Image deblurring is a relevant problem in many fields of science and engineering. To solve this problem, many different approaches have been proposed, and, among the various methods, variational ones are extremely popular. These approaches substitute the original problem with a minimization problem where the functional is composed of two terms, a data fidelity term and a regularization term. In this paper we propose, in the classical non-negative constrained '2-'1 minimization framework, the use of the graph Laplacian as regularization operator. Firstly, we describe how to construct the graph Laplacian from the observed noisy and blurred image. Once the graph Laplacian has been built, we efficiently solve the proposed minimization problem by splitting the convolution operator and the graph Laplacian by the Alternating Direction Multiplier Method (ADMM). Some selected numerical examples show the good performances of the proposed algorithm.

Graph Laplacian for Image Deblurring

Bianchi D.;
2021-01-01

Abstract

Image deblurring is a relevant problem in many fields of science and engineering. To solve this problem, many different approaches have been proposed, and, among the various methods, variational ones are extremely popular. These approaches substitute the original problem with a minimization problem where the functional is composed of two terms, a data fidelity term and a regularization term. In this paper we propose, in the classical non-negative constrained '2-'1 minimization framework, the use of the graph Laplacian as regularization operator. Firstly, we describe how to construct the graph Laplacian from the observed noisy and blurred image. Once the graph Laplacian has been built, we efficiently solve the proposed minimization problem by splitting the convolution operator and the graph Laplacian by the Alternating Direction Multiplier Method (ADMM). Some selected numerical examples show the good performances of the proposed algorithm.
2021
Graph Laplacian
Image deblurring
L2-l1 regularization
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11770/338909
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 5
  • ???jsp.display-item.citation.isi??? ND
social impact