A random block-coordinate primal-dual proximal algorithm with application to 3D mesh denoising

Repetti, Audrey; Chouzenoux, Émilie; Pesquet, Jean-Christophe

doi:10.1109/icassp.2015.7178634

Cited by 4 publications

(3 citation statements)

References 28 publications

(39 reference statements)

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“…Recently such parallel strategies were also examined by Pesquet and co-authors [7,34]. Further we want to mention the interesting stochastic block coordinate algorithms in [16,36].…”

Section: Algorithm 1: Pdhg For (4)mentioning

confidence: 99%

Removal of curtaining effects by a variational model with directional forward differences

Fitschen

Schuff

2017

Computer Vision and Image Understanding

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Focused ion beam (FIB) tomography provides high resolution volumetric images on a micro scale. However, due to the physical acquisition process the resulting images are often corrupted by a so-called curtaining or waterfall effect. In this paper, a new convex variational model for removing such effects is proposed. More precisely, an infimal convolution model is applied to split the corrupted 3D image into the clean image and two types of corruptions, namely a striped part and a laminar one. As regularizing terms different direction dependent first and second order differences are used to cope with the specific structure of the corruptions. This generalizes discrete unidirectional total variational (TV) approaches. A minimizer of the model is computed by well-known primal dual techniques. Numerical examples show the very good performance of our new method for artificial and real-world data. Besides FIB tomography, we have also successfully applied our technique for the removal of pure stripes in Moderate Resolution Imaging Spectroradiometer (MODIS) data.

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“…Recently such parallel strategies were also examined by Pesquet and co-authors [7,34]. Further we want to mention the interesting stochastic block coordinate algorithms in [16,36].…”

Section: Algorithm 1: Pdhg For (4)mentioning

confidence: 99%

Removal of curtaining effects by a variational model with directional forward differences

Fitschen

Schuff

2017

Computer Vision and Image Understanding

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“…Noisy mesh nodes z i , i ∈ [n], are observed. We try to recover the original mesh nodes by solving the following optimization problem [60]: (54) minimize…”

Section: Total Variation Imagementioning

confidence: 99%

Coordinate-friendly structures, algorithms and applications

Peng

et al. 2016

Annals of Mathematical Sciences and Applications

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This paper focuses on coordinate update methods, which are useful for solving problems involving large or high-dimensional datasets. They decompose a problem into simple subproblems, where each updates one, or a small block of, variables while fixing others. These methods can deal with linear and nonlinear mappings, smooth and nonsmooth functions, as well as convex and nonconvex problems. In addition, they are easy to parallelize.The great performance of coordinate update methods depends on solving simple subproblems. To derive simple subproblems for several new classes of applications, this paper systematically studies coordinate friendly operators that perform low-cost coordinate updates.Based on the discovered coordinate friendly operators, as well as operator splitting techniques, we obtain new coordinate update algorithms for a variety of problems in machine learning, image processing, as well as sub-areas of optimization. Several problems are treated with coordinate update for the first time in history. The obtained algorithms are scalable to large instances through parallel and even asynchronous computing. We present numerical examples to illustrate how effective these algorithms are.

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“…If fm and ψ can be decomposed w.r.t. sub-vectors of w, the stochastic primaldual proximal algorithm [18,19] would be another choice for solving (1). We refer the readers to [20] for more information.…”

Section: Sdca-admmmentioning

confidence: 99%

Image restoration using a stochastic variant of the alternating direction method of multipliers

Ono

Yamagishi

Miyata

et al. 2016

2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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We propose an efficient image restoration framework based on stochastic optimization. Image restoration usually requires some iterative methods for solving optimization problems that characterize restored images, where the multiplication of the observation matrix Φ ∈ R M ×N and variables has to be computed at each iteration. If an efficient implementation of the multiplication (e.g., using FFT) is unavailable, its computational cost becomes O(MN), which is quite expensive since both N and M are usually large in image restoration. Our method needs to load and apply only a part of the observation matrix of size M b × N (b: the number of parts), so that the computational cost is only O( MN b ). Moreover, the proposed method accepts various nonsmooth objectives effective for image restoration. Experiments on compressed sensing reconstruction and non-uniform deblurring show the advantage of the proposed method over state-of-the-art proximal optimization methods.

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A random block-coordinate primal-dual proximal algorithm with application to 3D mesh denoising

Cited by 4 publications

References 28 publications

Removal of curtaining effects by a variational model with directional forward differences

Removal of curtaining effects by a variational model with directional forward differences

Coordinate-friendly structures, algorithms and applications

Image restoration using a stochastic variant of the alternating direction method of multipliers

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