Where and when

speaker: Prof. Marco Donatelli  
affiliation: Full Professor at Department of Science and High Technology, Università degli Studi dell'Insubria, Como, Italy  
date: Friday, May 24^th 2024, 11am (Italian time)  
venue: Genoa (Italy), Polo Valletta Puggia – Università di Genova: DIBRIS-DIMA (room 705)  
link: Google Meet

Fractional graph Laplacian for image reconstruction

abstract: A popular approach for regularization involves replacing the original problem with an optimization problem that minimizes the sum of two terms: an ℓ2 term and an ℓq term with 0 < q ≤ 1. The first penalizes the distance between the measured and reconstructed data, while the second imposes sparsity on certain coefficients of the computed solution. In [1], we propose to use the fractional Laplacian of a properly constructed graph in the ℓq term to compute extremely accurate reconstructions of the desired images. Furthermore, we propose automatic approaches to determine the involved parameters so that the proposed method is completely plug-and-play. We show that the algorithm, under some reasonable assumptions, is a regularization method. Some selected numerical examples show the performances of our proposal.