Non-negatively constrained image deblurring with an inexact interior point method

Bonettini, Silvia; Serafini, Thomas

doi:10.1016/j.cam.2009.02.020

Cited by 12 publications

(9 citation statements)

References 34 publications

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“…In general, problem (2) does not have a closed-form solution on account of the inequality constraints, even for simple regularizations, hence an iterative solver must be used. Several resolution approaches are available, either based on projected gradient strategies [39,40], ADMM [41], primal-dual schemes [42], or interior point techniques [43]. Standard interior point methods require to invert several n × n linear systems, which leads to a high computational complexity for large scale problems.…”

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

103

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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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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

103

View full text Add to dashboard Cite

show abstract

“…Recently, various algorithms were developed on the basis of convex optimization techniques to compute the minimizer of the variational problem (1.2), such as SpaRSA (sparse reconstruction by separable approximation) [7], Nesterovs algorithm [8], FISTA (fast iterative shrinkage/thresolding algorithm) [9], TwIST (two-step IST) [10]. These methods were shown to be considerably faster than earlier methods, including interior-point methods [11,12] and iterative thresholding ideas [13,14]. Very recently, a new algorithm named SALSA (split augmented Lagrangian shrinkage algorithm) [15] was proposed and shown to be more efficient than TwIST, FISTA, and SpaRSA.…”

Section: Introductionmentioning

confidence: 98%

Restoration of images based on subspace optimization accelerating augmented Lagrangian approach

Chen

Cheng

2011

Journal of Computational and Applied Mathematics

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a b s t r a c tWe propose a new fast algorithm for solving a TV-based image restoration problem. Our approach is based on merging subspace optimization methods into an augmented Lagrangian method. The proposed algorithm can be seen as a variant of the ALM (Augmented Lagrangian Method), and the convergence properties are analyzed from a DRS (Douglas-Rachford splitting) viewpoint. Experiments on a set of image restoration benchmark problems show that the proposed algorithm is a strong contender for the current state of the art methods.Crown

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“…From a numerical perspective, IPMs have demonstrated very good performance on several challenging applications, such as image reconstruction [8] and multispectral image unmixing [9]. It is worth noting that most of interior point approaches rely on first or second-order methods and, therefore, assume that the objective function is at least twice-differentiable [10,11]. However, in many image processing applications, the quality of the solution and its robustness to noise may be improved by including a nondifferentiable regularization term in the objective function.…”

Section: Introductionmentioning

confidence: 99%

A Proximal Interior Point Algorithm with Applications to Image Processing

2019

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In this article, we introduce a new proximal interior point algorithm (PIPA). This algorithm is able to handle convex optimization problems involving various constraints where the objective function is the sum of a Lipschitz differentiable term and a possibly nonsmooth one. Each iteration of PIPA involves the minimization of a merit function evaluated for decaying values of a logarithmic barrier parameter. This inner minimization is performed thanks to a finite number of subiterations of a variable metric forward-backward method employing a line search strategy. The convergence of this latter step as well as the convergence the global method itself are analyzed. The numerical efficiency of the proposed approach is demonstrated in two image processing applications.

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Non-negatively constrained image deblurring with an inexact interior point method

Cited by 12 publications

References 34 publications

Deep unfolding of a proximal interior point method for image restoration

Deep unfolding of a proximal interior point method for image restoration

Restoration of images based on subspace optimization accelerating augmented Lagrangian approach

A Proximal Interior Point Algorithm with Applications to Image Processing

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