A first-order image denoising model for staircase reduction
- 29 Downloads
In this paper, we consider a total variation–based image denoising model that is able to alleviate the well-known staircasing phenomenon possessed by the Rudin-Osher-Fatemi model (Rudin et al., Phys. D 60, 259–268, 30). To minimize this variational model, we employ augmented Lagrangian method (ALM). Convergence analysis is established for the proposed algorithm. Numerical experiments are presented to demonstrate the features of the proposed model and also show the efficiency of the proposed numerical method.
KeywordsImage denoising Augmented Lagrangian method Variational model
Mathematics Subject Classification (2010)94A08 65K10 65M32
Unable to display preview. Download preview PDF.
The author would like to thank the anonymous referees for their valuable comments and suggestions, which have helped very much to improve the presentation of this paper.
- 2.Aubert, G., Kornprobst, P.: Mathematical problems in image processing: partial differential equations and the calculus of variations. Springer Science and Business Media (2006)Google Scholar
- 6.Beck, A.: First-Order Methods in Optimization, vol. 25, SIAM (2017)Google Scholar
- 11.Buttazzo, G.: Semicontinuity, relaxation and integral representation in the calculus of variations, Pitman Research Notes in Mathematics 207, Longman Scientific and Technical (1989)Google Scholar
- 15.Chan, T., Esedoglu, S., Park, F., Yip, M.H.: Recent developments in total variation image restoration. In: Paragios, N., Chen, Y., Faugeras, O. (eds.) Handbook of Mathematical Models in Computer Vision. Springer, Berlin (2005)Google Scholar
- 25.Meyer, Y.: Oscillating patterns in image processing and nonlinear evolution equations, University Lecture Series, Vol 22, Amer. Math. Soc.Google Scholar