In imaging problems, the graph Laplacian is proven to be a very effective regularization operator when a good approximation of the image to restore is available. In this paper, we study a Tikhonov method that embeds the graph Laplacian operator in a ℓ1 –norm penalty term. The novelty is that the graph Laplacian is built upon a first approximation of the solution obtained as the output of a trained neural network. Numerical examples in 2D computerized tomography demonstrate the efficacy of the proposed method.
Bianchi, D., Donatelli, M., Evangelista, D., Li, W., Piccolomini, E.L. (2023). Graph Laplacian and Neural Networks for Inverse Problems in Imaging: GraphLaNet [10.1007/978-3-031-31975-4_14].
Graph Laplacian and Neural Networks for Inverse Problems in Imaging: GraphLaNet
Evangelista D.Formal Analysis
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2023
Abstract
In imaging problems, the graph Laplacian is proven to be a very effective regularization operator when a good approximation of the image to restore is available. In this paper, we study a Tikhonov method that embeds the graph Laplacian operator in a ℓ1 –norm penalty term. The novelty is that the graph Laplacian is built upon a first approximation of the solution obtained as the output of a trained neural network. Numerical examples in 2D computerized tomography demonstrate the efficacy of the proposed method.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
