用于病态四元数反问题的灵活四元数广义极小残差法
Flexible Quaternion Generalized Minimal Residual Method for Ill-Posed Quaternion Inverse Problems
AI总结：
针对彩色图像处理等线性病态四元数反问题，提出基于协同全变分与迭代重加权范数的正则化模型，并用灵活QGMRES快速求解及给出收敛界。
摘要：
本文的主要目标是提出一种新的四元数全变分正则化模型，用于求解源于三维信号滤波或彩色图像处理的线性病态四元数反问题。该模型中的四元数全变分项由协同全变分正则化表示，并通过四元数迭代重加权范数进行近似。文中提出了一种新颖的灵活四元数广义极小残差法，以快速求解该模型。建立了改进的收敛理论，以获得四元数极小残差法（QGMRES）残差范数的紧致上界。该收敛理论也适用于预条件QGMRES。数值实验表明，所提出的模型和算法在迭代步数、CPU时间以及复原彩色图像的质量准则方面均优于现有最先进方法。
英文摘要：
The main goal of this paper is to propose a new quaternion total variation regularization model for solving linear ill-posed quaternion inverse problems, which arise from three-dimensional signal filtering or color image processing. The quaternion total variation term in the model is represented by collaborative total variation regularization and approximated by a quaternion iteratively reweighted norm. A novel flexible quaternion generalized minimal residual method is presented to quickly solve this model. An improved convergence theory is established to obtain a sharp upper bound of the residual norm of quaternion minimal residual method (QGMRES). The convergence theory is also presented for preconditioned QGMRES. Numerical experiments indicate the superiority of the proposed model and algorithms over the state-of-the-art methods in terms of iteration steps, CPU time, and the quality criteria of restored color images.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
