PDE-based hyperbolic-parabolic model for image denoising with forward-backward diffusivity

Kumar, Santosh; Alam, Khursheed

doi:10.22034/cmde.2020.37139.1646

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	PDE-based hyperbolic-parabolic model for image denoising with forward-backward diffusivity
Computational Methods for Differential Equations
مقاله 12، دوره 9، شماره 4، دی 2021، صفحه 1100-1108 اصل مقاله (1.6 M)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2020.37139.1646
نویسندگان
Santosh Kumar^* ؛ Khursheed Alam
Department of Mathematics, School of Basic Sciences and Research, Sharda University Greater Noida-201310, UP, India.
چکیده
In the present study, we propose an effective nonlinear anisotropic diffusion-based hyperbolic parabolic model for image denoising and edge detection. The hyperbolicparabolic model employs a second-order PDEs and has a second-time derivative to time t. This approach is very effective to preserve sharper edges and better-denoised images of noisy images. Our model is well-posed and it has a unique weak solution under certain conditions, which is obtained by using an iterative finite difference explicit scheme. The results are obtained in terms of peak signal to noise ratio (PSNR) as a metric, using an explicit scheme with forward-backward diffusivities.
کلیدواژه‌ها
Image denoising؛ Nonlinear hyperbolic-parabolic equation؛ Nonlinear diffusion equation؛ Explicit scheme؛ Forward-backward diffusivity

مراجع
[1] L. Alvarez, P. L. Lions, and J. M. Morel, Image selective smoothing and edge detection by nonlinear diffusion II∗, SIAM J. Numer. Anal., 29(3) (1992), 845–866. DOI: 10.1137/0729052 [2] L. Alvarez and L. Mazorra, Signal and image restoration using shock filters and anisotropic diffusion, SIAM J. Numer. Anal., 31(2) (1994), 590–605. DOI: 10.2307/2158018 [3] T. Barbu, Additive Noise Removal using a Nonlinear Hyperbolic PDE-based Model, 14th Inter- national Conference on Development and application systems, Suceava, Romania, May 24-26, 2018. DOI: 10.1109/DAAS.2018.8396061 [4] Y. Cao, J. Yin, Q. Liu, and M. Li, A class of nonlinear parabolic-hyperbolic equations applied to image restoration, Nonlinear Analysis: Real World Applications, 11 (2010), 253-261. DOI: 10.1016/j.nonrwa.2008.11.004 [5] P. Charbonnier, L. Blanc-Feraud, G. Aubert, and M. Barlaud, Two deterministic half-quadratic regularization algorithms for computed imaging, in Proceedings of IEEE International Confer- ence on Image Processing, 2 (1994), 168–172. DOI: 10.1109/ICIP.1994.413553 [6] T. F. Chan, G. H. Golub, and P. Mulet, A nonlinear primal-dual method for total variation-based image restoration, SIAM J. Sci. Comput., 20(6) (1999), 1964–1977. DOI: 10.1137/S1064827596299767 [7] F. Catte, P. L. Lions, J. M. Morel, and T. Coll, Image selective smoothing and edge detection by nonliear diffusion⋆, SIAM J. Numer. Anal., 29(1) (1992), 182–193. DOI: 10.1137/0729052 [8] Q. Chang and Chern I-Liang, Acceleration methods for total variation-based image denoising, SIAM J. Sci. Comput., 25(3) (2003), 982–994. DOI: 10.1137/S106482750241534X [9] T.F. Chan, A. Marquina, and P. Mulet, High-order total variation-based image restoration, SIAM J. Sci. Comput.,22(2) (2000) 503–516. DOI: 10.1137/S1064827598344169 [10] Q. Chang and Z. Hcrang, Efficient algebraic multigrid algorithms and their convergence, SIAM J. Sci. Comput., 24 (2004) 597–618. DOI: 10.1137/S1064827501389850 [11] K. Chen, Introduction to variational image-processing models and applications, International Journal of Computer Mathematics, 90 (2013), 1–8. DOI: 10.1080/00207160.2012.757073 [12] K. Chen, Adaptive smoothing via contextual and local discontinuities, IEEE Trans- actions Pattern Analysis and Machine Intelligence, 27(10) (2005) 1552–1567. DOI: 10.1109/TPAMI.2005.190 [13] B. Ghanbari, L. Rada, and K. Chen, A restarted iterative homotopy analysis method for two nonlinear models from image processing, International Journal of Computer Mathematics, 91 (2014), 661–687. DOI: 10.1080/00207160.2013.807340 [14] G. Gilboa, N. Sochen, and Y. Y. Zeevi, Image enhancement and denoising by complex dif- fusion process, IEEE Trans. Pattern Anal. Machine Intell., 26(8) (2004), 1020–1036. DOI: 10.1109/TPAMI.2004.47 [15] Z. Guo, J. Sun, D. Zhang, and B. Wu, Adaptive Perona-Malik model based on the variable exponent for image denoising, IEEE Transactions on Image Processing, 21(3) (2012), 58–67. DOI: 10.1109/TIP.2011.2169272 [16] M. Hajiaboli, M. Ahmad, and C. Wang, An edge-adapting Laplacian kernel for nonlin- ear diffusion filters, IEEE Transactions on Image Processing, 21(4) (2012), 1561-1572. DOI: 10.1109/TIP.2011.2172803 [17] K. Krissian, C. F. Westin, R. Kikinis, and K. Vosburgh, Oriented speckle reducing anisotropic diffusion, IEEE Transactions on Image Processing, 16(5) (2007), 1412-24. DOI: 10.1109/TIP.2007.891803 [18] S. Kim and K. Joo, PDE-based image restoration: a hybrid model and color image denoising, IEEE Transactions on Image Processing, 15 (2006), 1163–1170. DOI: 10.1109/TIP.2005.864184 [19] S. Kumar and M. K. Ahmad, A time-dependent model for image denoising, Journal of Signal and Information Processing, 6 (2015), 28-38. DOI: 10.4236/jsip.2015.61003 [20] S. Kumar, M. Sarfaraz, and M. K. Ahmad, An efficient PDE-based nonlinear anisotropic dif- fusion model for image denoising, Neural, Parallel and Scientific Computations, 24 (2016), 305–315. [21] S. Kumar, M. Sarfaraz, and M. K. Ahmad, Denoising method based on wavelet coefficients via diffusion equation, Iranian Journal of Science and Technology, Transactions A: Science, 42 (2018), 721–726. DOI: 10.1007/s40995-017-0228-7 [22] L. Lapidus and G. F. Pinder, Numerical solution of partial differential equations in science and engineering, SIAM Review, 25(4) (1983), 581–582. [23] M. Lysaker, A. Lundervold, and X. C. Tai, Noise removal using fourth-order partial differential equation with applications to medical magnetic resonance images in space and time, IEEE Tran. Image Process., 12(12) (2003), 1579–1590. DOI: 10.1109/TIP.2003.819229 [24] A. Marquina and S. Osher, A new time dependent model based on level set motion for nonlin- ear deblurring and noise removal. Scale-Space Theories in Computer Vision, Lecture Notes in Computer Science, 1682 (1999), 429-434. [25] P. Perona and J. Malik, Scale space and edge detection using anisotropic diffusion, IEEE Transactions on Pattern Analysis and Machine Intelligence, 12(7) (1990), 629–639. DOI: 10.1109/34.56205 [26] Q. Qiang, Z. A. Yao, and Y. Y. Ke, Entropy solutions for a fourth-order nonlinear de- generate problem for noise removal, Nonlinear Anal. TMA, 67(6) (2007), 1908–1918. DOI: 10.1016/j.na.2006.08.016 [27] L. I. Rudin, S. Osher, and E. Fatemi, Nonlinear total variation based noise removal algorithms, Physica D, 60 (1992), 259–268. DOI: 10.1016/0167-2789(92)90242-F [28] V. Ratner and Y. Y. Zeevi, Image enhancement using elastic manifolds, 14th International Con- ference on Image Analysis and Processing, 2007, 769–774. DOI: 10.1109/ICIAP.2007.4362869 [29] J. Sun, J. Yang, and L. Sun, A class of hyperbolic-parabolic coupled systems applied to image restoration, Boundary Value Problems, 187 (2016). DOI: 10.1186/s13661-016-0696-2 [30] C. R. Vogel and M. E. Oman, Iterative methods for total variation denoising, SIAM J. Sci. Comput., 17(1) (1996), 227–238. DOI: 10.1137/0917016 [31] M. Welk, D. Theis, T. Brox, and J. Weickert, PDE-based deconvolution with fordward-backward diffusivities and diffusion tensors. In scale space, LNCS, Springer Berlin, (2005) 585–597. DOI: 10.1007/114080315 [32] J. Weickert, A Review of nonlinear diffusion filtering, In Scale Space, LNCS, Springer Berlin, 1252 (1997), 1–28. DOI: 10.1007/3-540-63167-437
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PDE-based hyperbolic-parabolic model for image denoising with forward-backward diffusivity