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arXiv · 2607.17313

Iterated graph Laplacian for image restoration problems

Stefano Aleotti·Davide Bianchi·Florian Bossmann·Marco Donatelli·Pietro Maurino
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Abstract

We study the graph Laplacian operator as a regularizer in a generalized Tikhonov framework for linear ill-posed problems. The Laplacian is updated iteratively from the current reconstruction, so that progressively sharper structural information about the solution is fed into the regularization term. We introduce three schemes: a standard one that rebuilds the Laplacian from each new iterate; an error-equation scheme that, following the error-based formulation of iterated Tikhonov regularization, builds the Laplacian from an estimate of the reconstruction error rather than of the image itself; and a mixed scheme combining the two. We establish convergence of all three schemes for noisy data under a priori parameter and stopping rules as the noise level tends to zero. Numerical experiments in two-dimensional computed tomography and image deblurring show consistent gains in reconstruction quality and sharper recovery of fine details.

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Stefano Aleotti, Davide Bianchi, Florian Bossmann, Marco Donatelli, Pietro Maurino. 2026-07-19. Iterated graph Laplacian for image restoration problems. https://arxiv.org/abs/2607.17313

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