Abstract
Previous studies have shown that multi-way Wiener filtering improves the restoration of tensors impaired by an additive white Gaussian noise. Multi-way Wiener filtering is based on the distinction between noise and signal subspaces. In this paper, we show that the lower is the signal subspace dimension, the better is the restored tensor. To reduce the signal subspace dimension, we propose a method based on array processing technique to estimate main orientations in a flattened tensor. The rotation of a tensor of its main orientation values permits to concentrate the information along either rows or columns of the flattened tensor. We show that multi-way Wiener filtering performed on the rotated noisy tensor enables an improved recovery of signal tensor. Moreover, we propose in this paper a quadtree decomposition to avoid a blurry effect in the recovered tensor by multi-way Wiener filtering. We show that this proposed block processing reduces the whole blur and restores local characteristics of the signal tensor. Thus, we show that multi-way Wiener filtering is significantly improved thanks to rotations of the estimated main orientations of tensors and a block processing approach.
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References
Kroonenberg P. (1983). Three-mode principal component analysis. DSWO press, Leiden
Kiers H.A.L. (2000). Towards a standardized notation and terminology in multiway analysis. J. Chemom. 14: 105–122
Alex, M., Vasilescu, O., Terzopoulos, D.: Multilinear analysis of image ensembles: Tensorfaces (2002)
De Lathauwer L., De Moor B. and Vandewalle J. (2000). A multilinear singular value decomposition. SIAM J. Matrix Anal. Appl. 21: 1253–1278
Muti D. and Bourennane S. (2007). Survey on tensor signal algebraic filtering. Signal Process. 87: 237–249
Muti D. and Bourennane S. (2005). Multidimensional filtering based on a tensor approach. Signal Process. 85: 2338–2353
Aghajan H.K. and Kailath T. (1993). Sensor array processing techniques for super resolution multi-line-fitting and straight edge detection. IEEE Trans. Image Process. 2(4): 454–465
Sheinvald J. and Kiriati N. (1997). On the magic of SLIDE. Mach. vision Appl. 9: 251–261
Bourennane, S., Marot, J.: Contour estimation by array processing methods. Appl. signal process. Article ID 95634, 15 (2006)
Tucker L. (1966). Some mathematical notes on three-mode factor analysis. Psychometrika 31: 279–311
Zhang T. and Golub G. (2001). Rank-one approximation to high order tensor. SIAM J. Matrix Anal. Appl. 23(2): 534–550
Muti, D., Bourennane, S., Guillaume, M.: SVD based image filtering improvement by means of image rotation. In: Proc. ICASSP (2004)
Duda R.O. and Hart P.E. (1972). Use of the Hough transform to detect lines and curves in pictures. Commun. ACM 15: 11–15
Niblack, W., Petkovic, D.: On improving the accuracy of the Hough transform: theory, simulations and experiments. IEEE Trans. Comput. Vision Pattern Recognit. CVRP’88, pp. 574–579 (1988)
Vaisey, D.J., Gersho, A.: Variable block-size image coding. IEEE Int. Conf. ASSP, pp. 25.1–25.4 (1987)
Saupe D. and Jacob S. (1987). Variance-based quadtrees in fractal image compression. Electron. Lett. 33(1): 46–48
Samet H. (1984). The quadtree and related hierarchical data structure. ACM Comput. Surveys 16(2): 188–260
Bourennane S. and Marot J. (2006). Estimation of straight line offsets by a high resolution method. IEEE Proc. Vision Image Signal Process. 153(2): 224–229
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Letexier, D., Bourennane, S. & Blanc-Talon, J. Main flattening directions and Quadtree decomposition for multi-way Wiener filtering. SIViP 1, 253–265 (2007). https://doi.org/10.1007/s11760-007-0022-7
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DOI: https://doi.org/10.1007/s11760-007-0022-7