The numerical results for Clown image.

We propose an efficient preconditioning strategy to accelerate the convergence of Krylov subspace methods, specifically for solving complex nonlinear systems with a block five-by-five structure, commonly found in cell-centered finite difference discretizations for image deblurring using mean curvature techniques. Our method introduces two innovative preconditioned matrices, analyzed spectrally to show a favorable eigenvalue distribution that accelerates convergence in the Generalized Minimal Residual (GMRES) method. This technique significantly improves image quality, as measured by peak signal-to-noise ratio (PSNR), and demonstrates faster convergence compared to traditional GMRES, requiring minimal CPU time and few iterations for exceptional deblurring performance. The preconditioned matrices’ eigenvalues cluster around 1, indicating a beneficial spectral distribution. The source code is available at https://github.com/shahbaz1982/Precondition-Matrix.我们提出一种高效预处理策略，以加速克雷洛夫子空间方法（Krylov subspace methods）的收敛速度，该策略专门用于求解具有5×5块结构的复杂非线性系统——这类结构广泛见于基于平均曲率技术的图像去模糊问题的单元中心有限差分离散格式中。本方法引入两种创新性预处理矩阵，经谱分析证实，其拥有优良的特征值分布，可加快广义最小残差法（Generalized Minimal Residual, GMRES）的收敛速度。该技术可显著提升图像质量（以峰值信噪比(PSNR)作为评估指标），相较传统GMRES方法，其收敛速度更快，仅需极少量迭代次数与CPU耗时，即可实现优异的去模糊效果。经预处理的矩阵特征值聚集于1附近，表明其具备优异的频谱分布特性。相关源代码已公开于https://github.com/shahbaz1982/Precondition-Matrix。