Abstract
Analysis sparse model has been successfully used for a variety of tasks such as image denoising, deblurring, and most recently compressed sensing, so it arouses much attention. K-SVD is a mature dictionary learning approach for the analysis sparse model. However, it represents images as one dimension signals, which results in mistakes of spatial correlations. In this paper, we propose a novel analysis sparse model, where analysis dictionary derived from two analysis operators which act on an image, leading to a sparse outcome. And a two dimensional K-SVD (2D-KSVD) is proposed to train the analysis sparse dictionaries. Experiments on image denoising validate that the proposed analysis dictionary can express more image spatial and frequency characteristics and by using the dictionary, the two dimension analysis sparse model outperforms the traditional analysis model in terms of PSNR.
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References
Bruckstein, A.M., Donoho, D.L., Elad, M.: From sparse solutions of systems of equations to sparse modeling of signals and images. SIAM Review 51(1), 34–81 (2009)
Horev, I., Bryt, O., Rubinstein, R.: Adaptive image compression using sparse dictionaries. In: 2012 19th International Conference on Systems Signals and Image Processing, IWSSIP, pp. 592–595 (2012)
Yang, J.C., John, W., Ma, Y., Huang, T.: Image super-resolution as a sparse representation of raw image patches. In: Proceedings of IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2008, Anchorage, Alaska, pp. 333–340 (2008)
Aharon, M., Elad, M., Bruckstein, A.: K-SVD: an algorithm for designing overcomplete dictionaries for sparse representation. IEEE Transactions on Signal Processing 54(11), 4311–4322 (2006)
Elad, M., Milanfar, P., Rubinstein, R.: Analysis versus synthesis in signal priors. Inverse Problems 23(3), 947–968 (2007)
Nam, S., Davies, M.E., Elad, M., Gribonval, R.: Cosparse analysis modeling-uniqueness and algorithms. In: 2011 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP, pp. 5804–5807 (2011)
Selesnick, I.W., Figueiredo, M.A.T.: Signal restoration with overcomplete wavelet transforms: comparison of analysis and synthesis priors. In: Proc. SPIE, Wavelets XIII, vol. 7446, p. 74460D (September 04, 2009), doi:10.1117/12.826663
Portilla, J.: Image restoration through L0 analysis-based sparse optimization in tight frames. In: Proceedings of the 2009 16th IEEE International Conference on Image Processing, ICIP 2009, pp. 3909–3912 (2009)
Nam, S., Davies, M.E., Elad, M., Gribonval, R.: The Cosparse Analysis Model and Algorithms. To Appear in Applied and Computational Harmonic Analysis (2012), http://www.cs.technion.ac.il/~elad/publications/journals/
Ophir, B., Elad, M., Bertin, N., Plumbley, M.D.: Sequential minimal eigenvalues – an approach to analysis dictionary learning. In: Proceedings of EUSIPCO (2011)
Rubinstein, R., Peleg, T., Elad, M.: K-SVD Dictionary Learning for the Analysis Co-Sparse Model. In: ICASSP, Kyoto, Japan, March 25-30 (2012)
Rubinstein, R., Peleg, T., Elad, M.: Analysis K-SVD: A Dictionary-Learning Algorithm for the Analysis Sparse Model. Submitted to IEEE Trans. on Signal Processing (2012), http://www.cs.technion.ac.il/~elad/publications/journals/
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Shi, Y., Qi, N., Yin, B., Ding, W. (2012). Two Dimensional K-SVD for the Analysis Sparse Dictionary. In: Lin, W., et al. Advances in Multimedia Information Processing – PCM 2012. PCM 2012. Lecture Notes in Computer Science, vol 7674. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34778-8_81
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DOI: https://doi.org/10.1007/978-3-642-34778-8_81
Publisher Name: Springer, Berlin, Heidelberg
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