Abstract
This paper focuses on the denoising of multidimensional data by a tensor subspace-based method. In a seminal work, multiway Wiener filtering was developed to minimize the mean square error between an expected signal tensor and the estimated tensor. It was then placed in a wavelet framework. The reliable estimation of the subspace rank for each mode and wavelet decomposition level is still pending. For the first time in this paper, we aim at estimating the subspace ranks for all modes of the tensor data by minimizing a least squares criterion. To solve this problem, we adapt particle swarm optimization. An application involving an RGB image and hyperspectral images exemplifies our method: we compare the results obtained in terms of signal to noise ratio with a slice-by-slice ForWaRD denoising.
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References
Lin, T., Bourennane, S.: Hyperspectral image processing by jointly filtering wavelet component tensor. IEEE Transactions on Geoscience and Remote Sensing 51(6), 3529–3541 (2013)
Kerekes, J.P., Baum, J.E.: Full spectrum spectral imaging system analytical model. IEEE Trans. on Geosc. and Remote Sensing 43(3), 571–580 (2005)
Muti, D., Bourennane, S.: Multidimensional filtering based on a tensor approach. Elsevier Signal Proceesing Journal 85(12), 2338–2353 (2005)
Renard, N., Bourennane, S., Blanc-Talon, J.: Denoising and dimensionality reduction using multilinear tools for hyperspectral images. IEEE Geoscience and Remote Sensing Letters 5(2), 138–142 (2008)
Lin, T., Marot, J., Bourennane, S.: Small target detection improvement in hyperspectral image. In: Blanc-Talon, J., Kasinski, A., Philips, W., Popescu, D., Scheunders, P. (eds.) ACIVS 2013. LNCS, vol. 8192, pp. 460–469. Springer, Heidelberg (2013)
Kennedy, J., Eberhart, R.: Particle swarm optimization. In: IEEE International Conference on Neural Networks, Perth, pp. 1942–1948 (1995)
Neelamani, R., Choi, H., Baraniuk, R.: Forward: Fourier-wavelet regularized deconvolution for ill-conditioned systems. IEEE Trans. on Signal Processing 52(2), 418–433 (2004)
Muti, D., Bourennane, S., Marot, J.: Lower-rank tensor approximation and multiway filtering. SIAM Journal on Matrix Analysis and Applications 30(3), 1172–1204 (2008)
Parra, L., Spence, C., Sajda, P., Ziehe, A., Müller, K.: Unmixing hyperspectral data. In: Advances in Neural Information Processing Systems, vol. 12, pp. 942–948 (2000)
Liu, X., Bourennane, S., Fossati, C.: Nonwhite Noise Reduction in Hyperspectral Images. IEEE Geoscience and Remote Sensing Letters 9(3), 368–372 (2012)
Letexier, D., Bourennane, S., Blanc-Talon, J.: Main flattening directions and quadtree decomposition for multi-way wiener filtering. Signal, Image and Video Processing 1(3), 253–256 (2007)
Jones, D.R., Pertunen, C.D., Stuckman, B.E.: Lipschitzian optimization without the lipschitz constant. Journal of Optimization Theory and Application 79(1), 157–181 (1993)
Lagarias, J.C., Reeds, J.A., Wright, M.H., Wright, P.E.: Convergence properties of the nelder-mead simplex method in low dimensions. SIAM Journal of Optimization 9(1), 112–147 (1998)
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Marot, J., Bourennane, S. (2015). Improvement of a Wavelet-Tensor Denoising Algorithm by Automatic Rank Estimation. In: Battiato, S., Blanc-Talon, J., Gallo, G., Philips, W., Popescu, D., Scheunders, P. (eds) Advanced Concepts for Intelligent Vision Systems. ACIVS 2015. Lecture Notes in Computer Science(), vol 9386. Springer, Cham. https://doi.org/10.1007/978-3-319-25903-1_67
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DOI: https://doi.org/10.1007/978-3-319-25903-1_67
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