An Algorithm for Total Variation Minimization and Applications

By Antonin Chambolle. Journal of Mathematical Imaging and Vision, 2004

2,496 citations recorded by the source corpus.

Subfields: Computer Vision and Pattern Recognition

View Paper: https://www.semanticscholar.org/paper/b5090b58438d5845411edfa3abb12541caa82ba6

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In Computer Vision and Pattern Recognition

Citations in the corpus

Nonlocal Operators with Applications to Image Processing (2008, methodology): “The projection algorithm of Chambolle [12] generalizes easily in this case.”
Image inpainting through neural networks hallucinations (2016, methodology): “The TV norm has been extensively used as a regularizer in several inverse problems, such as denoising [4] and superresolution [1] due to its edge-preserving properties.”
Restoration of Poissonian Images Using Alternating Direction Optimization (2010, neutral): “In this paper, we will consider three types of regularization: total variation [4], [31] and both frame-based analys is and frame-based synthesis formulations [14].”
Dual Norms and Image Decomposition Models (2005, methodology): “…as in Chambolle (2004), one sees that this problem can be numerically solved by a fixed point method: p0 = 0 , and pn+1i, j = pni, j − τ (∇( div (pn) + f/λ))i, j 1 + τ |(∇( div (pn) + f/λ))i, j | (3.39) And as in Chambolle (2004), we show that if τ is small enough, f + λ div pn → û as n → ∞.”
Recent Developments in Total Variation Image Restoration (2004, methodology): “The update formula for g used in [8] is a simple relaxation g = g +τH(g) 1+τ |H(gn)| where τ > 0 is chosen to be small enough so that the iteration converges.”
Proximal Markov chain Monte Carlo algorithms (2013, neutral): “…set to a small value and use the approximation (12) proxδ/2g (x) ≈ proxδ/2g2 {x + δ∇g1(x)/2} with g1(x) = −‖ y − H x‖2/2σ 2 and g2(x) = −α‖∇x‖1, and where we note that ∇g1 is Lipschitz continuous and that proxδ/2g2 (x) can be efficiently computed using a parallel implementation of Chambolle (2004).”
Fast Global Minimization of the Active Contour/Snake Model (2007, methodology): “Proof of Proposition 1 The proof is based on [17, 19].”
Reflection methods for user-friendly submodular optimization (2013, neutral): “, [9] and references therein) that also occurs in other regularization problems [1].”
A Globally Optimal Algorithm for Robust TV-L1 Range Image Integration (2007, methodology): “Since this algorithm is an essential part of our method, we briefly reproduce the main results from [8]:”
Learning Explainable Models Using Attribution Priors (2019, methodology): “To encode this intuition, we apply a total variation loss on pixel-level attributions as follows [4]: where φ ‘i,j is the attribution for the i, j -th pixel in the ‘ -th training image.”
Image denoising using deep CNN with batch renormalization (2020, neutral): “Roose, 1997), gradient methods (Beck & Teboulle, 2009; Zuo, Zhang, Song, Zhang, & Gao, 2014) and total-variation (TV) methods (Chambolle, 2004; Rudin, Osher, & Fatemi, 1992) are also very popular image-denoising methods.”
Optimal Primal-Dual Methods for a Class of Saddle Point Problems (2013, background): “It can be easily see that LG = λmax(A A) and LK = λ √ 8 (see [8]).”
Attention-guided CNN for image denoising (2020, methodology): “Additionally, there were other excellent methods such as total-variation (TV) [4] for image denoising.”
An introduction to continuous optimization for imaging (2016, methodology): “In fact a minimizer of (7.23) is obtained by minimizing (7.1), with u = w being the input image, and then thresholding the solution u at the 0 level (Chambolle 2004a, 2005).”
A New TwIST: Two-Step Iterative Shrinkage/Thresholding Algorithms for Image Restoration (2007, methodology): “In the original formulation of total-variation (TV) [10], [14], [41], X is an infinite-dimensional Hilbert space L(2)(I), whereI is a bounded open domain of R(2), e.”
Bayesian computation: a perspective on the current state, and sampling backwards and forwards (2015, methodology): “We compute the proximity mapping of g 2 with a highly parallelised implementation of the specialised algorithm of Chambolle (2004).”
Noninvasive Transmural Electrophysiological Imaging Based on Minimization of Total-Variation Functional (2014, background): “Thus, it is important to preserve the unique spatial feature of during the reconstruction of , and this can be accomplished by total-variation (TV) minimization, which promotes a solution with sharp boundaries/gradients between piecewise smooth regions [21].”