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In this paper, we propose a novel overlapping domain decomposition method that can be applied to various problems in variational imaging such as total variation minimization. Most of recent domain decomposition methods for total variation…
Image restoration is one of the most important areas in imaging science. Mathematical tools have been widely used in image restoration, where wavelet frame based approach is one of the successful examples. In this paper, we introduce a…
An optical imaging system forms an object image by recollecting light scattered by the object. However, intact optical information of the object delivered through the imaging system is deteriorated by imperfect optical elements and unwanted…
In this paper, we study the problem of image recovery from given partial (corrupted) observations. Recovering an image using a low-rank model has been an active research area in data analysis and machine learning. But often, images are not…
A parallel splitting method is proposed for solving systems of coupled monotone inclusions in Hilbert spaces. Convergence is established for a wide class of coupling schemes. Unlike classical alternating algorithms, which are limited to two…
Inpainting-based image compression is a promising alternative to classical transform-based lossy codecs. Typically it stores a carefully selected subset of all pixel locations and their colour values. In the decoding phase the missing…
In the constraint programming framework, state-of-the-art static and dynamic decomposition techniques are hard to apply to problems with complete initial constraint graphs. For such problems, we propose a hybrid approach of these techniques…
The total variation-based image denoising model has been generalized and extended in numerous ways, improving its performance in different contexts. We propose a new penalty function motivated by the recent progress in the statistical…
Total Generalized Variation (TGV) regularization in image reconstruction relies on an infimal convolution type combination of generalized first- and second-order derivatives. This helps to avoid the staircasing effect of Total Variation…
To compute the spatially distributed dielectric constant from the backscattering data, we study a coefficient inverse problem for a 1D hyperbolic equation. To solve the inverse problem, we establish a new version of Carleman estimate and…
A wide array of image recovery problems can be abstracted into the problem of minimizing a sum of composite convex functions in a Hilbert space. To solve such problems, primal-dual proximal approaches have been developed which provide…
In this paper, we study a generalized finite element method for solving second-order elliptic partial differential equations with rough coefficients. The method uses local approximation spaces computed by solving eigenvalue problems on…
This paper introduces an abstract framework for randomized subspace correction methods for convex optimization, which unifies and generalizes a broad class of existing algorithms, including domain decomposition, multigrid, and block…
In this paper, we propose a new Fully Composite Formulation of convex optimization problems. It includes, as a particular case, the problems with functional constraints, max-type minimization problems, and problems of Composite…
This paper considers a networked system with a finite number of users and supposes that each user tries to minimize its own private objective function over its own private constraint set. It is assumed that each user's constraint set can be…
In this paper we investigate the convergence behavior of a primal-dual splitting method for solving monotone inclusions involving mixtures of composite, Lipschitzian and parallel sum type operators proposed by Combettes and Pesquet in [7].…
In this paper we propose a new inexact dual decomposition algorithm for solving separable convex optimization problems. This algorithm is a combination of three techniques: dual Lagrangian decomposition, smoothing and excessive gap. The…
Parallel and cyclic projection algorithms are proposed for minimizing the sum of a finite family of convex functions over the intersection of a finite family of closed convex subsets of a Hilbert space. These algorithms are of…
Nonlocal equations effectively preserve textures but exhibit weak regularization effects in image denoising, whereas local equations offer strong denoising capabilities yet fail to protect textures. To integrate the advantages of both…
A subgradient method is presented for solving general convex optimization problems, the main requirement being that a strictly-feasible point is known. A feasible sequence of iterates is generated, which converges to within user-specified…