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CLC number: O241.82

On-line Access: 2020-06-12

Received: 2020-02-10

Revision Accepted: 2020-04-01

Crosschecked: 2020-05-06

Cited: 0

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Citations:  Bibtex RefMan EndNote GB/T7714


Xing-ran Liao


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Frontiers of Information Technology & Electronic Engineering  2020 Vol.21 No.6 P.856-865


An improved ROF denoising model based on time-fractional derivative

Author(s):  Xing-ran Liao

Affiliation(s):  School of Mathematics, Sichuan University, Chengdu 610065, China

Corresponding email(s):   xrliao_scu@163.com

Key Words:  Improved ROF denoising model, Time-fractional derivative, Caputo derivative, Image denoising

Xing-ran Liao. An improved ROF denoising model based on time-fractional derivative[J]. Frontiers of Information Technology & Electronic Engineering, 2020, 21(6): 856-865.

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T1 - An improved ROF denoising model based on time-fractional derivative
A1 - Xing-ran Liao
J0 - Frontiers of Information Technology & Electronic Engineering
VL - 21
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PB - Zhejiang University Press & Springer
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In this study, we discuss mainly the image denoising and texture retention issues. Usually, the time-fractional derivative has an adjustable fractional order to control the diffusion process, and its memory effect can nicely retain the image texture when it is applied to image denoising. Therefore, we design a new Rudin-Osher-Fatemi model with a time-fractional derivative based on a classical one, where the discretization in space is based on the integer-order difference scheme and the discretization in time is the approximation of the caputo derivative (i.e., Caputo-like difference is applied to discretize the caputo derivative). Stability and convergence of such an explicit scheme are analyzed in detail. We prove that the numerical solution to the new model converges to the exact solution with the order of O(τ2−α+h2), where τ, α, and h are the time step size, fractional order, and space step size, respectively. Finally, various evaluation criteria including the signal-to-noise ratio, feature similarity, and histogram recovery degree are used to evaluate the performance of our new model. Numerical test results show that our improved model has more powerful denoising and texture retention ability than existing ones.





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[1]Abirami A, Prakash P, Thangavel K, 2018. Fractional diffusion equation-based image denoising model using CN-GL scheme. Int J Comput Math, 95(6-7):1222-1239.

[2]Bai J, Feng XC, 2018. Image denoising using generalized anisotropic diffusion. J Math Imag Vis, 60(7):994-1007.

[3]Bergounioux M, Piffet L, 2010. A second-order model for image denoising. Set-Valued Var Anal, 18(3-4):277-306.

[4]Blomgren P, Chan TF, Mulet P, et al., 1997. Total variation image restoration: numerical methods and extensions. Proc Int Conf on Image Processing, p.384-387.

[5]Bredies K, Kunisch K, Pock T, 2010. Total generalized variation. SIAM J Imag Sci, 3(3):492-526.

[6]Knoll F, Bredies K, Pock T, et al., 2011. Second order total generalized variation (TGV) for MRI. Mag Reson Med, 65(2):480-491.

[7]Podlubny I, 1998. Fractional Differential Equations. Academic Press, Cambridge, USA.

[8]Rosen JB, 1961. The gradient projection method for nonlinear programming. Part II. Nonlinear constraints. J Soc Ind Appl Math, 9(4):514-532.

[9]Rudin LI, Osher S, Fatemi E, 1992. Nonlinear total variation based noise removal algorithms. Phys D, 60(1-4):259- 268.

[10]Vogel CR, 2002. Computational Methods for Inverse Problems. SIAM, Philadelphia, USA.

[11]Wu GC, Baleanu D, Bai YR, 2019. Discrete fractional masks and their applications to image enhancement. In: Bǎleanu D, Lopes AM (Eds.), Applications in Engineering, Life and Social Sciences, Part B. De Gruyter, Berlin, Boston, p.261-270.

[12]Zhang L, Zhang L, Mou XQ, et al., 2011. FSIM: a feature similarity index for image quality assessment. IEEE Trans Imag Process, 20(8):2378-2386.

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