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Analysis and Partial Differential Equations: Perspectives from Developing Countries pp 159–171Cite as

Correspondence Between Multiscale Frame Shrinkage and High-Order Nonlinear Diffusion

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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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Acknowledgement

The author would like to thank Professor Charles K. Chui for helpful discussions on the correspondence between wavelet shrinkage and diffusion filtering. Thanks to Dr. Qun Mo for some detailed and careful comments.

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Authors and Affiliations

  1. School of Mathematics and System Science, Beihang University, No. 37, Xueyuan Road, Haidian District, Beijing, 100191, China

    Haihui Wang & Qi Huang

  2. School of Energy and Power Enigineering, Beihang University, No. 37, Xueyuan Road, Haidian District, Beijing, 100191, China

    Bo Meng

Authors
  1. Haihui Wang
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  2. Qi Huang
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  3. Bo Meng
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Corresponding author

Correspondence to Haihui Wang .

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Editors and Affiliations

  1. School of Mathematical Sciences, Queen Mary University of London, London, UK

    Julio Delgado

  2. Department of Mathematics: Analysis, Logic and Discrete Mathematics, Ghent University, Ghent, Belgium

    Michael Ruzhansky

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Wang, H., Huang, Q., Meng, B. (2019). Correspondence Between Multiscale Frame Shrinkage and High-Order Nonlinear Diffusion. In: Delgado, J., Ruzhansky, M. (eds) Analysis and Partial Differential Equations: Perspectives from Developing Countries. Springer Proceedings in Mathematics & Statistics, vol 275. Springer, Cham. https://doi.org/10.1007/978-3-030-05657-5_10

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