Structure-preserving Quaternion Generalized Conjugate Residual Method

Abstract

Color image deblurring problem, one of the primary goals in color image processing, can be mathematically represented by quaternion linear systems. In this paper, we propose a new quaternion generalized conjugate residual method for solving the general quaternion linear systems. The main advantages are that the proposed method saves three-quarters of the theoretical costs compared to the traditional GCR iterations for the real representation of quaternion linear systems, and also converges faster and smoother than the quaternion biconjugate gradient (QBiCG) method. Finally, we provide several numerical examples to illustrate the effectiveness of the proposed method compared with some existing methods.