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2585. Fractional graph Laplacian for image reconstruction
Invited abstract in session MA-34: Optimization and learning for data science and imaging (Part I), stream Advances in large scale nonlinear optimization.
Monday, 8:30-10:00Room: 43 (building: 303A)
Authors (first author is the speaker)
| 1. | Marco Donatelli
|
| Università degli studi dell'Insubria | |
| 2. | Stefano Aleotti
|
| Scienza ed alta tecnologia, Università degli Studi dell'Insubria | |
| 3. | Alessandro Buccini
|
| Università degli Studi di Cagliari |
Abstract
A popular approach for regularization involves replacing the original problem with an optimization problem that minimizes the sum of two terms: an l^2 term and an l^q term with q smaller than or equal to one. 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 l^q 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.
[1] S. Aleotti, A. Buccini, M. Donatelli, Fractional graph Laplacian for image reconstruction, Applied Numerical Mathematics, 2023.
Keywords
- Mathematical Programming
- Continuous Optimization
- Algorithms
Status: accepted
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