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Author(s): B. D. Patel1

Email(s): 1bdpatelcoer@gmail.com

Address:

    College of Engineering, Roorkee (COER), Roorkee, Uttarakhand 247667 India

Published In:   Volume - 1,      Issue - 1,     Year - 2021

DOI: Not Available

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ABSTRACT:
This paper generalizes the computational applicability of non-integer ordered derivative based PDE (Partial Differential Equation) in image restoration process. The fractional derivative of Riemann-Liouville form gives the several choices of fractional order in image de-noising. The fractional form of Euler Lagrange equation is the non-integer ordered generalization of gradient type equations which can be used in minimization problems. The Grunwald approximation discretizes the fractional PDE used in image restoration, which shows some satisfactory results.

Cite this article:
B. D. Patel (2021)Fractional PDE based Image Restoration using Grunwald Approximation, Spectrum of Emerging Sciences, 1(1), pp. 16-20.


[1]    P. Perona and J. Malik, Scale-space and edge detection using anisotropic diffusion, IEEE Trans. on Pattern Anal. Mach. Intell., 12 (1990), pp.629-639.

[2]    G. Aubert and P. Kornprobst, Mathematical Problems in Image Processing, no. 147 in Applied Mathematics Sciences, Springer-Verlag, New York, 2002.

[3]    P. V. Blomgren and T. F. Chan, Color TV: Total Variation Methods for Restoration of Vector Valued Images, IEEE Trans. Image Processing, 7 (1998),pp. 304-309.

[4]    F. Catte, P. Lions, M. Morel, and T. Coll, Image selective smoothing and edge detection by nonlinear diffusion., SIAM J. Numer. Anal., 29 (1992), pp. 182-193.

[5]    L. Rudin, S. Osher, and E. Fatemi, Nonlinear total variation based noise removal algorithms, Physica D, 60 (1992), pp.259-268.

[6]    Y. You, W. Xu, A. Tannenbaum, and M. Kaveh, Behavioral analysis of anisotropic diffusion in image processing, IEEE Trans. Image Process., 5 (1996), pp.1539-1553.

[7]    T. F. Chan and J. Shen, Variational restoration of non-flat image features: Models and algorithms, SIAM Journal of Applied Mathematics, 61 (2000),pp. 1338-1361.

[8]    A. Marquina and S. Osher, Explicit algorithms for a new time dependent model based on level set motion for nonlinear deblurring and noise removal, SIAM J. Sci. Comput., 22 (2000), pp. 387-405.

[9]    R. Weinstock, Calculus of Variations, Dover Pubilcations, Inc., New York,1974.

[10] G. Leibniz, Mathematische Schiften. Georg Olms Verlagsbuchhandlung, Hildesheim, 1962.

[11] K. Oldham and J. Spanier, The Fractional Calculus. New York . London: Academic Press, 1974.

[12] K. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations. New York: John Wiley & Sons Inc., 1993.

[13] M. Ortigueira, .Introduction to fractional linear systems. Part 1: Continuous-time case,. IEE Proceedings Vision,Image, Signal Processing, vol. 147, no. 1, pp. 62.70, 2000.

[14] I. Podlubny, Fractional Differential Equations. San Diego: Academic Press, 1999.

[15] L. Rudin and S. Osher, Total variation based image restoration with free local constraints, Proc. 1st IEEE ICIP, 1 (1994), pp.31-35.

[16] L. Rudin, S. Osher, and E. Fatemi, Nonlinear total variation based noise removal algorithms, Physica D, 60 (1992), pp.259-268.

[17] Carpinteri A and Mainardi F, Fractals and Fractional Calculus in Continuum Mechanics (New York :Springer), 1997.

[18] B. Baeumer, M. M. Meerschaert, Stochastic solutions for fractional Cauchy problems, Frac. Calc. Appl. Anal. 4, pp.481-500, 2001.

[19] M. M. Meerschaert, H. P. Scheffler, Semistable Levy Motion, Frac. Calc. Appl. Anal. 5, pp. 27-54, 2002.

[20] Avez A.,Calcul diff´erentiel, Masson,1983.

[21]  M. M. Meerschaert, C. Tadjeran, Finite difference approximations for fractional advection-dispersion flow equations, J. Comput. Appl. Math. 172, pp. 65-77, 2004.

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