Abstract
Poisson noise suppression is a challenging and important preprocessing stage for higher level image analysis. Therefore, in this paper, a new attempt has been made using telegraph equation and variational theory for Poisson noise suppression. The proposed approach enjoys the benefits of both telegraph-diffusion equation and Hessian edge detector, which is not only robust to noise but also preserves image structural details. The Hessian function has been used to distinguish between edges and noise. However, to the best of author’s knowledge, the Hessian edge detector driven telegraph-diffusion scheme has not been used before for Poisson noise suppression. With the proposed model, restoration is carried out on several natural images. The experimental results of proposed model are found better in terms of noise suppression and detail/edge preservation, with respect to the existing approaches.
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References
Weickert, J.: Anisotropic Diffusion in Image Processing, vol. 1. Teubner, Stuttgart (1998)
Aubert, G., Kornprobst, P.: Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus of Variations, vol. 147. Springer, Berlin (2006)
Le, T., Chartrand, R., Asaki, T.J.: A variational approach to reconstructing images corrupted by poisson noise. J. Math. Imaging Vis. 27(3), 257–263 (2007)
Srivastava, R., Srivastava, S.: Restoration of poisson noise corrupted digital images with nonlinear pde based filters along with the choice of regularization parameter estimation. Pattern Recognit. Lett. 34(10), 1175–1185 (2013)
Gong, Z., Shen, Z., Toh, K.C.: Image restoration with mixed or unknown noises. Multiscale Model. Simul. 12(2), 458–487 (2014)
Liu, H., Zhang, Z., Xiao, L., Wei, Z.: Poisson noise removal based on nonlocal total variation with eulers elastica pre-processing. J. Shanghai Jiaotong Univ. (Sci.) 22(5), 609–614 (2017)
Perona, P., Malik, J.: Scale-space and edge detection using anisotropic diffusion. IEEE Trans. Pattern Anal. Mach. Intell. 12(7), 629–639 (1990)
Srivastava, R., Gupta, J., Parthasarathy, H.: Enhancement and restoration of microscopic images corrupted with poisson’s noise using a nonlinear partial differential equation-based filter. Def. Sci. J. 61(5) (2011)
Zhou, W., Li, Q.: Adaptive total variation regularization based scheme for poisson noise removal. Math. Methods Appl. Sci. 36(3), 290–299 (2013)
Rudin, L.I., Osher, S., Fatemi, E.: Nonlinear total variation based noise removal algorithms. Phys. D: Nonlinear Phenom. 60(1), 259–268 (1992)
Ratner, V., Zeevi, Y.Y.: Image enhancement using elastic manifolds. In: 14th International Conference on Image Analysis and Processing. ICIAP 2007, pp. 769–774. IEEE (2007)
Jain, S.K., Ray, R.K.: Edge detectors based telegraph total variational model for image filtering. Information Systems Design and Intelligent Applications, pp. 119–126. Springer, Berlin (2016)
Thomas, J.W.: Numerical Partial Differential Equations: Finite Difference Methods, vol. 22. Springer, Berlin (1995)
Wang, Z., Bovik, A.C.: Mean squared error: love it or leave it? a new look at signal fidelity measures. IEEE Signal Process. Mag. 26(1), 98–117 (2009)
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Jain, S.K., Yadav, J., Rao, M., Sharma, M., Ray, R.K. (2020). A Nonlinear Telegraph Equation for Edge-Preserving Image Restoration. In: Das, A., Nayak, J., Naik, B., Pati, S., Pelusi, D. (eds) Computational Intelligence in Pattern Recognition. Advances in Intelligent Systems and Computing, vol 999. Springer, Singapore. https://doi.org/10.1007/978-981-13-9042-5_71
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DOI: https://doi.org/10.1007/978-981-13-9042-5_71
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