Duality-based algorithms for total-variation-regularized image restoration

Zhu, Mingqiang; Wright, Stephen J.; Chan, Tony F.

doi:10.1007/s10589-008-9225-2

Cited by 159 publications

(124 citation statements)

References 17 publications

(38 reference statements)

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“…We remark that with our formulation of the problem it is difficult to relate the parameter to the error x − x * 2 a priori (while this is possible in the dual formulation in [24] where the primal variable is a function of the dual variable).…”

Section: The First-order Methodsmentioning

confidence: 99%

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Algorithms and software for total variation image reconstruction via first-order methods

et al. 2009

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This paper describes new algorithms and related software for total variation (TV) image reconstruction, more specifically: denoising, inpainting, and deblurring. The algorithms are based on one of Nesterov's first-order methods, tailored to the image processing applications in such a way that, except for the mandatory regularization parameter, the user needs not specify any parameters in the algorithms. The software is written in C with interface to Matlab (version 7.5 or later), and we demonstrate its performance and use with examples.

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Section: The First-order Methodsmentioning

confidence: 99%

“…Many customized algorithms have been suggested in the literature, such as subgradient methods [1,7], dual formulations [4,24], primal-dual methods [6,16,21], graph optimization [9], second-order cone programming [13], etc. However, the implementation of all these methods for large-scale problem is not straightforward.…”

Section: Introductionmentioning

confidence: 99%

Algorithms and software for total variation image reconstruction via first-order methods

et al. 2009

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“…Further, since A k is binary we opt for schemes other than split Bregman/shrinkage or dual minimization [7,32,77]. We refrain from convex relaxation and instead are inspired by the Merriman-Bence-Osher (MBO) scheme for motion my mean curvature of interfaces [50].…”

Section: N-d-tv-vmd Subminimization Wrt a Kmentioning

confidence: 99%

Two-Dimensional Compact Variational Mode Decomposition

et al. 2017

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Decomposing multidimensional signals, such as images, into spatially compact, potentially overlapping modes of essentially wavelike nature makes these components accessible for further downstream analysis. This decomposition enables space-frequency analysis, demodulation, estimation of local orientation, edge and corner detection, texture analysis, denoising, inpainting, or curvature estimation. Our model decomposes the input signal into modes with narrow Fourier bandwidth; to cope with sharp region boundaries, incompatible with narrow bandwidth, we introduce binary support functions that act as masks on the narrow-band mode for image recomposition. L 1 and TV terms promote sparsity and spatial compactness. Constraining the support functions to partitions of the signal domain, we effectively get an image segmentation model based on spectral homogeneity. By coupling several submodes together with a single support function, we are able to decompose an image into several crystal grains. Our efficient algorithm is based on variable splitting and alternate direction optimization; we employ Merriman-Bence-Osher-like threshold dynamics to handle efficiently the motion by mean curvature of the support function boundaries under the sparsity promoting terms. The versatility and effectiveness of our proposed model is demonstrated on a broad variety of example images from different modalities. These demonstrations include the decomposition of images into overlapping modes with smooth or sharp boundaries, segmentation of images of crystal grains, and inpainting of damaged image regions through artifact detection.

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“…u f y of ( , , ) Q u f y [7]. Using the existence of the saddle point of ( , , ) Q u f y , convex analysis can be applied to show that the minimization and the maximum in (2.5) can be swapped, i.e., .8) respectively.…”

Section: B Primal-dual Approach For Uniform Noise Removlmentioning

confidence: 99%

Primal-Dual Approach for Uniform Noise Removal

Zhang¹,

Wei²

2015

Proceedings of the First International Conference on Information Science and Electronic Technology

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Abstract-In this paper, we consider the problem of uniform noise removal, which can be formulated as a minimization problem with L  norm based constraints. A numerical difficult arises due to the property of the non-differentiability of the L  norm. In this paper, we apply first-order primal dual approach to solve the problem of uniform noise removal. Numerical results are given to demonstrate the performance of the proposed method.

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Duality-based algorithms for total-variation-regularized image restoration

Cited by 159 publications

References 17 publications

Algorithms and software for total variation image reconstruction via first-order methods

Algorithms and software for total variation image reconstruction via first-order methods

Two-Dimensional Compact Variational Mode Decomposition

Primal-Dual Approach for Uniform Noise Removal

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