Total Generalized Variation

By Kristian Bredies, Karl Kunisch, Thomas Pock. SIAM Journal of Imaging Sciences, 2010

1,593 citations recorded by the source corpus.

Subfields: Computational Mechanics, Mathematical Physics, Radiology, Nuclear Medicine and Imaging

View Paper: https://www.semanticscholar.org/paper/9b29b9c03a43d77d59d5cf6c49428bcfae2355b5

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In Computational Mechanics

In Mathematical Physics

In Radiology, Nuclear Medicine and Imaging

Citations in the corpus

Bilevel approaches for learning of variational imaging models (2015, methodology): “If we had an additional lower bound 0 c ≤ α in ( P ), we could without the conditions (3) for TV and (4) for TGV 2 [10] denoising, show the existence of an optimal parameter α .”
Learning a Variational Network for Reconstruction of Accelerated MRI Data (2017, methodology): “We compared our learning-based VN to the linear PI reconstruction method CG SENSE (12) and a combined PI-CS non-linear reconstruction method based on Total Generalized Variation (TGV) (22,34).”
Regularization of linear inverse problems with total generalized variation (2014, background): “As already mentioned, we will not only consider the scalar version introduced in [9], but also study a natural generalization to symmetric tensor fields of order l, first introduced in [29] and its underlying spaces.”
Image Guided Depth Upsampling Using Anisotropic Total Generalized Variation (2013, neutral): “[1].”
Image restoration: Total variation, wavelet frames, and beyond (2012, background): “The interested reader should consult [30] for details.”
Discriminatively Trained Dense Surface Normal Estimation (2014, background): “Since our aim is to obtain piecewise constant normal directions – as reflected typically in man-made environments – we leverage (second order) Total Generalized Variation (TGV) [50] for denoising.”
Computer Vision for Autonomous Vehicles: Problems, Datasets and State-of-the-Art (2017, methodology): “Thus, higher-order regularizations like the Total Generalized Variation (TGV) model have been proposed by Bredies et al. (2010). TGV priors can better represent real data as they leverage a piecewise affine motion model. The non-local Total Generalized Variation by Ranftl et al. (2014) is an extensi”
Non-local Color Image Denoising with Convolutional Neural Networks (2016, background): “Common choices for L are differential operators of the first or of higher orders such as the gradient [3, 31], the structure tensor [23], the Laplacian and the Hessian [21,24], or wavelet-like operators such as wavelets, curvelets and ridgelets (see [13] and references therein).”
Universal Denoising Networks : A Novel CNN Architecture for Image Denoising (2017, background): “Typical choices for the operator L are first or higher-order differential operators such as the gradient [4, 36], the structure tensor [26], the Laplacian and the Hessian [24,27].”
Second order total generalized variation (TGV) for MRI (2011, background): “One example is TGV(2)α-based denoising which is briefly outlined in the following; for a detailed discussion of the noise suppression characteristics and a comparison with TV-based denoising, we refer to (9).”
The structure of optimal parameters for image restoration problems (2015, methodology): “With K = K0 and Y = Z, this yields second-order total generalised variation (TGV2) denoising [11] for the sub-problem (Dα).”
Distributed Proximal Splitting Algorithms with Rates and Acceleration (2020, background): “But the ability to handle a nontrivial K is behind the success of the Chambolle and Pock (2011) or \Condat (2013), Vũ (2013): they are well suited for regularized inverse problems in imaging (Chambolle and Pock, 2016a), for instance with the total variation and its variants (Bredies et al., 2010; Co”
Optical flow modeling and computation: A survey (2015, background): “The Total Generalized Variation (TGV) [43], generalizes L 1 penalization to arbitrarily high order derivatives.”