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A Novel Image Denoising Algorithm Based on Riemann-Liouville Definition | HU | Journal of Computers
Journal of Computers, Vol 6, No 7 (2011), 1332-1338, Jul 2011
doi:10.4304/jcp.6.7.1332-1338

A Novel Image Denoising Algorithm Based on Riemann-Liouville Definition

Jinrong HU, Yifei Pu, Jiliu Zhou

Abstract


In this paper, a novel image denoising algorithm named fractional integral image denoising algorithm (FIIDA) is proposed, which based on fractional calculus Riemann-Liouville definition. The structures of n*n fractional integral masks of this algorithm on the directions of 135 degrees, 90 degrees, 45 degrees, 0 degrees, 180 degrees, 315 degrees, 270 degrees and 225 degrees are constructed and discussed. The denoising performance of FIIDA is measured using experiments according to subjective and objective standards of visual perception and PSNR values. The simulation results show that the FIIDA’s performance is prior to the Gaussian smoothing filter, especially when the noise standard deviation is less than 30.


Keywords


fractional calculus; fractional integral; fractional integral mask; image denoising; Gaussian smoothing filter

References


[1] “Special issue: Fractional signal processing and applications”, Signal Processing, 2003, 83(11):2285-2286.
http://dx.doi.org/10.1016/S0165-1684(03)00181-6

[2] K. B. Oldham, J Spanier. “The Fractional Calculus ”. New York: Academic Press, 1974.

[3] B. Mathieu, P. Melchior, A. Oustaloup. “Fractional differentiation for edge detection”. Signal Processing, 2003, 83(11):2421-2432.
http://dx.doi.org/10.1016/S0165-1684(03)00194-4

[4] YF Pu, JL Zhou, X Yuan. “Fractional differential mask: a fractional differential-based approach for multiscale texture enhancement”. IEEE Transactions on Image Processing, 2010, 19(2):491-511.
http://dx.doi.org/10.1109/TIP.2009.2035980
PMid:19933015

[5] Dennis M., Healy Jr. “Modern Signal Processing ”. London: Cambridge University Press, 2004.

[6] Namias V. “The fractional order Fourier transform and its application to quantum mechanics”. Inst Math Appl., 1980, 25:241-265.
http://dx.doi.org/10.1093/imamat/25.3.241

[7] McBride A C, Kerr F H. “On Namias’s fractional fourier transform”. IMA Journal of Applied Mathematics, 1987, 39: 159-175.
http://dx.doi.org/10.1093/imamat/39.2.159

[8] Y. Huang and B. Suter, “The fractional wave packet transform”. Multidimensional System Signal Process, 1998, 9 (4):399–402.
http://dx.doi.org/10.1023/A:1008414608970

[9] T. Blu and M. Unser, “The fractional spline wavelet transform: definition and implementation ”. Proceedings of the Twenty-Fifth IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP’00), vol. I Istanbul, Turkey, 2000, June 5–9:512–515.

[10] Feyel, D., and de La Pradelle, A.: “Fractional Integrals and Brownian Processes”, Potential Analysis, 1996, 10: 273-288.
http://dx.doi.org/10.1023/A:1008630211913

[11] Tatom F.B. “The Relationship between Fractional Calculus and Fractals”. Fractals, 1995, 3(1):217-229.
http://dx.doi.org/10.1142/S0218348X95000175

[12] Rocco Andrea, West Bruce. “Fractional calculus and the evolution of fractal phenomena”. Physical A, 1999, 265(3,4):535-546.

[13] E.R.Davies. “Machine Vision: Theory, Algorithms, Practicalities (3rd Ed)”. London: Academic Press, 2005.

[14] B. Ross. “A brief history and exposition of the fundatmental theory of fractional calculus”. NewYork: Spring-Verlay, 1975.

[15] J. Portilla, V. Strela, M.J. Wainwright, and E.P. Simoncelli,. “Image denoising using scale mixtures of gaussians in the wavelet domain ”. IEEE Transactions on Image Processing, 2003. 12(11):1338-1351. Nov. 2003.

[16] Perona, J. Malik, “Scale-space and edge detection using anisotropic diffusion ”. IEEE Pattern Analysis and Machine Intelligence, 1990, 12(7): 629–639.
http://dx.doi.org/10.1109/34.56205

[17] Rudin LI, Osher S, Fatemi E. “Nonlinear Total Variation Based Noise Removal Algorithms”. Physica D, 1992, 60(1):259-268.
http://dx.doi.org/10.1016/0167-2789(92)90242-F

[18] D. L. Donoho, De-noising by soft-thresholding [J], IEEE Transactions on Information Theory, 1995, 41(3):613–627.
http://dx.doi.org/10.1109/18.382009


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