Correspondence Between Multiscale Frame Shrinkage and High-Order Nonlinear Diffusion

  • Haihui WangEmail author
  • Qi Huang
  • Bo Meng
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 275)


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.


Wavelets Nonlinear diffusion Signal analysis 



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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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.School of Mathematics and System ScienceBeihang UniversityBeijingChina
  2. 2.School of Energy and Power EnigineeringBeihang UniversityBeijingChina

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