Alternating Minimization Method for Total Variation Based Wavelet Shrinkage Model

Zeng, Tieyong; Li, Xiaolong; Ng, Michael K.

doi:10.4208/cicp.210709.180310a

Cited by 31 publications

(5 citation statements)

References 32 publications

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“…Redistribution subject to SIAM license or copyright; see http://www.siam.org/journals/ojsa.php A2863 equivalent to solving N minimizers of the function φ(w i ) = |w i | + (α + β)|w i − t i | 2 , and the exact minimizer w * i of φ(w i ) is given as (cf. [30,54])…”

Section: Algorithm To Reconstruct the Imagesmentioning

confidence: 98%

Two-Step Approach for the Restoration of Images Corrupted by Multiplicative Noise

Huang

Zeng³

2013

SIAM J. Sci. Comput.

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The restoration of images corrupted by blurring and multiplicative noise is a challenging problem in applied mathematics that has attracted much attention in recent years. In this article, we propose a two-step approach to solve the problem of restoring images degraded by multiplicative noise and blurring, where the multiplicative noise is first reduced by nonlocal filters and then a convex variational model is adopted to obtain the final restored images. The variational model of the second step is composed of an L 1 -L 2 data-fidelity term and a total variation regularization term. The alternating direction method (ADM) is utilized to solve this variational problem, and we also prove that the ADM algorithm converges at least linearly. Experimental results show that the proposed two-step approach performs better than the existing methods for restoring images with multiplicative noise and blurring, both in the quality of the restored images and the convergence speed of the algorithms.

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Section: Algorithm To Reconstruct the Imagesmentioning

confidence: 98%

Two-Step Approach for the Restoration of Images Corrupted by Multiplicative Noise

Huang

Zeng³

2013

SIAM J. Sci. Comput.

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“…In the last few decades, deblurring methods based on sparse representation prior are widely studied, such as wavelet based methods [18,43], wavelet tight framelet based methods [7,28]. As a generalization of wavelet, wavelet tight framelet can provide better representation of images and has been applied to image deblurring under various types of noise [19].…”

Section: Introductionmentioning

confidence: 99%

Image Deblurring Via Total Variation Based Structured Sparse Model Selection

Zeng

2015

J Sci Comput

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In this paper, we study the image deblurring problem based on sparse representation over learned dictionary which leads to promising performance in image restoration in recent years. However, the commonly used overcomplete dictionary is not well structured. This shortcoming makes the approximation be unstable and demand much computational time. To overcome this, the structured sparse model selection (SSMS) over a family of learned orthogonal bases was proposed recently. In this paper, We further analyze the properties of SSMS and propose a model for deblurring under Gaussian noise. Numerical experimental results show that the proposed algorithm achieves competitive performance. As a generalization, we give a modified model for deblurring under salt-and-pepper noise. The resulting algorithm also has a good performance.

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“…Moreover, to better preserve textures and small features, wavelet-based methods [20][21][22][23][24] and nonlocal methods [25][26][27][28] have been proposed. Although wavelet-based methods better preserve textures, they may exhibit pseudo-Gibbs phenomena and bring artifacts into the recovered image [24,29]. Moreover, while nonlocal-based approaches take advantage of the similarity of image patches, a low similarity or dissimilarity of the image patches limits their applicability.…”

Section: Introductionmentioning

confidence: 99%

Image Restoration under Cauchy Noise with Sparse Representation Prior and Total Generalized Variation

Jung¹

2021

JCM

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This article introduces a novel variational model for restoring images degraded by Cauchy noise and/or blurring. The model integrates a nonconvex data-fidelity term with two regularization terms, a sparse representation prior over dictionary learning and total generalized variation (TGV) regularization. The sparse representation prior exploiting patch information enables the preservation of fine features and textural patterns, while adequately denoising in homogeneous regions and contributing natural visual quality. TGV regularization further assists in effectively denoising in smooth regions while retaining edges. By adopting the penalty method and an alternating minimization approach, we present an efficient iterative algorithm to solve the proposed model. Numerical results establish the superiority of the proposed model over other existing models in regard to visual quality and certain image quality assessments.

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Alternating Minimization Method for Total Variation Based Wavelet Shrinkage Model

Cited by 31 publications

References 32 publications

Two-Step Approach for the Restoration of Images Corrupted by Multiplicative Noise

Two-Step Approach for the Restoration of Images Corrupted by Multiplicative Noise

Image Deblurring Via Total Variation Based Structured Sparse Model Selection

Image Restoration under Cauchy Noise with Sparse Representation Prior and Total Generalized Variation

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