A Proximal Interior Point Algorithm with Applications to Image Processing

Chouzenoux, Émilie; Corbineau, Marie-Caroline; Pesquet, Jean-Christophe

doi:10.1007/s10851-019-00916-w

Cited by 8 publications

(6 citation statements)

References 84 publications

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“…However, solving exactly each subproblem P γj with a given algorithm is practically impossible and not desirable for computational time reasons. When R is differentiable, the following proposed inexact exterior penalty method, inspired by [22], [23], allows an inexact resolution (i.e., early stopping) for the sequence of subproblems (P γj ) j∈N , while still benefiting from the same convergence properties as above.…”

Section: Proposed Exterior Penalty Framework a Exact Exterior Penalty Methodsmentioning

confidence: 99%

A Penalized Subspace Strategy for Solving Large-Scale Constrained Optimization Problems

Martin

Chouzenoux

Pesquet

2021

2021 29th European Signal Processing Conference (EUSIPCO)

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Many data science problems can be efficiently addressed by minimizing a cost function subject to various constraints. In this paper a new method for solving largescale constrained differentiable optimization problems is proposed. To account efficiently for a wide range of constraints, our approach embeds a subspace algorithm into an exterior penalty framework. The subspace strategy, combined with a Majoration-Minimization step search, takes great advantage of the smoothness of the penalized cost function. Assuming that the latter is convex, the convergence of our algorithm to a solution of the constrained optimization problem is proved. Numerical experiments carried out on a large-scale image restoration application show that the proposed method outperforms stateof-the-art algorithms in terms of computational time.

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Section: Proposed Exterior Penalty Framework a Exact Exterior Penalty Methodsmentioning

confidence: 99%

A Penalized Subspace Strategy for Solving Large-Scale Constrained Optimization Problems

Martin

Chouzenoux

Pesquet

2021

2021 29th European Signal Processing Conference (EUSIPCO)

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“…The integrated heuristics of PSO-IPM is exploited to train the networks, while the essential parameter settings of importance elements for PSO-IPM are given in Table 1. Few recently IP scheme applications are power flow security constraint optimization (Casacio et al 2019), image processing (Chouzenoux et al 2020), multistage nonlinear nonconvex problems (Zanelli et al 2020) and nonlinear benchmark models (Wambacq et al 2021). The PSO-IP scheme is used to train the networks as per process and parameter settings provided in Table 1.…”

Section: Optimization: Pso-ipmmentioning

confidence: 99%

Neuro-swarm computational heuristic for solving a nonlinear second-order coupled Emden–Fowler model

Sabir

Raja²,

Băleanu

et al. 2022

Soft Comput

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The aim of the current study is to present the numerical solutions of a nonlinear second-order coupled Emden–Fowler equation by developing a neuro-swarming-based computing intelligent solver. The feedforward artificial neural networks (ANNs) are used for modelling, and optimization is carried out by the local/global search competences of particle swarm optimization (PSO) aided with capability of interior-point method (IPM), i.e., ANNs-PSO-IPM. In ANNs-PSO-IPM, a mean square error-based objective function is designed for nonlinear second-order coupled Emden–Fowler (EF) equations and then optimized using the combination of PSO-IPM. The inspiration to present the ANNs-PSO-IPM comes with a motive to depict a viable, detailed and consistent framework to tackle with such stiff/nonlinear second-order coupled EF system. The ANNs-PSO-IP scheme is verified for different examples of the second-order nonlinear-coupled EF equations. The achieved numerical outcomes for single as well as multiple trials of ANNs-PSO-IPM are incorporated to validate the reliability, viability and accuracy.

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“…Standard interior point methods require to invert several n × n linear systems, which leads to a high computational complexity for large scale problems. Nonetheless, it has recently been shown that combining the interior point framework with a proximal forward-backward strategy [44,45] leads to very competitive solvers for inverse problems [46,47,48].…”

Section: Interior Point Approachesmentioning

confidence: 99%

Deep unfolding of a proximal interior point method for image restoration

Bertocchi¹,

Chouzenoux²,

Corbineau³

et al. 2020

Inverse Problems

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106

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Variational methods are widely applied to ill-posed inverse problems for they have the ability to embed prior knowledge about the solution. However, the level of performance of these methods significantly depends on a set of parameters, which can be estimated through computationally expensive and timeconsuming methods. In contrast, deep learning offers very generic and efficient architectures, at the expense of explainability, since it is often used as a black-box, without any fine control over its output. Deep unfolding provides a convenient approach to combine variational-based and deep learning approaches. Starting from a variational formulation for image restoration, we develop iRestNet, a neural network architecture obtained by unfolding a proximal interior point algorithm. Hard constraints, encoding desirable properties for the restored image, are incorporated into the network thanks to a logarithmic barrier, while the barrier parameter, the stepsize, and the penalization weight are learned by the network. We derive explicit expressions for the gradient of the proximity operator for various choices of constraints, which allows training iRestNet with gradient descent and backpropagation. In addition, we provide theoretical results regarding the stability of the network for a common inverse problem example. Numerical experiments on image deblurring problems show that the proposed approach compares favorably with both state-of-the-art variational and machine learning methods in terms of image quality.

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A Proximal Interior Point Algorithm with Applications to Image Processing

Cited by 8 publications

References 84 publications

A Penalized Subspace Strategy for Solving Large-Scale Constrained Optimization Problems

A Penalized Subspace Strategy for Solving Large-Scale Constrained Optimization Problems

Neuro-swarm computational heuristic for solving a nonlinear second-order coupled Emden–Fowler model

Deep unfolding of a proximal interior point method for image restoration

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