Abstract
In this paper, a novel data-driven sparse coding framework is proposed to solve image restoration problem based on a robust empirical mode decomposition. This powerful analysis tool for multi-dimensional signals can adaptively decompose images into multiscale oscillating components according to intrinsic modes of data self. This treatment can obtain very effective sparse representation, and meanwhile generates a dictionary at multiple geometric scales and frequency bands. The distribution of sparse coefficients is reliably approximated by generalized Gaussian model. Moreover, a sparse approximation of blur kernel is also obtained as a strong prior. Finally, latent image and blur kernel can be jointly estimated via alternating optimization scheme. The extensive experiments show that our approach can effectively and efficiently recover the sharpness of local structures and suppress undesirable artifacts.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Figueiredo, M., Bioucas-Dias, J., Nowak, R.: Majorization-minimization algorithms for wavelet-based image restoration. IEEE Trans. Image Process. 16(12), 2980–2991 (2007)
Dong, W., Shi, G., Ma, Y., Li, X.: Image restoration via simultaneous sparse coding: where structured sparsity meets Gaussian scale mixture. Int. J. Comput. Vis. 114(2), 217–232 (2015)
Elad, M., Figueiredo, M., Ma, Y.: On the role of sparse and redundant representations in image processing. Proc. IEEE 98, 972–982 (2010)
Levin, A., Weiss, Y., Durand, F., Freeman, T.: Efficient marginal likelihood optimization in blind deconvolution. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp. 2657–2664 (2011)
Papyan, V., Elad, M.: Multi-scale patch-based image restoration. IEEE Trans. Image Process. 25(1), 249–261 (2016)
Ram, I., Cohen, I., Elad, M.: Patch-ordering-based wavelet frame and its use in inverse problems. IEEE Trans. Image Process. 23(7), 2779–2792 (2014)
Cai, J., Ji, H., Liu, C., Shen, Z.: High-quality curvelet-based motion deblurring from an image pair. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp. 1566–1573 (2009)
Cai, J., Ji, H., Liu, C., Shen, Z.: Framelet-based blind motion deblurring from a single image. IEEE Trans. Image Process. 21(2), 562–572 (2012)
Zhang, Y., Hirakawa, K.: Blur processing using double discrete wavelet transform. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp. 1091–1098 (2013)
Quan, Y., Ji, H., Shen, Z.: Data-driven multi-scale non-local wavelet frame construction and image recovery. J. Sci. Comput. 63(2), 307–329 (2015)
Chen, R., Jia, Z., Xie, X., Gao, W.: A structure-preserving image restoration method with high-level ensemble constraints. In: Proceedings of the IEEE Conference on Visual Communications and Image Processing (VCIP), pp. 1–4 (2016)
Huang, N., Shen, Z., Long, S., et al.: The empirical model decomposition and Hilbert spectrum for nonlinear and nonstationary time series analysis. Proc. R. Soc. A 454(1971), 903–995 (1998)
Hou, T., Shi, Z.: Data-driven time-frequency analysis. Appl. Comput. Harmon. Anal. 35(2), 284–308 (2013)
Pattichis, M., Bovik, A.: Analyzing image structure by multidimensional frequency modulation. IEEE Trans. Patt. Anal. Mach. Intell. 29(5), 753–766 (2007)
Wu, Z., Huang, N., Chen, X.: The multi-dimensional ensemble empirical mode decomposition method. Adv. Adapt. Data Anal. 1(3), 339–372 (2009)
Bhuiyan, S., Atton-Okine, N., Barner, K., Ayenu-Prah, A., Adhami, R.: Bidimensional empirical mode decomposition using various interpolation techniques. Adv. Adapt. Data Anal. 1(2), 309–338 (2009)
Daubechies, I., Lu, J., Wu, H.: Synchrosqueezed wavelet transforms: an empirical mode decomposition-like tool. Appl. Comput. Harmon. Anal. 30(2), 243–261 (2011)
Diop, E., Alexandre, R., Moisan, L.: Intrinsic nonlinear multiscale image decomposition: a 2D empirical mode decomposition-like tool. Comput. Vis. Image Und. 116(1), 102–119 (2012)
Gilles, J., Tran, G., Osher, S.: 2D empirical transform. wavelets, ridgelets, and curvelets revisited. SIAM J. Imaging Sci. 7(1), 157–186 (2014)
Hu, X., Peng, S., Hwang, W.: EMD revisited: a new understanding of the envelope and resolving the mode-mixing problem in AM-FM signals. IEEE Trans. Signal Process. 60(3), 1075–1086 (2012)
Park, M., Kim, D., Oh, H.: Quantile-based empirical mode decomposition: an efficient way to decompose noisy signals. IEEE Trans. Instrum. Meas. 64(7), 1802–1813 (2015)
Oberlin, T., Meignen, S., Perrier, V.: An alternative formulation for the empirical mode decomposition. IEEE Trans. Signal Process. 60(5), 2236–2246 (2012)
Subr, K., Soler, C., Durand, F.: Edge-preserving multiscale image decomposition based on local extrema. ACM Trans. Graph. 28(5), 1472–1479 (2009)
Sonogashira, M., Funatomi, T., Liyama, M., Minoh, M.: Variational Bayesian approach to multiframe image restoration. IEEE Trans. Image Process. 26(5), 2163–2178 (2017)
Zhong, L., Cho, S., Metaxas, D., Paris, S., Wang, J.: Handling noise in single image deblurring using directional filters. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp. 612–619 (2013)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG, part of Springer Nature
About this paper
Cite this paper
Chen, R., Jia, H., Xie, X., Wen, G. (2018). Sparsity-Promoting Adaptive Coding with Robust Empirical Mode Decomposition for Image Restoration. In: Zeng, B., Huang, Q., El Saddik, A., Li, H., Jiang, S., Fan, X. (eds) Advances in Multimedia Information Processing – PCM 2017. PCM 2017. Lecture Notes in Computer Science(), vol 10735. Springer, Cham. https://doi.org/10.1007/978-3-319-77380-3_36
Download citation
DOI: https://doi.org/10.1007/978-3-319-77380-3_36
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-77379-7
Online ISBN: 978-3-319-77380-3
eBook Packages: Computer ScienceComputer Science (R0)