A Nonlocal Structure Tensor-Based Approach for Multicomponent Image Recovery Problems

• Published in: IEEE transactions on image processing Vol. 23; no. 12; pp. 5531 - 5544
• Main Authors: Chierchia, Giovanni, Pustelnik, Nelly, Pesquet-Popescu, Beatrice, Pesquet, Jean-Christophe
• Format: Journal Article
• Language: English
• Published: United States IEEE 01.12.2014; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Convex analysis; Convex functions; Convex optimization; Degradation; epigraph; hyperspectral imagery; Hyperspectral imaging; image restoration; Imaging; multicomponent images; Noise; nonlocal total variation; Optimization; Recovery; Regularization; singular value decomposition; structure tensor; Tensile stress; Tensors; Variational methods; image restoration; Convex optimization; nonlocal total variation; hyperspectral imagery; multicomponent images; singular value decomposition; epigraph; structure tensor
• ISSN: 1057-7149; 1941-0042; 1941-0042
• DOI: 10.1109/TIP.2014.2364141

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.