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Francis K. A. Allotey (Saltpond, Ghana 9 August 1932 – Accra, Ghana 2 November 2017) Read chapter Read first chapter

2019 | OriginalPaper | Chapter

Correspondence Between Multiscale Frame Shrinkage and High-Order Nonlinear Diffusion

Authors : Haihui Wang, Qi Huang, Bo Meng

Published in: Analysis and Partial Differential Equations: Perspectives from Developing Countries

Publisher: Springer International Publishing

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Abstract

Wavelet frame and nonlinear diffusion filters are two popular tools for signal denoising. The correspondence between Ron-Shen’s framelet and high-order nonlinear diffusion has been proved at multilevel setting. However, for the general framelet, the correspondence is established only at one level. In this paper we extend the relationship between framelet shrinkage and high-order nonlinear diffusion in Jiang (Appl Numerical Math 51–66, 2012 [19]) from one level framelet shrinkage to the multilevel framelet shrinkage setting. Subsequently, we complete the correspondence between framelet shrinkage and high-order nonlinear diffusion. Furthermore, we propose a framelet-diffused denoising method for processing the dynamic pressure signals which are generated by a transonic axial compressor. Numerical results show that our algorithm has superior noise removal ability than traditional algorithms and presents the ability in analyzing the pressure signals from an axial transonic compressor.

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previous chapter “Strong” Turing-Hopf Instability for Reaction-Diffusion Systems
next chapter Pseudo-differential Operators Associated to General Type I Locally Compact Groups
Literature
1.
Rudin, L., Osher, S., Fatemi, E.: Nonlinear total variation based noise removal algorithms. Phys. D 60, 259–268 (1992)MathSciNetCrossRef
2.
Catte, F., Lions, P., Morel, J., Coll, T.: Image selective smoothing and edge detection by nonlinear diffusion. SIAM J. Numer. Anal. 29, 182–193 (1992)MathSciNetCrossRef
3.
Perona, P., Malik, J.: Scale-space and edge detection using anisotropic diffusion. IEEE Trans. Pattern Anal. Mach. Intell. 12, 629–639 (1990)CrossRef
4.
Wei, G.W.: Generalized perona-malik equation for image restoration. IEEE Signal Process. Lett. 6(7), 165–167 (2002)CrossRef
5.
Bates, P.W., Chen, Z., Sun, Y., et al. Geometric and potential driving formation and evolution of biomolecular surfaces. J. Math. Biol. 59(2), 193–231 (2009)MathSciNetCrossRef
6.
Chambolle, A., DeVore, R.A., Lee, N., Lucier, B.L.: Nonlinear wavelet image processing: variationa problems, compression and noise removal through wavelet shrinkage. IEEE Trans. Image Process., 319–335 (1998)MathSciNetCrossRef
7.
Catte, F., L.Lions, P., Morel, J.M., Coll, T.: Image selective smoothing and edge detection by nonlinear diffusion. SIAM J. Numer. Anal., 845–866 (1992)
8.
9.
Mallat, S.: A Wavelet Tour of Signal Processing, 2nd edn. Academic Press, San Diego (1999)MATH
10.
Keeling, S.L., Stollberger, R.: Nonlinear anisotropic diffusion filtering for multi scale edge enhancement wide range edge. Inverse Probl., 175–190 (2002)
11.
Coifman, R.R., Donoho, D.: Translation-invariant de-noising. In: Wavelets and Statistics. Springer Lecture Notes in Statistics, pp. 125–150 (1994)CrossRef
12.
Weickert, J.: Anisotropic diffusion in image processing. B.g. teubner Stuttgart, p. 272 (1998)
13.
Didas, S., Denoising: Enhancement of digital imagesvariational methods, Integro differential Equations, and Wavelets, Ph.D. Dissertation, Saarland University (2008)
14.
Cai, J., Chan, R., Shen, Z.: Simultaneous cartoon and texture inpainting. Inverse Proble. Imaging 4, 379–395 (2010)MathSciNetCrossRef
15.
Didas, S., Weickert, J., Burgeth, B.: Properties of higher order nonlinear diffusion filtering. J. Math. Imaging Vis., 208–226 (2009)MathSciNetCrossRef
16.
Steidl, G., Weickert, J., Brox, T., Mrazek, P.: On the equivalence of soft wavelet shrinkage, total variation diffusion, total variation reguarization, and sides. SIJM J. Numer. Anal., 683–713 (2004)
17.
Plonka, G., Steidl, G.: A multiscale wavelet-inspired scheme for nonlinear diffusion. Int. J. Wavelets, Multiresolution Inf. Process., 1–21 (2006)MathSciNetCrossRef
18.
Wang, H., Kong, X.: A multiscale tight frame inspired scheme for nonlinear diffusion. Int. J. Wavelets, Multiresolution Inf. Process., 1250041-1-1250041-22 (2012)
19.
Jiang, Q.: Correspondence between frame shrinkage and high-order nonlinear diffusion. Appl. Numerical Math., 51–66 (2012)MathSciNetCrossRef
20.
Mrazek, P., Weickert, J., Steidl, G.: Diffusion-inspired shrinkage function and stability results for wavelet denoising. Int. J. Comput. Vis., 171–186 (2005)CrossRef
21.
Mrazek, P., Weickert, J., Steidl, G.: Correspondences between wavelet shrinkage and nonlinear diffusion. In: Proceedings of the Scale Space Methods in Computer Vision, International Conference, Scale-Space 2003, Isle of Skye, Uk, June 10–12, 2003, pp. 101–116 (2003)CrossRef
22.
Cai, J., Dong, B., Osher, S., Shen, Z.: Image restorations: total variation, wavelet frames and beyond. J. Am. Math. Soc. 25, 1033–1089 (2012)MathSciNetCrossRef
Metadata
Title
Correspondence Between Multiscale Frame Shrinkage and High-Order Nonlinear Diffusion
Authors
Haihui Wang
Qi Huang
Bo Meng
Copyright Year
2019
Book
Analysis and Partial Differential Equations: Perspectives from Developing Countries

Print ISBN: 978-3-030-05656-8

Electronic ISBN: 978-3-030-05657-5

Copyright Year: 2019

DOI
https://doi.org/10.1007/978-3-030-05657-5_10

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