Image Decomposition and Restoration Using Total Variation Minimization and the H1

By Stanley J. Osher, Andres Fco. Solé, Luminita A. Vese. Multiscale Modeling & simulation, 2003

552 citations recorded by the source corpus.

Subfields: Computer Vision and Pattern Recognition

View Paper: https://www.semanticscholar.org/paper/348a8c6f43bcf537ccae5017fe3f346be4421599

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computer Vision and Pattern Recognition

Citations in the corpus

Structure-Texture Image Decomposition—Modeling, Algorithms, and Parameter Selection (2006, methodology): “In the case when H = L2, then (6) is the ROF model (Rudin et al. 1992), and when H = H−1 then (6) is the OSV model (Osher et al., 2003).”
Iterative Image Restoration Combining Total Variation Minimization and a Second-Order Functional (2005, background): “…higher-order PDEs have been of special interest over the last few years (Lysaker et al., 2003; Chan et al., 2000; You and Kaveh, 2000; Lysaker et al., 2004; Osher et al., 2003; Bertozzi and Greer, 2004; Greer and Bertozzi, 2003a, 2003b, 2004; Scherzer, 1998; Hinterberger and Scherzer, 2004).”
An Iterative Regularization Method for Total Variation-Based Image Restoration (2005, methodology): “Note that in the particular case of the Osher, Sole, Vese model [ 35 ] in equation (1.12) we have A = r 1 and f = r 1f0, where f0 is the actual noisy image we obtain, and therefore the noise estimate is kr 1(f0 ~ u)k2L2 2 ;”
Fractional-Order Anisotropic Diffusion for Image Denoising (2007, methodology): “Related works inspired from the OSV model [ 28 ] and also using the Fourier transform for computations and variants are by Roudenko [29] and Lieu [30].”
On image denoising methods (2004, methodology): “Because of the difierent and more ambitious scopes of the Meyer method, [2, 38, 29 ], which makes it parameter and implementation-dependent, we could not draw it into the discussion.”
A Review of Image Denoising Algorithms, with a New One (2005, methodology): “Because of the difierent and more ambitious scopes of the Meyer method, [2, 37, 26 ], which makes it parameter and implementation-dependent, we could not draw it into the discussion.”
Signal Recovery by Proximal Forward-Backward Splitting (2005, background): “Despite its simplicity, Problem 1.1 will be shown to cover a wide range of apparently unrelated signal recovery formulations, including constrained least-squares problems [35, 48, 63], multiresolution sparse regularization problems [10, 30, 31, 36], Fourier regularization problems [46, 50], geometry”
From Local Kernel to Nonlocal Multiple-Model Image Denoising (2009, methodology): “Several other methods are derived from the original ROF model by Meyer (2001), Osher et al. (2003), Vese and Osher (2003).”
From Information Scaling of Natural Images to Regimes of Statistical Models (2007, methodology): “See also [44] for an image decomposing scheme in terms of cartoons and textures.”
Natural image denoising: Optimality and inherent bounds (2011, background): “Image denoising algorithms have drastically advanced over the last few decades [ 17 , 7, 20, 21, 3, 10, 8]. Various image priors have been learned [20, 21, 26], and particularly impressing results have been obtained with non parametric techniques such as non local means [3] or BM3D [8], and sparse r”
Recent Developments in Total Variation Image Restoration (2004, background): “In a later work [25], Osher et al.”
Local adaptivity to variable smoothness for exemplar-based image denoising and representation (2005, background): “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.”
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.”
Dual Norms and Image Decomposition Models (2005, methodology): “And it also appears slightly better than the OSV model (Osher et al., 2003).”
Image Decomposition into a Bounded Variation Component and an Oscillating Component (2005, methodology): “These two authors, together with Solé, have proposed another approach to this problem in [9], where they propose a more direct algorithm in the case λ = +∞ and p = 2.”
Active unsupervised texture segmentation on a diffusion based feature space (2003, background): “For the application to texture features total variation (TV) flow [23, 2, 16] seems to suit very well, since it removes oscillations and leads to piecewise constant results.”
Aspects of Total Variation Regularized L[sup 1] Function Approximation (2005, unknown): “For example, following up on Meyer’s ideas Vese and Osher [24], and then Osher, Sole, and Vese [20] came up with variants of the original model that replace the ﬁdelity term with weaker norms.”