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Unconstrained Structural Similarity-Based Optimization

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

Abstract

We establish a general framework, along with a set of algorithms, for the incorporation of the Structural Similarity (SSIM) quality index measure as the fidelity, or “data fitting,” term in objective functions for optimization problems in image processing. The motivation for this approach is to replace the widely used Euclidean distance, known as a poor measure of visual quality, by the SSIM, which has been recognized as one of the best measures of visual closeness. Some experimental results are also presented.

Keywords

Visual Quality Human Visual System Tikhonov Regularization Coordinate Descent Structural Similarity Index Measure 
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.
    Albuquerque, G., Eisemann, M., Magnor, M.A.: Perception-based visual quality measures. In: 2011 IEEE Conference on Visual Analytics Science and Technology (VAST), pp. 13–20 (2011)Google Scholar
  2. 2.
    Brunet, D.: A Study of the Structural Similarity Image Quality Measure with Applications to Image Processing. Ph.D. Thesis, Department of Applied Mathematics, University of Waterloo (2012)Google Scholar
  3. 3.
    Brunet, D., Vrscay, E.R., Wang, Z.: Structural similarity-based approximation of signals and images using orthogonal bases. In: Campilho, A., Kamel, M. (eds.) ICIAR 2010. LNCS, vol. 6111, pp. 11–22. Springer, Heidelberg (2010) CrossRefGoogle Scholar
  4. 4.
    Brunet, D., Vrscay, E.R., Wang, Z.: On the mathematical properties of the structural similarity index. Proc. IEEE Trans. Image Processing 21(4), 1488–1499 (2012)MathSciNetCrossRefGoogle Scholar
  5. 5.
    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
  6. 6.
    Boyd, S., Vandenberghe, L.: Convex Optimization. Cambridge University Press (2004)Google Scholar
  7. 7.
    Channappayya, S.S., Bovik, A.C., Caramanis, C., Heath Jr, R.W.: Design of linear equalizers optimized for the structural similarity index. IEEE Transactions on Image Processing 17(6), 857–872 (2008)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Donoho, D.: Denoising by Soft-Thresholding. IEEE Transactions on Information Theory 41(3), 613–627 (1995)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Efron, B., Hastie, T., Johnstone, I., Tibshirani, R.: Least Angle Regression. The Annals of Statistics 32, 407–451 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Elad, M., Aharon, M.: Image denoising via sparse and redundant representations over learned dictionaries. IEEE Transactions on Image Processing 15(12), 3736–3745 (2006)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Mairal, J., Bach, F., Jenatton, R., Obozinski, G.: Convex Optimization with Sparsity-Inducing Norms. Optimization for Machine Learning. MIT Press (2011)Google Scholar
  12. 12.
    Ortega, J.M.: The Newton-Kantorovich Theorem. The American Mathematical Monthly 75(6), 658–660 (1968)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Rehman, A., Rostami, M., Wang, Z., Brunet, D., Vrscay, E.R.: SSIM-inspired image restoration using sparse representation. EURASIP J. Adv. Sig. Proc. (2012). doi: 10.1186/1687-6180-2012-16 Google Scholar
  14. 14.
    Rehman, A., Gao, Y., Wang, J., Wang, Z.: Image classification based on complex wavelet structural similarity. Sig. Proc. Image Comm. 28(8), 984–992 (2013)CrossRefGoogle Scholar
  15. 15.
    Tseng, P., Yun, S.: A Coordinate Gradient Descent Method for Non-smooth Separable Minimization. Journal of Mathematical Programming 117(1–2), 387–423 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    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
  17. 17.
    Wang, Z., Bovik, A.C.: A universal image quality index. IEEE Signal Processing Letters 9(3), 81–84 (2002)CrossRefGoogle Scholar
  18. 18.
    Wang, Z., Bovik, A.C., Sheikh, H.-R., Simoncelli, E.S.: Image quality assessment: From error visibility to structural similarity. IEEE Trans. Image Processing 13(4), 600–612 (2004)CrossRefGoogle Scholar
  19. 19.
    Wang, S., Rehman, A., Wang, Z., Ma, S., Gao, W.: SSIM-motivated rate-distortion optimization for video coding. IEEE Trans. Circuits Syst. Video Techn. 22(4), 516–529 (2012)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Department of Applied Mathematics, Faculty of MathematicsUniversity of WaterlooWaterlooCanada

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