Image Decomposition into a Bounded Variation Component and an Oscillating Component

By Jean-François Aujol, Gilles Aubert, Laure Blanc-Féraud, Antonin Chambolle. Journal of Mathematical Imaging and Vision, 2005

396 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computer Vision and Pattern Recognition, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/c536901cc3b1e7e620bad6ed4ef4c3d33e4c3509

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Citations in the corpus

Forward-Douglas–Rachford splitting and forward-partial inverse method for solving monotone inclusions (2012, background): “ization [18, 44], variational inequalities [31, 46, 47], monotone operator theory [23, 37, 32, 43], partial diﬀerential equations [26, 27, 31, 34, 51], economics [29, 36], signal and image processing [2, 3, 13, 14, 21, 22, 39, 40, 48], evolution inclusions [1, 28, 42], and traﬃc theory [8, 9, 25, 38”
Structure-Texture Image Decomposition—Modeling, Algorithms, and Parameter Selection (2006, methodology): “We refer the reader to Aujol and Chambolle (2005) for some numerical computations of typical image G norm. In Meyer (2001), the author did not propose any numerical scheme to compute the decomposition. Vese and Osher (2003) were the first to propose a numerical scheme to solve this model using Euler”
Optimal Spatial Adaptation for Patch-Based Image Denoising (2006, background): “Another competitive approach consists in decomposing the image into its primary noise, texture and bounded variation (BV) components [1], [38], [42], which actually can be hard to compute, in practice.”
Infimal convolution regularizations with discrete ℓ1-type functionals (2011, neutral): “, for image decomposition in [1, 2, 36].”
The asymptotic behavior of the composition of two resolvents (2005, methodology): “MSC:47H05; 47H09; 47J25; 90C25 Keywords:Duality; Firmly nonexpansive operator; Gradient projection method; Hilbert space; Monotone inclusion; Monotone operator; Proximal iteration; Resolvent”
Proximal Splitting Methods in Signal Processing (2009, positive): “This framework captures in particular problem formulations found in [5], [6], [77], [85], [125].”
A Variational Approach to Removing Multiplicative Noise (2008, methodology): “A last class of methods are variational methods as in [37, 36, 6], where the solution is computed with PDEs.”
Dual Norms and Image Decomposition Models (2005, methodology): “Figure 6 shows a comparison between the OSV model and the algorithm of Aujol et al. (2005).”
A Review of Image Denoising Algorithms, with a New One (2005, methodology): “Because of the different and more ambitious scopes of the Meyer method [2, 36, 26], which makes it parameter- and implementation-dependent, we could not draw it into the discussion.”
Nonlocal Operators with Applications to Image Processing (2008, methodology): “(4.6), and modify the iterative projection algorithm of [2] to be nonlocal, in a similar manner as the algorithms presented above.”
Local adaptivity to variable smoothness for exemplar-based image denoising and representation (2005, neutral): “Another competitive approach consists in decomposing the image into its primary noise, texture and bounded variation (BV) components [53, 58, 1], which actually can be hard to compute in practice.”
Signal Recovery by Proximal Forward-Backward Splitting (2005, background): “…sparse regularization problems [10, 30, 31, 36], Fourier regularization problems [46, 50], geometry/texture image decomposition problems [5, 6, 7, 57, 71], hard-constrained inconsistent feasibility problems [26], alternating projection signal synthesis problems [38, 60], least…”