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

Abstract

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.

Keywords:

• Denoising
• deblurring
• regularization
• variational models
• two-level methods
• ill-posed problem

2010 AMS SUBJECT CLASSIFICATIONS:

• 47A52
• 35R30
• 65F22

Acknowledgments

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).

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

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