15–19, 1999, Vol.5, 2443–2446.
R. Xu and D. Wunsch. Survey of clustering algorithms. IEEE Transactions on Neural Networks, 16(2005)3, 645–678.
D. B. Fogel. An introduction to simulated evolutionary optimization. IEEE Transactions on Neural Networks, 5(1994)1, 3–14.
S. Kirkpatrick, C. Gelatt, and M. Vecchi. Optimization by simulated annealing. Science, 220(1983)4598, 671–680.
M. W. Berry, S. T. Dumais, and G. W. O’Brien. Using linear algebra for intelligent information retrieval. SIAM Review, 37(1995), 573–595.
K. K. Delgado, J. F. Murray, B. D. Rao, K. Engan, and T. Lee. Dictionary learning algorithms for sparse representation. Neural Computation, 15(2003), 349–396.
K. Engan, S. O. Aase, and J. H. Husey. Multi-frame compression: theory and design. Signal Processing, 80(2000), 2121–2140.
M. Aharon, M. Elad, and A. Bruckstein. K-SVD: An Algorithm for Designing Overcomplete Dictionaries for Sparse Representation. IEEE Transactions on Signal Processing, 54(2006)11, 4311–4322.
M. Aharon and M. Elad. Image denoising via sparse and redundant representations over learned dictionaries. IEEE Transactions on Image Processing, 15(2006)12, 3736–3745.
J. A. Tropp and A. C. Gilbert. Signal recovery from random measurements via orthogonal matching pursuit. IEEE Transactions on Information Theory, 53(2007)12, 4655–4666.
Author information
Authors and Affiliations
Corresponding author
Additional information
Supported by the National Natural Science Foundation of China under Grants (No. 60872123 & U0835001), and by Natural Science Foundation of Guangdong Province, China (No. 07006496).
Communication author: Feng Jiuchao, born in 1964, male, Professor.
About this article
Cite this article
Xie, Z., Feng, J. An algorithm for dictionary generation in sparse representation. J. Electron.(China) 26, 836–841 (2009). https://doi.org/10.1007/s11767-008-0077-9
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11767-008-0077-9