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Performance Analysis of Adaptive Variable Exponent Based Total Variation Image Regularization Algorithm

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Computer, Communication, and Signal Processing (ICCCSP 2022)

Abstract

In this paper, a new adaptive variable exponent based total variation image regularization algorithm is proposed. In the proposed algorithm a regularizing term based on variable exponent is used. The model adaptively switches between TV-ROF model and Tikhonov model. At the edges the model behaves like a ROF model preserving edges effectively. In the inner region the model behaves like a Tikhonov model which enables strong smoothing. The weight of the fidelity term is also adaptive. The weight is large at edges and small in the constant flat area. In this paper the performance of proposed adaptive variable exponent based total variation model is compared with TV-ROF model and Tikhonov model. The performance of the proposed model is compared with other classical diffusion algorithms such as perona-malik model and self-snake model. In addition the proposed model is also compared with nonlocal means filter. The performance of the proposed algorithm is validated by denoising rician noise corrupted brain magnetic resonance images as well as denoising salt and pepper noise corrupted standard images.

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References

  1. Chan, T., Shen, J., Vese, L.: Variational PDE models in image processing. https://doi.org/10.21236/ada437477

  2. Wang, Y.Y., Wu, S.Y.: Adaptive image denoising approach based on generalized Lp norm variational model. Appl. Mech. Mater. 556–562, 4851–4855 (2014). https://doi.org/10.4028/www.scientific.net/amm.556-562.4851

  3. Chen, D., Chen, Y.Q., Xue, D.: Fractional-order total variation image denoising based on proximity algorithm. Appl. Math. Comput. 257, 537–545 (2015). https://doi.org/10.1016/j.amc.2015.01.012

  4. Chen, Q., Montesinos, P., Sun, Q.S., Heng, P.A., Xia, D.S.: Adaptive total variation denoising based on difference curvature. Image Vision Comput. 28(3), 298–306 (2010)

    Article  Google Scholar 

  5. Liu, K., Tan, J., Su, B.: An adaptive image denoising model based on tikhonov and TV regularizations. Adv. Multimedia 2014, Article ID 934834 (2014)

    Google Scholar 

  6. Osher, S., Burger, M., Goldfarb, D., Xu, J., Yin, W.: An iterative regularization method for total variation based on image restoration. Multiscale Model. Simul. 4(2), 460–489 (2005)

    Article  MathSciNet  Google Scholar 

  7. Nikolova, M.: Minimizers of cost-functions involving non smooth data-fidelity terms. SIAM J. Numer. Anal. 40(3), 965–994 (2002)

    Article  MathSciNet  Google Scholar 

  8. Chan, T., Esedoglu, S.: Aspects of total variation regularized L1 function approximation. SIAM J. Appl. Math. 65(5), 1817–1837 (2005)

    Article  MathSciNet  Google Scholar 

  9. Esedoglu, S., Osher, S.: Decomposition of images by the anisotropic Rudin–Osher–Fatemi model. Commun. Pure Appl. Math. 57(12), 1609–1626 (2004)

    Article  MathSciNet  Google Scholar 

  10. Blomgren, P., Mulet, P., Chan, T., Wong, C.: Total variation image restoration numerical methods and extensions. In: ICIP, Santa Barbara, pp. 384–387 (1997)

    Google Scholar 

  11. Gilboa, G., Zeevi, Y.Y., Sochen, N.: Texture preserving variational denoising using an adaptive fidelity term. In: Proceedings of the VLSM, Nice, France, pp. 137–144 (2003)

    Google Scholar 

  12. Blomgren, P., Chan, T.F., Mulet, P.: Extensions to total variation denoising. In: Proceedings of SPIE, San Diego, vol. 3162 (1997)

    Google Scholar 

  13. Yadav, R.B., Srivastava, S., Srivastava, R.: A partial differential equation based general framework adapted to Rayleigh’s, Rician’s, and Gaussian’s distributed noise for restoration and enhancement of magnetic resonance image. J. Med. Phys. 41(4), 254–265 (2016)

    Article  Google Scholar 

  14. Kamalaveni, V., Veni, S., Narayanankutty, K.A.: Improved self-snake based anisotropic diffusion model for edge preserving image denoising using structure tensor. Multimedia Tools Appl. 76(18), 18815–18846 (2017)

    Article  Google Scholar 

  15. Yuan, Q., Zhang, L., Shen, H.: Hyperspectral image denoising employing a spectral–spatial adaptive total variation model. IEEE Trans. Geosci. Remote Sens. 50(10), 3660–3677 (2012)

    Article  Google Scholar 

  16. Kamalaveni, V., Narayanankutty, K.A., Veni, S.: Performance comparison of total variation based image regularization algorithms. Int. J. Adv. Sci. Eng. Inf. Technol. 6(4), 419–425 (2016)

    Article  Google Scholar 

  17. Yang, J., et al.: An efficient TV-L1 algorithm for deblurring multichannel images corrupted by impulsive noise. SIAM J. Sci. Comput. 31(4), 2842–2865 (2009)

    Article  MathSciNet  Google Scholar 

  18. Beck, A., Teboulle, M.: Fast gradient-based algorithms for constrained total variation image denoising and deblurring problems. IEEE Trans. Image Process. 18(11), 2419–2434 (2009)

    Article  MathSciNet  Google Scholar 

  19. Wang, Y., Zhou, H.: Total variation wavelet based medical image denoising. Int. J. Biomed. Imaging (2006)

    Google Scholar 

  20. Rudin, I., Osher, S., Fatemi, E.: Nonlinear total variation based noise removal algorithms. Phys. D Nonlinear Phenom. 60(1), 259–268 (1992)

    Article  MathSciNet  Google Scholar 

  21. Yang, F., Chen, K., Yu, B.: Adaptive second order variational model for image denoising. Int. J. Numer. Anal. Model. 5(1), 85–98 (2014)

    Google Scholar 

  22. Chopra, A., Lian, H.: Total Variation, adaptive total variation, and nonconvex smoothly clipped absolute deviation penalty for denoising blocky images. Pattern Recognit. 43(8), 2609–2619 (2010)

    Article  Google Scholar 

  23. Guo, L., Chen, W., Liao, Y., Liao, H., Li, J.: An edge-preserved an image denoising algorithm based on local adaptive regularization. J. Sens. 2016, Article ID 2019569 6 p. (2016). https://doi.org/10.1155/2016/2019569

  24. Chan, T.F., Chen, K., Tai, X.C.: Nonlinear multilevel schemes for solving the total variation image minimization problem. In: Tai, X.C., Lie, K.A., Chan, T.F., Osher, S. (eds.) Image Processing Based on Partial Differential Equations. Mathematics and Visualization, pp. 265–288. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-33267-1_15

    Chapter  Google Scholar 

  25. You, Y.L., Kavesh, M.: Fourth-order partial differential equations for noise removal. IEEE Trans. Image Process. 9(10), 1723–1730 (2000)

    Article  MathSciNet  Google Scholar 

  26. Charbonnier, P., Blanc-Feraud, L., Aubert, G., Barlaud, M.: Deterministic edge preserving regularization in computed imaging. IEEE Trans. Image Process. 6(2), 298–311 (1997)

    Article  Google Scholar 

  27. Guo, Z., Sun, J., Zhang, D., Wu, B.: Adaptive Perona–Malik model based on the variable exponent for image denoising. IEEE Trans. Image Process. 21(3), 958–967 (2012)

    Article  MathSciNet  Google Scholar 

  28. Wang, Y.Q., Guo, J., Chen, W., Zhang, W.: Image denoising using modified Perona-Malik model based on directional laplacian. Signal Process. 93, 2548–2558 (2013)

    Article  Google Scholar 

  29. Tang, L., Fang, Z.: Edge and contrast preserving in total variation image denoising. EURASIP J. Adv. Signal Process. 2016(1), 1–21 (2016). https://doi.org/10.1186/s13634-016-0315-5

    Article  MathSciNet  Google Scholar 

  30. Buades, A., et al.: A non-local algorithm for image denoising. In: Proceeding CVPR 2005 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, vol. 2, pp. 60–65 (2005)

    Google Scholar 

  31. Kumar, S.S., Mohan, N., Prabaharan, P., Soman, K.P.: Total variation denoising based approach for R-peak detection in ECG signals. Procedia Comput. Sci. 93, 697–705 (2016). https://doi.org/10.1016/j.procs.2016.07.26

    Article  Google Scholar 

  32. Karthik, S., Hemanth, V.K., Soman, K.P., Balaji, V., Kumar, S., Manikandan, M.S.: Directional total variation filtering based image denoising method. Int. J. Comput. Sci. 9(2), 1694–1814 (2012)

    Google Scholar 

  33. Rosso, F.: Performance evaluation of noise reduction filters for color images through normalized color difference (NCD) decomposition. ISRN Mach. Vis. 2014, Article ID 579658 (2014)

    Google Scholar 

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Correspondence to V. Kamalaveni .

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Kamalaveni, V., Veni, S., Narayanankuttty, K.A. (2022). Performance Analysis of Adaptive Variable Exponent Based Total Variation Image Regularization Algorithm. In: Neuhold, E.J., Fernando, X., Lu, J., Piramuthu, S., Chandrabose, A. (eds) Computer, Communication, and Signal Processing. ICCCSP 2022. IFIP Advances in Information and Communication Technology, vol 651. Springer, Cham. https://doi.org/10.1007/978-3-031-11633-9_11

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  • DOI: https://doi.org/10.1007/978-3-031-11633-9_11

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