Volume 15, Issue 2 (9-2018)                   JSDP 2018, 15(2): 17-30 | Back to browse issues page

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Bagherzadeh H, Harati A, Amiri Z, KamyabiGol R. Video Denoising Using block Shearlet Transform. JSDP. 2018; 15 (2) :17-30
URL: http://jsdp.rcisp.ac.ir/article-1-547-en.html
Ferdowsi university of mashhad
Abstract:   (636 Views)

Parabolic scaling and anisotropic dilation form the core of famous multi-resolution transformations such as curvelet and shearlet, which are widely used in signal processing applications like denoising. These non-adaptive geometrical wavelets are commonly used to extract structures and geometrical features of multi-dimensional signals and preserve them in noise removal treatments. In discrete setups, it is shown that shearlets can outperform other rivals since in addition to scaling, they are formed by shear operator which can fully remain on integer grid. However, the redundancy of multidimensional shearlet transform exponentially grows with respect to the number of dimensions which in turn leads to the exponential computational and space complexity. This, seriously limits the applicability of shearlet transform in higher dimensions. In contrast, separable transforms process each dimension of data independent of other dimensions which result in missing the informative relations among different dimensions of the data.
Therefore, in this paper a modified discrete shearlet transform is proposed which can overcome the redundancy and complexity issues of the classical transform. It makes a better tradeoff between completeness of the analysis achieved by processing full relations among dimensions on one hand and the redundancy and computational complexity of the resulting transform on the other hand. In fact, how dilation matrix is decomposed and block diagonalized, gives a tuning parameter for the amount of inter dimension analysis which may be used to control computation complexity and also redundancy of the resultant transform.
In the context of video denoising, three different decompositions are proposed for 3x3 dilation matrix. In each block diagonalization of this dilation matrix, one dimension is separated and the other two constitute a 2D shearlet transform. The three block shearlet transforms are computed for the input data up to three levels and the resultant coefficients are treated with automatically adjusted thresholds. The output is obtained via an aggregation mechanism which combine the result of reconstruction of these three transforms. Using experiments on standard set of videos at different levels of noise, we show that the proposed approach can get very near to the quality of full 3D shearlet analysis while it keeps the computational complexity (time and space) comparable to the 2D shearlet transform.

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Type of Study: Applicable | Subject: Paper
Received: 2017/10/6 | Accepted: 2018/05/16 | Published: 2018/09/16 | ePublished: 2018/09/16

1. [1] N. Kingsbury, "Adaptive Wavelet Thresholding for Image Denoising and Compression," IEEE TRANSACTIONS ON IMAGE PROCESSING, vol. 9, no. 9, pp. 1532-1546, 2000. [DOI:10.1109/83.862633] [PMID]
2. [2] G. Gao, "Image denoising by non-subsampled shearlet domain multivariate model and its method noise thresholding," Optik, vol. 124, no. 22, pp. 5756-5760, 2013. [DOI:10.1016/j.ijleo.2013.04.014]
3. [3] S. Hauser and G. Steidl, "Convex Multiclass Segmentation with Shearlet Regularization," International Journal of Computer Mathe-matics, vol. 90, no. 1, pp. 62-81, 2013. [DOI:10.1080/00207160.2012.688960]
4. [4] S. Liu, S. Hu and Y. Xiao, "Image separation using wavelet-complex shearlet dictionary," Journal of Systems Engineering and Electronics, vol. 25, no. 2, pp. 314-321, 2014. [DOI:10.1109/JSEE.2014.00036]
5. [5] G. Easley, D. Labate and W. Q. Lim, "Sparse Directional Image Representations using the Discrete Shearlet Transform," Applied and Computational Harmonic Analysis, vol. 25, no. 1, pp. 25-46, 2008. [DOI:10.1016/j.acha.2007.09.003]
6. [6] P. S. Negi and D. Labate, "3-D Discrete Shearlet Transform and Video Processing," IEEE Trans-action on Image Processing, vol. 21, no. 6, pp. 2944-2954, 2012. [DOI:10.1109/TIP.2012.2183883] [PMID]
7. [7] D. L. Donoho and M. R. Duncan, "Digital Curvelet Transform: Strategy, Implementation and Experiments," Proc. SPIE 4056, Wavelet Applications VII, pp. 12-29, 2000.
8. [8] E. J. Candes and D. L. Donoho, "New tight frames of curvelets and optimal representation of objects with piecewise C^2 singularities," Comm. Pure and Appl. Math., vol. 56, pp. 216-266, 2004.
9. [9] E. J. Candes, L. Demanet, D. L. Donoho and L. Ying, "Fast Discrete Curvelet Transforms," SIAM Multiscale Model, vol. 5, no. 3, pp. 861-899, 2006. [DOI:10.1137/05064182X]
10. [10] A. Lisowska, Geometrical Multiresolution Adaptive Transforms: Theory and Applications, Springer International Publishing, 2014. [DOI:10.1007/978-3-319-05011-9]
11. [11] J. L. Strack, F. Murtagh and J. M. Fadili, Sparse Image and Signal Processing, Cambridge Uni-versity Press, 2010. [DOI:10.1017/CBO9780511730344]
12. [12] M. N. Do and M. Vetterli, "The finite ridgelet transform for image representation," IEEE Transactions on Image Processing, vol. 12, no. 1, pp. 16-28, 2003. [DOI:10.1109/TIP.2002.806252] [PMID]
13. [13] J. Ma and G. Plonka, "A review of curvelets and recent applications," IEEE Signal Processing Magazine, 2009.
14. [14] D. Labate, W. Q. Lim, G. Kutyniok and G. Weiss, "Sparse multidimensional representation using shearlets," Wavelets XI, Proceedings of the SPIE, pp. 254-262, 2005.
15. [15] S. Yi, D. Labate, G. R. Easley and H. Krim, "A Shearlet Approach to Edge Analysis and Detection," IEEE Transaction on Image Proce-ssing, vol. 18, no. 5, pp. 929 - 941, 2009. [DOI:10.1109/TIP.2009.2013082] [PMID]
16. [16] S. Dahlke and G. Teschke, "The continuous shearlet transform in higher dimensions: varia-tions of a theme," Group Theory: Classes, Repr-esentation and Connections, and Appli-cations, vol. 1, pp. 167-175, 2010.
17. [17] P. Grohs and G. Kutyniok, "Parabolic mol-ecules," Foundations of Computational Math-ematics, vol. 14, no. 2, pp. 229-337, 2013.
18. [18] P. Grohs, S. Keiper, G. Kutyniok and M. Schafer, "α-Molecules," in Seminar for Applied Mathemetics, 2014.

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