Augmented Lagrangian Method, Dual Methods and Split Bregman Iteration for ROF Model

Tai, Xue–Cheng; Wu, Chunlin

doi:10.1007/978-3-642-02256-2_42

Cited by 163 publications

(144 citation statements)

References 25 publications

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“…Unlike previous approaches for augmented Lagrangian TV regularization [36], our approach differs in the measure of smoothness we use. We note that while the update step for v comes from minimizing the cost function, it is highly linked to the intuitive choice of updating u and then projecting it, as well as to optimization by proximal operators [11], and can be made provably convergent with minor modifications, as shown in [31].…”

Section: Methodsmentioning

confidence: 99%

“…In order to efficiently regularize images on parametric surfaces, we sample the parametrization domain on a Cartesian grid. The scheme we present is based on the augmented Lagrangian TV optimization scheme [36]. We use an auxiliary variable p to describe the surface-domain gradient, rather than the image-domain gradient.…”

Section: Augmented Lagrangian Tv Optimization Of Vector Valued Functimentioning

confidence: 99%

“…We use an auxiliary variable p to describe the surface-domain gradient, rather than the image-domain gradient. That is, we add an auxiliary variable p = J M ∇u, and optimize with respect to it using a shrinkage operator, similar to the image-domain TV case [36]. J M denotes the Jacobian relating image coordinates and surface coordinates.…”

Section: Augmented Lagrangian Tv Optimization Of Vector Valued Functimentioning

confidence: 99%

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Group-Valued Regularization for Analysis of Articulated Motion

Rosman

Bronstein

et al. 2012

Computer Vision – ECCV 2012. Workshops and Demonstrations

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Abstract. We present a novel method for estimation of articulated motion in depth scans. The method is based on a framework for regularization of vector-and matrix-valued functions on parametric surfaces.We extend augmented-Lagrangian total variation regularization to smooth rigid motion cues on the scanned 3D surface obtained from a range scanner. We demonstrate the resulting smoothed motion maps to be a powerful tool in articulated scene understanding, providing a basis for rigid parts segmentation, with little prior assumptions on the scene, despite the noisy depth measurements that often appear in commodity depth scanners.

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Section: Methodsmentioning

confidence: 99%

Section: Augmented Lagrangian Tv Optimization Of Vector Valued Functimentioning

confidence: 99%

Section: Augmented Lagrangian Tv Optimization Of Vector Valued Functimentioning

confidence: 99%

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Group-Valued Regularization for Analysis of Articulated Motion

Rosman

Bronstein

et al. 2012

Computer Vision – ECCV 2012. Workshops and Demonstrations

Self Cite

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show abstract

“…For example, for image deblurring where the blur is assumed to be a result of a circular convolution using L 2 regularization of the unknown image, the estimation of the noise-free image is best done in the discrete Fourier domain: the least squares formulation then leads to a point-wise Wiener filter. Alternatively, many sparse solvers (e.g., based on ADMM, 12 augmented Lagrangrian, 13 primal-dual techniques 14 ) use splitting variables to split the problem into a set of subproblems that are more easy to solve. Then, depending on the structure of the involved matrices and the cost function, a particular solver can be used for each subproblem.…”

Section: Modularitymentioning

confidence: 99%

GASPACHO: a generic automatic solver using proximal algorithms for convex huge optimization problems

Goossens

Luong

Philips

2017

Wavelets and Sparsity XVII

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Many inverse problems (e.g., demosaicking, deblurring, denoising, image fusion, HDR synthesis) share various similarities: degradation operators are often modeled by a specific data fitting function while image prior knowledge (e.g., sparsity) is incorporated by additional regularization terms. In this paper, we investigate automatic algorithmic techniques for evaluating proximal operators. These algorithmic techniques also enable efficient calculation of adjoints from linear operators in a general matrix-free setting. In particular, we study the simultaneous-direction method of multipliers (SDMM) and the parallel proximal algorithm (PPXA) solvers and show that the automatically derived implementations are well suited for both single-GPU and multi-GPU processing. We demonstrate this approach for an Electron Microscopy (EM) deconvolution problem.

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“…Moreover, another set of algorithms employs the splitting idea [22] in developing an alternating minimisation approach for image recovery with TV regularisation, such as RecRF [23], TVAL3 [24,25], and ADMM [26,27] utilizing techniques like the split Bregman algorithm [28], the augmented Lagrangian method or the alternating direction method and gaining also fast convergence. The interrelations of these techniques have been pointed out in [29] and [30].…”

Section: Introductionmentioning

confidence: 99%

TV-based conjugate gradient method and discrete L-curve for few-view CT reconstruction of X-ray in vivo data

Yang¹,

Hofmann²,

Dapp³

et al. 2015

Opt. Express

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High-resolution, three-dimensional (3D) imaging of soft tissues requires the solution of two inverse problems: phase retrieval and the reconstruction of the 3D image from a tomographic stack of two-dimensional (2D) projections. The number of projections per stack should be small to accommodate fast tomography of rapid processes and to constrain X-ray radiation dose to optimal levels to either increase the duration of in vivo time-lapse series at a given goal for spatial resolution and/or the conservation of structure under X-ray irradiation. In pursuing the 3D reconstruction problem in the sense of compressive sampling theory, we propose to reduce the number of projections by applying an advanced algebraic technique subject to the minimisation of the total variation (TV) in the reconstructed slice. This problem is formulated in a Lagrangian multiplier fashion with the parameter value determined by appealing to a discrete L-curve in conjunction with a conjugate gradient method. The usefulness of this reconstruction modality is demonstrated for simulated and in vivo data, the latter acquired in parallel-beam imaging experiments using synchrotron radiation.

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Augmented Lagrangian Method, Dual Methods and Split Bregman Iteration for ROF Model

Cited by 163 publications

References 25 publications

Group-Valued Regularization for Analysis of Articulated Motion

Group-Valued Regularization for Analysis of Articulated Motion

GASPACHO: a generic automatic solver using proximal algorithms for convex huge optimization problems

TV-based conjugate gradient method and discrete L-curve for few-view CT reconstruction of X-ray in vivo data

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