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Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 328))

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Abstract

In this paper we propose and compare the use of two iterative solvers using the Crank-Nicolson finite difference method, for image denoising via Partial differential equations (PDE) models such as Bilateral-filter-based model. The solvers considered here are: Successive-over-Relaxation (SOR) and an advanced solver known as Hybrid Bi-Conjugate Gradient Stabilized (Hybrid BiCGStab) method. We demonstrate that proposed hybrid BiCGStab solver for denoising yields better performance in terms of MSSIM and PSNR, and is more efficient than existing SOR solver and a state-of-the-art approach.

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References

  1. Witkin, A.P.: Scale-space filtering: A new approach to multi-scale description. In: IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 1984, vol. 9, pp. 150–153. IEEE (1984)

    Google Scholar 

  2. Perona, P., Malik, J.: Scale-space and edge detection using anisotropic diffusion. IEEE Transactions on Pattern Analysis and Machine Intelligence 12(7), 629–639 (1990)

    Article  Google Scholar 

  3. Weickert, J.: Anisotropic diffusion in image processing, vol. 1. Teubner Stuttgart (1998)

    Google Scholar 

  4. Kichenassamy, S.: The perona–malik paradox. SIAM Journal on Applied Mathematics 57(5), 1328–1342 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  5. Catté, F., Lions, P.L., Morel, J.M., Coll, T.: Image selective smoothing and edge detection by nonlinear diffusion. SIAM Journal on Numerical analysis 29(1), 182–193 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  6. Bazan, C., Blomgren, P.: Image smoothing and edge detection by nonlinear diffusion and bilateral filter. In: CSRCR 2007, vol. 21, pp. 2–15 (2007)

    Google Scholar 

  7. Bazán, C., Miller, M., Blomgren, P.: Structure enhancement diffusion and contour extraction for electron tomography of mitochondria. Journal of Structural Biology 166(2), 144–155 (2009)

    Article  Google Scholar 

  8. Gh, M., Bazan, C., Frey, G.: olume se spatia esholdin xtraction (2010)

    Google Scholar 

  9. Weickert, J., Romeny, B.T.H., Viergever, M.A.: Efficient and reliable schemes for nonlinear diffusion filtering. IEEE Transactions on Image Processing 7(3), 398–410 (1998)

    Article  Google Scholar 

  10. Thomas, J.W.: Numerical partial differential equations: finite difference methods, vol. 22. Springer (1995)

    Google Scholar 

  11. Wang, W., Shi, Y.: An image denoising algorithm in the matrix form. In: 2011 International Conference on Multimedia Technology (ICMT), pp. 176–179. IEEE (2011)

    Google Scholar 

  12. Crank, J., Nicolson, P.: A practical method for numerical evaluation of solutions of partial differential equations of the heat-conduction type. Advances in Computational Mathematics 6(3), 207–226 (1996)

    Article  MathSciNet  Google Scholar 

  13. Saad, Y.: Iterative methods for sparse linear systems, 2nd edn. SIAM, Philadelphia (2003)

    Google Scholar 

  14. Sickel, S., Yeung, M.C., Held, M.J.: A comparison of some iterative methods in scientific computing. Summer Reserch Apprentice Program (2005)

    Google Scholar 

  15. Sleijpen, G.L., Van der Vorst, H.A.: Hybrid bi-conjugate gradient methods for cfd problems. Computational Fluid Dynamics Review 1995, 457–476 (1995)

    Google Scholar 

  16. Mrázek, P., Navara, M.: Selection of optimal stopping time for nonlinear diffusion filtering. International Journal of Computer Vision 52(2-3), 189–203 (2003)

    Article  Google Scholar 

  17. Wang, Z., Bovik, A.C., Sheikh, H.R., Simoncelli, E.P.: Image quality assessment: from error visibility to structural similarity. IEEE Transactions on Image Processing 13(4), 600–612 (2004)

    Article  Google Scholar 

  18. Wang, Z., Bovik, A.C.: Mean squared error: love it or leave it? a new look at signal fidelity measures. IEEE Signal Processing Magazine 26(1), 98–117 (2009)

    Article  Google Scholar 

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Correspondence to Subit K. Jain .

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Jain, S.K., Ray, R.K., Bhavsar, A. (2015). A Comparative Study of Iterative Solvers for Image De-noising. In: Satapathy, S., Biswal, B., Udgata, S., Mandal, J. (eds) Proceedings of the 3rd International Conference on Frontiers of Intelligent Computing: Theory and Applications (FICTA) 2014. Advances in Intelligent Systems and Computing, vol 328. Springer, Cham. https://doi.org/10.1007/978-3-319-12012-6_34

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  • DOI: https://doi.org/10.1007/978-3-319-12012-6_34

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-12011-9

  • Online ISBN: 978-3-319-12012-6

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