Modified special HSS method for discrete ill-posed problems and image restoration

ABSTRACT

For solving ill-posed inverse problems, we establish a modified version of special Hermitian and skew-Hermitian splitting (SHSS) iteration method, called the modified SHSS (MSHSS) method in this paper. Based on an augmented system formulation, we apply the modified splitting to solve ill-posed inverse problems, and theoretically study its convergence and determine its optimal iteration parameters. Furthermore, the SOR acceleration scheme for MSHSS iterative method is discussed. Finally, numerical experiments arising from a Fredholm integral equation of the first kind and image restoration are used to further examine the effectiveness of the new method.

KEYWORDS:

• Hermitian and skew-Hermitian splitting
• Tikhonov regularization
• ill-posed problems
• image restoration
• iteration method

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 65F10
• 65D18
• 65N20

Acknowledgements

We would like to express our sincere thanks to the anonymous reviewers for their valuable suggestions and constructive comments which greatly improved the presentation of this paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This research was supported by the National Natural Science Foundation of China (No. 10802068).