A Non-Local Structure Tensor Based Approach for Multicomponent Image Recovery Problems

Giovanni Chierchia 1 Nelly Pustelnik 2 Béatrice Pesquet-Popescu 3 Jean-Christophe Pesquet 1
1 LIGM - Laboratoire d'Informatique Gaspard-Monge
2 Phys-ENS - Laboratoire de Physique de l'ENS Lyon
3 LTCI - Laboratoire Traitement et Communication de l'Information
Abstract : Non-local 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 non-local variations, jointly for the different components, through various mixed matrix-norms. To facilitate the choice of the hyper-parameters, 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 thanks to 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 non-local structure tensor 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.
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INSMI | INSTITUT-TELECOM | TDS-MACS | UPEC-UPEM | ENS-LYON | LIGM | LIGM_A3SI | LIGM_SIGNAL | PARISTECH | ENPC | UNIV-LYON1 | ESIEE-PARIS | LTCI

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Giovanni Chierchia, Nelly Pustelnik, Béatrice Pesquet-Popescu, Jean-Christophe Pesquet. A Non-Local Structure Tensor Based Approach for Multicomponent Image Recovery Problems. IEEE Transactions on Image Processing, Institute of Electrical and Electronics Engineers, 2014, 23 (12), pp.5531-5544. ⟨10.1109/TIP.2014.2364141⟩. ⟨hal-01372564⟩

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