Abstract
In this paper, we address the problem of dictionary learning for sparse representation. Considering the regularized form of the dictionary learning problem, we propose a method based on a homotopy approach, in which the regularization parameter is overall decreased along iterations. We estimate the value of the regularization parameter adaptively at each iteration based on the current value of the dictionary and the sparse coefficients, such that it preserves both sparse coefficients and dictionary optimality conditions. This value is, then, gradually decreased for the next iteration to follow a homotopy method. The results show that our method has faster implementation compared to recent dictionary learning methods, while overall it outperforms the other methods in recovering the dictionaries.
This work was partially funded by European project 2012-ERC-AdG-320684 CHESS.
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References
Aharon, M., Elad, M., Bruckstein, A.: K-SVD: an algorithm for designing of overcomplete dictionaries for sparse representation. IEEE Trans. Sig. Process. 54, 4311–4322 (2006)
Efron, B., Hastie, T., Johnstone, I., Tibshirani, R., et al.: Least angle regression. Ann. Stat. 32(2), 407–499 (2004)
Elad, M.: Sparse and redundant representations: from theory to applications in signal and image processing. Springer, New York (2010)
Elad, M., Aharon, M.: Image denoising via sparse and redundant representations over learned dictionaries. IEEE Trans. Image Process. 15, 3736–3745 (2006)
Engan, K., Aase, S.O., Hakon-Husoy, J.H.: Method of optimal directions for frame design. In: IEEE International Conference on Acoustics, Speech and Signal Processing, vol. 5, pp. 2443–2446 (1999)
Jafari, M., Plumbley, M.: Fast dictionary learning for sparse representations of speech signals. IEEE Sel. Top. Sign. Process. 5, 1025–1031 (2011)
Kreutz-Delgado, K., Murray, J.F., Rao, B.D., Engan, K., Lee, T., Sejnowski, T.: Dictionary learning algorithms for sparse representation. Neural Comput. 15(2), 349–396 (2003)
Liao, S.: Homotopy analysis method in nonlinear differential equations. Springer, Heidelberg (2012)
Mancera, L., Portilla, J.: Non-convex sparse optimization through deterministic annealing and applications. In: 15th IEEE International Conference on Image Processing, pp. 917–920 (2008)
Pati, Y., Rezaiifar, R., Krishnaprasad, P.: Orthogonal matching pursuit: recursive function approximation with applications to wavelet decomposition. In: 27th Annual Asilomar Conference Signals, Systems and Computers vol. 1, pp. 40–44 (1993)
Smith, L.N., Elad, M.: Improving dictionary learning: multiple dictionary updates and coefficient reuse. IEEE Signal Process. Lett. 20(1), 79–82 (2013)
Wright, S.J., Nowak, R.D., Figueiredo, M.: Sparse reconstruction by separable approximation. IEEE Trans. Signal Process. 57(7), 2479–2493 (2009)
Yaghoobi, M., Blumensath, T., Davies, M.E.: Dictionary learning for sparse approximations with the majorization method. IEEE Trans. Signal Process. 57(6), 2178–2191 (2009)
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Niknejad, M., Sadeghi, M., Babaie-Zadeh, M., Rabbani, H., Jutten, C. (2015). A Dictionary Learning Method for Sparse Representation Using a Homotopy Approach. In: Vincent, E., Yeredor, A., Koldovský, Z., Tichavský, P. (eds) Latent Variable Analysis and Signal Separation. LVA/ICA 2015. Lecture Notes in Computer Science(), vol 9237. Springer, Cham. https://doi.org/10.1007/978-3-319-22482-4_31
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DOI: https://doi.org/10.1007/978-3-319-22482-4_31
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