A two-level method for image denoising and image deblurring models using mean curvature regularization

Faisal Fairag, Ke Chen, Carlos Brito-Loeza, Shahbaz Ahmad*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


The mean curvature (MC)-based image denoising and image deblurring models are used to enhance the quality of the denoised images and deblurred images respectively. These models are very efficient in removing staircase effect, preserving edges and other nice properties. However, high order derivatives appear in the Euler–Lagrange equations of the MC-based models which create problems in developing an efficient numerical algorithm. To overcome this difficulty, we present a robust and efficient Two-Level method for MC-based image denoising and image deblurring models. The Two-Level method consists of solving one small problem and one large problem. The small problem is a nonlinear system, having high order derivative, on Level I (image having small number of pixels). The large problem is one less expensive system, having low order derivative, on Level II (image having large number of pixels). The derivation of the optimal regularization parameter of Level II is studied and formula is presented. Numerical experiments on digital images are presented to exhibit the performance of the Two-Level method.

Original languageEnglish
Pages (from-to)693-713
Number of pages21
JournalInternational Journal of Computer Mathematics
Issue number4
StatePublished - 2022

Bibliographical note

Funding Information:
The first and last authors would like to acknowledge the support provided by the Deanship of Scientific Research at KFUPM for funding this work through small business project (SB181013).

Publisher Copyright:
© 2021 Informa UK Limited, trading as Taylor & Francis Group.


  • 35R30
  • 47A52
  • 65F22
  • Denoising
  • deblurring
  • ill-posed problem
  • regularization
  • two-level methods
  • variational models

ASJC Scopus subject areas

  • Computer Science Applications
  • Computational Theory and Mathematics
  • Applied Mathematics


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