Wavelet Decomposition Method for $L_2/$/TV-Image Deblurring

Fornasier, Massimo; Kim, Yunho; Langer, Andreas; Schönlieb, Carola-Bibiane

doi:10.1137/100819801

Cited by 17 publications

(15 citation statements)

References 34 publications

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“…Therefore, it could oversmooth the texture and achieve worse performance in fine structures, as it only accounts for the local statistical characteristics. Some additional studies on total variation have been proposed to further improve its denoising quality [22,23].…”

Section: Regularization Model Based Image Denoisingmentioning

confidence: 99%

Hyperspectral Image Denoising with Composite Regularization Models

Chen

Lin

et al. 2016

Journal of Sensors

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Denoising is a fundamental task in hyperspectral image (HSI) processing that can improve the performance of classification, unmixing, and other subsequent applications. In an HSI, there is a large amount of local and global redundancy in its spatial domain that can be used to preserve the details and texture. In addition, the correlation of the spectral domain is another valuable property that can be utilized to obtain good results. Therefore, in this paper, we proposed a novel HSI denoising scheme that exploits composite spatial-spectral information using a nonlocal technique (NLT). First, a specific way to extract patches is employed to mine the spatial-spectral knowledge effectively. Next, a framework with composite regularization models is used to implement the denoising. A number of HSI data sets are used in our evaluation experiments and the results demonstrate that the proposed algorithm outperforms other state-of-the-art HSI denoising methods.

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Section: Regularization Model Based Image Denoisingmentioning

confidence: 99%

Hyperspectral Image Denoising with Composite Regularization Models

Chen

Lin

et al. 2016

Journal of Sensors

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“…For nonsmooth and nonadditive energies, however, the research on subspace correction methods is far from being complete, and for some problem classes counterexamples do exist indicating failure of splitting techniques; see e.g. [24,57].…”

mentioning

confidence: 99%

Overlapping Domain Decomposition Methods for Total Variation Denoising

Langer

Gaspoz

2019

SIAM J. Numer. Anal.

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Alternating and parallel overlapping domain decomposition methods for the minimization of the total variation are presented. Their derivation is based on the predual formulation of the total variation minimization problem. In particular, the predual total variation minimization problem is decomposed into overlapping domains yielding subdomain problems in the respective dual space. Subsequently these subdomain problems are again dualized, forming a splitting algorithm for the original total variation minimization problem. The convergence of the proposed domain decomposition methods to a solution of the global problem is proven. In contrast to other works, the analysis is carried out in an infinite dimensional setting. Numerical experiments are shown to support the theoretical results and to demonstrate the effectiveness of the algorithms.

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“…Moreover, for image deblurring problems preconditioning effects of a specific subspace correction algorithm for minimizing a nonsmooth energy are shown in [51]. For nonsmooth and nonadditive energies, however, the research on subspace correction methods is far from being complete, and for some problem classes counterexamples exist indicating failure of subspace correction; see, e.g., [28,52].…”

mentioning

confidence: 99%

“…Recently, in [28,29,30], nonoverlapping and overlapping domain decomposition strategies were introduced for solving the L 2 -TV problem. In this context, the major difficulty lies in the correct treatment of the interfaces of the domain decomposition patches, i.e., the preservation of crossing discontinuities and the correct matching where the solution is continuous.…”

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confidence: 99%

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Subspace Correction Methods for a Class of Nonsmooth and Nonadditive Convex Variational Problems with Mixed $L^1/L^2$ Data-Fidelity in Image Processing

Hintermüller¹,

Langer²

2013

SIAM J. Imaging Sci.

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The minimization of a functional composed of a nonsmooth and nonadditive regularization term and a combined L 1 and L 2 data-fidelity term is proposed. It is shown analytically and numerically that the new model has noticeable advantages over popular models in image processing tasks. For the numerical minimization of the new objective, subspace correction methods are introduced which guarantee the convergence and monotone decay of the associated energy along the iterates. Moreover, an estimate of the distance between the outcome of the subspace correction method and the global minimizer of the nonsmooth objective is derived. This estimate and numerical experiments for image denoising, inpainting, and deblurring indicate that in practice the proposed subspace correction methods indeed approach the global solution of the underlying minimization problem.

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Wavelet Decomposition Method for $L_2/$/TV-Image Deblurring

Cited by 17 publications

References 34 publications

Hyperspectral Image Denoising with Composite Regularization Models

Hyperspectral Image Denoising with Composite Regularization Models

Overlapping Domain Decomposition Methods for Total Variation Denoising

Subspace Correction Methods for a Class of Nonsmooth and Nonadditive Convex Variational Problems with Mixed $L^1/L^2$ Data-Fidelity in Image Processing

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