Accelerated Alternating Descent Methods for Dykstra-Like Problems

Chambolle, Antonin; Tan, Pauline; Vaiter, Samuel

doi:10.1007/s10851-017-0724-6

Cited by 14 publications

(24 citation statements)

References 22 publications

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“…This can severely impact the required computational load and the convergence time to a meaningful result. To mitigate this issue, in the following section we propose to use few reasonable approximations to turn the minimization of (22) into an optimization problem separable in A C and A D . This will remove the interdependency between the different image pixels, and allow the extension of the ALS strategy to consider the optimization w.r.t.…”

Section: Optimizing With Respect To a At The I-th Iterationmentioning

confidence: 99%

“…Hypothesis A1 consists of assuming that the inner product RE C , RE D between the residuals/reconstruction errors RE C and RE D in the coarse and detail image scales is comparatively small, when compared to the first two terms of the cost function (22). To illustrate the validity of this claim, we compare here the values of RE C , RE D with those of the first two terms of the cost function, given by RE C The results are presented below in Table IV.…”

Section: Hypothesismentioning

confidence: 99%

“…This in turn leads to intricate, large scale and computationally demanding optimization problems. Even though some approaches have been investigated to accelerate the minimization of convex TVregularized functionals [22], [23], this is still a computationally demanding operation which, in the context of HU, have been primarily addressed using variable splitting (e.g. ADMM) techniques [8], [9], [10].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A Data Dependent Multiscale Model for Hyperspectral Unmixing With Spectral Variability

Borsoi

Imbiriba

Bermudez

2020

IEEE Trans. on Image Process.

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Spectral variability in hyperspectral images can result from factors including environmental, illumination, atmospheric and temporal changes. Its occurrence may lead to the propagation of significant estimation errors in the unmixing process. To address this issue, extended linear mixing models have been proposed which lead to large scale nonsmooth ill-posed inverse problems. Furthermore, the regularization strategies used to obtain meaningful results have introduced interdependencies among abundance solutions that further increase the complexity of the resulting optimization problem. In this paper we present a novel data dependent multiscale model for hyperspectral unmixing accounting for spectral variability. The new method incorporates spatial contextual information to the abundances in the Extended Linear Mixing Model by using a multiscale transform based on superpixels. The proposed method results in a fast algorithm that solves the abundance problem only once in each scale during each iteration. Simulation results using synthetic and real images compare the performances, both in accuracy and execution time, of the proposed algorithm and other state-of-the-art solutions.

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Section: Optimizing With Respect To a At The I-th Iterationmentioning

confidence: 99%

Section: Hypothesismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A Data Dependent Multiscale Model for Hyperspectral Unmixing With Spectral Variability

Borsoi

Imbiriba

Bermudez

2020

IEEE Trans. on Image Process.

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“…We will show in this paper that such a generalization can be carried out in the framework introduced in [31]. Besides, the convergence speed issue has already been successfully tackled in the convex optimization by using inertia [40,23,5,15,22] and for some nonconvex proximal schemes [32,39]. We will show in this paper that ASAP and its Bregman-distance based generalization can also incorporate such a speed-up strategy, which leads to our proposed method.…”

Section: Biconvex Optimizationmentioning

confidence: 88%

“…If α k 2 = 0, (15) and (16) are the same, so (16) holds whenever α k 2 ≥ 0. Now, since b X is L X -convex, one can lowerbound the previous inequality using (4), which gives:…”

Section: Convergence Analysismentioning

confidence: 99%

Inertial Alternating Generalized Forward–Backward Splitting for Image Colorization

2019

Self Cite

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In this paper, we propose a novel accelerated alternating optimization scheme to solve block-biconvex nonsmooth problems whose objectives can be split into smooth (separable) regularizers and simple coupling terms. The proposed method performs a Bregman distance based generalization of the well-known forward-backward splitting for each block, along with an inertial strategy which aims at getting empirical acceleration. We discuss the theoretical convergence of the proposed scheme and provide numerical experiments on image colorization.

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Integer Optimal Control with Fractional Perimeter Regularization

Antil,

Manns

2024

Appl Math Optim

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Motivated by many applications, optimal control problems with integer controls have recently received a significant attention. Some state-of-the-art work uses perimeter-regularization to derive stationarity conditions and trust-region algorithms. However, the discretization is difficult in this case because the perimeter is concentrated on a set of dimension $$d - 1$$ d - 1 for a domain of dimension d. This article proposes a potential way to overcome this challenge by using the fractional nonlocal perimeter with fractional exponent $$0<\alpha <1$$ 0 < α < 1 . In this way, the boundary integrals in the perimeter regularization are replaced by volume integrals. Besides establishing some non-trivial properties associated with this perimeter, a $$\Gamma $$ Γ -convergence result is derived. This result establishes convergence of minimizers of fractional perimeter-regularized problem, to the standard one, as the exponent $$\alpha $$ α tends to 1. In addition, the stationarity results are derived and algorithmic convergence analysis is carried out for $$\alpha \in (0.5,1)$$ α ∈ ( 0.5 , 1 ) under an additional assumption on the gradient of the reduced objective. The theoretical results are supplemented by a preliminary computational experiment. We observe that the isotropy of the total variation may be approximated by means of the fractional perimeter functional.

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Accelerated Alternating Descent Methods for Dykstra-Like Problems

Cited by 14 publications

References 22 publications

A Data Dependent Multiscale Model for Hyperspectral Unmixing With Spectral Variability

A Data Dependent Multiscale Model for Hyperspectral Unmixing With Spectral Variability

Inertial Alternating Generalized Forward–Backward Splitting for Image Colorization

Integer Optimal Control with Fractional Perimeter Regularization

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