Error-Based Restarted Simpler QGMRES for Image Denoising Problem

QGMRES is an effective approach for solving quaternion linear systems. Without solving upper Hessenberg minimization problem, SQGMRES is the simpler version of QGMRES. Similar to restarted GMRES and SGMRES, the residual vectors at the end of each restart cycle in SQGMRES also alternate direction in a cyclic manner. Motivated by LGMRES and SLGMRES, in this paper, we present an acceleration strategy for SQGMRES by disrupting the alternation, and the convergence theory of new algorithm is provided. Finally, we apply new algorithms to color image denoising problems, and the experimental results showed a significant decrease in both the number of iterations and the required time compared to QGMRES.