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An Examination of Several Methods of Hyperspectral Image Denoising: Over Channels, Spectral Functions and Both Domains

  • Daniel OteroEmail author
  • Oleg V. Michailovich
  • Edward R. Vrscay
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8814)

Abstract

The corruption of hyperspectral images by noise can compromise tasks such as classification, target detection and material mapping. For this reason, many methods have been proposed to recover, as best as possible, the uncorrupted hyperspectral data from a given noisy observation. In this paper, we propose and compare the results of four denoising methods which differ in the way the hyperspectral data is treated: (i) as 3D data sets, (ii) as collections of frequency bands and (iii) as collections of spectral functions. In the case of additive noise, these methods can be easily adapted to accommodate different degradation models. Our methods and results help to address the question of how hyperspectral data sets should be processed in order to obtain useful denoising results.

Keywords

Spectral Function Sparse Representation Hyperspectral Image Spectral Domain Hyperspectral Data 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
  2. 2.
    Amir Beck, A., Teboulle, M.: A fast iterative shrinkage-thresholding algorithm for linear inverse problems. SIAM Journal on Imaging Sciences Archive 2(1), 183–202 (2009)CrossRefzbMATHGoogle Scholar
  3. 3.
    Bioucas-Dias, J.M., Nascimento, J.M.P.: Hyperspectral Subspace Identification. IEEE Trans. Geoscience and Remote Sensing 46, 2435–2445 (2008)CrossRefGoogle Scholar
  4. 4.
    Boyd, S.P., Parikh, N., Chu, E., Peleato, B., Eckstein, J.: Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers. Foundations and Trends in Machine Learning 3, 1–122 (2011)CrossRefGoogle Scholar
  5. 5.
    Bresson, X., Chan, T.: Fast Dual Minimization of the Vectorial Total Variation Norm and Applications to Color Image Processing. Inverse Problems and Imaging 2(4), 455–484 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Chambolle, A.: An algorithm for total variation minimization and applications. Journal of Mathematical Imaging and Vision 20(1–2), 89–97 (2004)MathSciNetGoogle Scholar
  7. 7.
    Chan, T., Shen, J.: Image Processing and Analysis. Society for Industrial and Applied Mathematics, Philadelphia (2005)CrossRefzbMATHGoogle Scholar
  8. 8.
    Chang, Y., Yan, L., Fang, H., Liu, H.: Simultaneous Destriping and Denoising for Remote Sensing Images With Unidirectional Total Variation and Sparse Representation. IEEE Geoscience and Remote Sensing Letters 11(6), 1051–1055 (2014)CrossRefGoogle Scholar
  9. 9.
    Chen, G., Qian, S.E.: Denoising of Hyperspectral Imagery Using Principal Component Analysis and Wavelet Shrinkage. IEEE Trans. Geoscience and Remote Sensing 49, 973–980 (2011)CrossRefGoogle Scholar
  10. 10.
    Donoho, D.: Denoising by Soft-Thresholding. IEEE Trans. Information Theory 41(3), 613–627 (1995)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Donoho, D., Johnstone, I.M.: Adapting to Unknown Smoothness Via Wavelet Shrinkage. J. of the Amer. Stat. Assoc. 90(432), 1220–1224 (1995)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Donoho, D., Johnstone, I.M., Kerkyacharian, G., Picard, D.: Wavelet shrinkage: asymptopia. Journal of the Royal Statistical Society, Ser. B, 371–394 (1995)Google Scholar
  13. 13.
    Elad, M., Aharon, M.: Image denoising via sparse and redundant representations over learned dictionaries. IEEE Trans. Image Proc. 15(12), 3736–3745 (2006)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Goldlücke, B., Strekalovskiy, E., Cremers, D.: The Natural Vectorial Total Variation Which Arises from Geometric Measure Theory. SIAM J. Imaging Sciences 5, 537–563 (2012)CrossRefzbMATHGoogle Scholar
  15. 15.
    Goldstein, T., Osher, S.: The Split Bregman Method for \(\ell _1\)-Regularized Problems. SIAM J. Imaging Sciences 2, 323–343 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
  17. 17.
    Mairal, J., Bach, F., Jenatton, R., Obozinski, G.: Convex Optimization with Sparsity-Inducing Norms. Optimization for Machine Learning. MIT Press (2011)Google Scholar
  18. 18.
    Martín-Herrero, J.: Anisotropic Diffusion in the Hypercube. IEEE Trans. Geoscience and Remote Sensing 45, 1386–1398 (2007)CrossRefGoogle Scholar
  19. 19.
    Othman, H., Qian, S.E.: Noise Reduction of Hyperspectral Imagery Using Hybrid Spatial-Spectral Derivative-Domain Wavelet Shrinkage. IEEE Trans. Geoscience and Remote Sensing 44, 397–408 (2006)CrossRefGoogle Scholar
  20. 20.
    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)CrossRefGoogle Scholar
  21. 21.
    Rasti, B., Sveinsson, J.R., Ulfarsson, M.O., Benediktsson, J.A.: Hyperspectral image denoising using 3D wavelets. In: 2012 IEEE International Geoscience and Remote Sensing Symposium (IGARSS), pp. 1349–1352 (2012)Google Scholar
  22. 22.
    Rudin, L., Osher, S., Fatemi, E.: Nonlinear total variation based noise removal algorithms. Physica D: Nonlinear Phenomena 60(1–4), 259–268 (1992)CrossRefzbMATHGoogle Scholar
  23. 23.
    Shippert, P.: Why use Hyperspectral imaging? Photogrammetric Engineering and Remote Sensing, 377–380 (2004)Google Scholar
  24. 24.
    Turlach, B.A.: On algorithms for solving least squares problems under an \(\ell _1\) penalty or an \(\ell _1\) constraint. In: Proceedings of the American Statistical Association, Statistical Computing Section, pp. 2572–2577 (2005)Google Scholar
  25. 25.
    Wang, Z., Bovik, A.C., Sheikh, H.R., Simoncelli, E.P.: Image Quality Assessment: from Error Visibility to Structural Similarity. IEEE Trans. Image Processing 13, 600–612 (2004)CrossRefGoogle Scholar
  26. 26.
    Yuan, Q., Zhang, L., Shen, H.: Hyperspectral Image Denoising Employing a Spectral-Spatial Adaptive Total Variation Model. IEEE Trans. Geoscience and Remote Sensing 50, 3660–3677 (2012)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Daniel Otero
    • 1
    Email author
  • Oleg V. Michailovich
    • 2
  • Edward R. Vrscay
    • 1
  1. 1.Department of Applied Mathematics, Faculty of MathematicsUniversity of WaterlooWaterlooCanada
  2. 2.Department of Electrical and Computer Engineering, Faculty of EngineeringUniversity of WaterlooWaterlooCanada

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