Abstract
Recent studies have demonstrated that the Structural Similarity Index Measure (SSIM) is the top choice for quantifying both visual quality and image similarity. Although the SSIM is not convex, it has been successfully employed in a wide range of imaging tasks over the last years. In this paper, the authors propose a new method based on the Alternate Direction Method of Multipliers (ADMM) for solving an unconstrained SSIM-based optimization problem. We focus our analysis on the case in which the regularizing term is convex. The paper also includes numerical examples and experiments that showcase the effectiveness of the proposed method.
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Boyd, S., Vandenberghe, L.: Convex Optimization. Cambridge University Press, Cambridge (2004)
Boyd, S., Parikh, N., Chu, E., Peleato, B., Eckstein, J.: Distributed optimization and statistical learning via the alternating direction method of multipliers. Found. Trends Mach. Learn. 3, 1–122 (2010)
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). https://doi.org/10.1007/978-3-642-13772-3_2
Brunet, D., Vrscay, E.R., Wang, Z.: On the mathematical properties of the structural similarity index. IEEE Trans. Image Process. 21, 1488–1499 (2012)
Brunet, D., Channappayya, S., Wang, Z., Vrscay, E.R., Bovik, A.: Optimizing image quality. In: Handbook of Convex Optimization Methods in Imaging Science, pp. 15–41 (2017)
Chambolle, A.: An algorithm for total variation minimization and applications. J. Math. Imaging Vis. 20, 89–97 (2004)
Chambolle, A., Caselles, V., Cremers, D., Novaga, M., Pock, T.: An introduction to total variation for image analysis. Theor. Found. Numer. Methods Sparse Recover. 9, 263–340 (2010)
Chambolle, A., Pock, T.: A first-order primal-dual algorithm for convex problems with applications to imaging. J. Math. Imaging Vis. 40, 120–145 (2011)
Channappayya, S., Bovik, A.C., Caramanis, C., Heath Jr., R.W.: Design of linear equalizers optimized for the structural similarity index. IEEE Trans. Image Process. 17, 857–872 (2008)
Elad, M., Aharon, M.: Image denoising via sparse and redundant representations over learned dictionaries. IEEE Trans. Image Process. 15, 3736–3745 (2006)
Otero, D.: Function-valued mappings and SSIM-based optimization in imaging, Ph.D. thesis, University of Waterloo, Waterloo, ON, Canada (2015)
Otero, D., Vrscay, E.R.: Unconstrained structural similarity-based optimization. In: Campilho, A., Kamel, M. (eds.) ICIAR 2014. LNCS, vol. 8814, pp. 167–176. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-11758-4_19
Otero, D., Vrscay, E.R.: Solving optimization problems that employ structural similarity as the fidelity measure. In: Proceedings of the International on Image Processing, Computer Vision and Pattern Recognition, pp. 474–479. CSREA Press (2014)
Parikh, N., Boyd, S.: Proximal algorithms. Found. Trends Optim. 1, 123–231 (2013)
Rehman, A., Rostami, M., Wang, Z., Brunet, D., Vrscay, E.R.: SSIM-inspired image restoration using sparse representation. EURASIP J. Adv. Signal Process. 2012, 1–12 (2012)
Rehman, A., Gao, Y., Wang, J., Wang, Z.: Image classification based on complex wavelet structural similarity. Signal Process. Image Commun. 28, 984–992 (2013)
Shao, Y., Sun, F., Li, H., Liu, Y.: Structural similarity-optimal total variation algorithm for image denoising. In: Sun, F., Hu, D., Liu, H. (eds.) Foundations and Practical Applications of Cognitive Systems and Information Processing. AISC, vol. 215, pp. 833–843. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-642-37835-5_72
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, 516–529 (2012)
Wang, Z., Bovik, A.C.: A universal image quality index. IEEE Signal Process. Lett. 9, 81–84 (2002)
Wang, Z., Bovik, A.C., Sheikh, H.R., Simoncelli, E.P.: Image quality assessment: from error visibility to structural similarity. IEEE Trans. Image Process. 13, 600–612 (2004)
Acknowledgements
This work has been supported in part by Discovery Grants (ERV and OM) from the Natural Sciences and Engineering Research Council of Canada (NSERC). Financial support from the Faculty of Mathematics and the Department of Applied Mathematics, University of Waterloo (DO) is also gratefully acknowledged.
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Otero, D., Torre, D.L., Michailovich, O.V., Vrscay, E.R. (2018). Alternate Direction Method of Multipliers for Unconstrained Structural Similarity-Based Optimization. In: Campilho, A., Karray, F., ter Haar Romeny, B. (eds) Image Analysis and Recognition. ICIAR 2018. Lecture Notes in Computer Science(), vol 10882. Springer, Cham. https://doi.org/10.1007/978-3-319-93000-8_3
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DOI: https://doi.org/10.1007/978-3-319-93000-8_3
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