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.

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