Multilevel algorithm for a Poisson noise removal model with total-variation regularization

Abstract

Many commonly used models for the fundamental image processing task of noise removal can deal with Gaussian white noise. However, such Gaussian models are not effective in restoring images with Poisson noise, which is ubiquitous in certain applications. Recently, Le–Chartrand–Asaki derived a new data-fitting term in the variational model for Poisson noise. This paper proposes a multilevel algorithm for efficiently solving this variational model. As expected of a multilevel method, it delivers the same numerical solution many orders of magnitude faster than the standard single-level method of coordinate descent time-marching. Supporting numerical experiments on 2D gray scale images are presented.

Keywords:

• Image restoration
• Poisson noise
• Regularization
• Nonlinear solvers
• Multilevel methods

Acknowledgements

The authors wish to thank J. F. Cai and Y. Q. Dong, CUHK, for various discussions and assistance relating to this work. The work of the first author was supported by HKRGC grants CUHK 400405 and CUHK DAG 2060257. The second author acknowledges support from the Leverhulme Trust RF/9/RFG/2005/0482 as well as the support and hospitality of the Department of Mathematics, CUHK.