title: A nonlocal structure tensor-based approach for multicomponent image recovery problems.
abstract: Nonlocal total variation (NLTV) has emerged as a useful tool in variational methods for image recovery problems. In this paper, we extend the NLTV-based regularization to multicomponent images by taking advantage of the structure tensor (ST) resulting from the gradient of a multicomponent image. The proposed approach allows us to penalize the nonlocal variations, jointly for the different components, through various l(1, p)-matrix-norms with p ≥ 1. To facilitate the choice of the hyperparameters, we adopt a constrained convex optimization approach in which we minimize the data fidelity term subject to a constraint involving the ST-NLTV regularization. The resulting convex optimization problem is solved with a novel epigraphical projection method. This formulation can be efficiently implemented because of the flexibility offered by recent primal-dual proximal algorithms. Experiments are carried out for color, multispectral, and hyperspectral images. The results demonstrate the interest of introducing a nonlocal ST regularization and show that the proposed approach leads to significant improvements in terms of convergence speed over current state-of-the-art methods, such as the alternating direction method of multipliers.
authors.forename: Giovanni
authors.initials: G
authors.lastname: Chierchia
authors.forename: Nelly
authors.initials: N
authors.lastname: Pustelnik
authors.forename: Béatrice
authors.initials: B
authors.lastname: Pesquet-Popescu
authors.forename: Jean-Christophe
authors.initials: JC
authors.lastname: Pesquet