Efficient preconditioning strategies for accelerating GMRES in block-structured nonlinear systems for image deblurring

Rizwan Khalid, Shahbaz Ahmad, Mohamed Medani, Yahia Said and Iftikhar Ali

PLOS ONE, 2025, vol. 20, issue 6, 1-26

Abstract: 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.

Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:plo:pone00:0322146

DOI: 10.1371/journal.pone.0322146

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