Abstract
One-dimensional total variation (TV) regularization can be used for signal denoising. We consider one-dimensional signals distorted by additive white Gaussian noise. TV regularization minimizes a functional consisting of the sum of fidelity and regularization terms. We derive exact solutions to one-dimensional TV regularization problem that help us to recover signals with the proposed algorithm. The proposed approach to finding exact solutions has a clear geometrical meaning. Computer simulation results are provided to illustrate the performance of the proposed algorithm for signal denoising.
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References
Rudin, L., Osher, S., Fatemi, E.: Nonlinear total variation based noised removal algorithms. Phys. D. 60, 259–268 (1992)
Chambolle, A., Lions, P.L.: Image recovery via total variational minimization and related problems. Numer. Math. 76, 167–188 (1997)
Osher, S., Burger, M., Goldfarb, D., Xu, J., Yin, W.: An iterative regularization method for total variation based image restoration. Multiscale Model. Simul. 4, 460–489 (2005)
Chambolle, A.: An algorithm for total variation minimization and applications. J. Math. Imag. Vis. 20, 89–97 (2004)
Barbero, A., Sra, S.: Fast newton-type methods for total variation regularization. In: ICML (2011)
Combettes, P., Pesquet, J.: Proximal splitting methods in signal processing. In: Bauschke, H.H., Burachik, R.S., Combettes, P.L., Elser, V., Luke, D.R., Wolkowicz, H. (eds.) Fixed-Point Algorithms for Inverse Problems in Science and Engineering, vol. 49, pp. 185–212. Springer, New York (2011)
Wahlberg, B., Boyd, S., Annergren, M., Wang, Y.: An ADMM algorithm for a class of total variation regularized estimation problems. In: IFAC (2012)
Chambolle, A.: An algorithm for total variation minimization and applications. J. Math. Imag. Vis. 20(1), 89–97 (2004)
Yang, S., Wang, J., Fan, W., Zhang, X., Wonka, P., Ye, J.: An efficient ADMM algorithm for multidimensional anisotropic total variation regularization problems. In: Proceedings of the 19th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 641–649 (2013)
Strong, D.M., Chan, T.F.: Exact Solutions to Total Variation Regularization Problems, UCLA CAM Report (1996)
Strong, D.M., Chan, T.F.: Edge-preserving and scale-dependent properties of total variation regularization. Inverse Probl. 19, 165–187 (2003)
Condat, L.: A direct algorithm for 1-D total variation denoising. IEEE Signal Process. Lett. 20(11), 1054–1057 (2013)
Davies, P.L., Kovac, A.: Local extremes, runs, strings and multiresolution. Ann. Stat. 29(1), 1–65 (2001)
Makovetskii, A. Kober, V.: Modified gradient descent method for image restoration. In: Proceedings of SPIE Applications of Digital Image Processing XXXVI, vol. 8856 (2013). 885608-1
Makovetskii, A., Kober, V.: Image restoration based on topological properties of functions of two variables. In: Proceedings of SPIE Applications of Digital Image Processing XXXV, vol. 8499 (2012). 84990A
Acknowledgments
The work was supported by the Ministry of Education and Science of Russian Federation (grant 2.1766.2014К).
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Makovetskii, A., Voronin, S., Kober, V. (2017). An Efficient Algorithm for Total Variation Denoising. In: Ignatov, D., et al. Analysis of Images, Social Networks and Texts. AIST 2016. Communications in Computer and Information Science, vol 661. Springer, Cham. https://doi.org/10.1007/978-3-319-52920-2_30
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DOI: https://doi.org/10.1007/978-3-319-52920-2_30
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