A nonconvex $$\hbox{TV}_q-l_1$$ regularization model and the ADMM based algorithm

Fang, Zhuang; Tang, Liming; Wu, Liang; Hanxin, Liu

doi:10.1038/s41598-022-11938-7

Cited by 7 publications

(3 citation statements)

References 52 publications

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“…Then, the image pixels are classified as corrupted by impulsive or Gaussian noise and the final output is obtained using a variational approach. A method based on the total variation 73 – 75 with -norm fidelity was described in 76 . Although designed for impulsive noise, it can efficiently reduce various mixtures of noise models, too.…”

Section: Related Workmentioning

confidence: 99%

Robust mean shift filter for mixed Gaussian and impulsive noise reduction in color digital images

Kusnik

Smołka

2022

Sci Rep

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Noise reduction is one of the most important topics of digital image processing and despite the fact that it has been studied for a long time it remains the subject of active research. In the following work, we present an extension of the Mean Shift technique, which is efficiently reducing the Gaussian noise, so that it is able to cope with the impulsive disturbances. Furthermore, the elaborated technique can be applied to enhance the images corrupted by a mixture of strong Gaussian and impulsive noise, severely decreasing the quality of color digital images. By means of our approach, which is based on a novel similarity measure between a pixel and a patch located in the center of the processing block, even heavily disturbed images can be effectively restored, which enables the success of further stages of the image processing pipeline. We evaluate the efficiency of the proposed method using a publicly available database of test color images and compare the restored images applying a set of standard quality metrics with the results delivered by state-of-the-art denoising methods. Additionally, we compare our method with the Medoid and Quick Shift techniques, accelerating the original Mean Shift algorithm, in terms of objective quality criteria and computational complexity. The results of the performed experiments indicate that the proposed technique is superior to the widely used denoising techniques and can be used as a robust extension of the Mean Shift procedure. In the paper, a particular emphasis is placed on the ability of the presented algorithm to preserve and enhance image edges. The performed experiments evaluated with the use of the Pratt’s index, quantitatively confirm the superiority of the proposed design over the Mean Shift and standard denoising methods. The preservation of edges and even their sharpening is a very important feature of our algorithm whereas the final goal is segmentation, playing a crucial role in various computer vision tasks. The proposed algorithm is intended for the mixed noise reduction in color images, but it can be also applied in multispectral imaging and clustering of multidimensional data. To enable the comparison of our method with the standard denoising techniques and to help applying it in other image processing fields, we made its code freely available.

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Section: Related Workmentioning

confidence: 99%

Robust mean shift filter for mixed Gaussian and impulsive noise reduction in color digital images

Kusnik

Smołka

2022

Sci Rep

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“…To solve these problems, they employed a penalty decomposition (PD) method [45], which achieved satisfactory numerical results. Some other related work can be found in [46][47][48][49].…”

Section: Introductionmentioning

confidence: 99%

Proximal linearized alternating direction method of multipliers algorithm for nonconvex image restoration with impulse noise

Tang,

Deng,

Peng

et al. 2023

IET Image Processing

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Image restoration with impulse noise is an important task in image processing. Taking into account the statistical distribution of impulse noise, the ℓ1‐norm data fidelity and total variation () model has been widely used in this area. However, the model usually performs worse when the noise level is high. To overcome this drawback, several nonconvex models have been proposed. In this paper, an efficient iterative algorithm is proposed to solve nonconvex models arising in impulse noise. Compared to existing algorithms, the proposed algorithm is a completely explicit algorithm in which every subproblem has a closed‐form solution. The key idea is to transform the original nonconvex models into an equivalent constrained minimization problem with two separable objective functions, where one is differentiable but nonconvex. As a consequence, the proximal linearized alternating direction method of multipliers is employed to solve it. Extensive numerical experiments are presented to demonstrate the efficiency and effectiveness of the proposed algorithm.

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“…One of these algorithms is the 'Alternating Direction Method of Multipliers' (ADMM) algorithm, which was first described by Glowinski and Marroco [7] and Gabay and Mercier [8]. It has proven to be a good tool to solve these kinds of ill-posed inverse problems successfully and thus has gained huge interest within the last decade, during which huge efforts were made to optimize specialized priors or regularizers for all types of structure occurring in images [9][10][11][12][13][14][15]. Many of these algorithms interpret the principle of 'Total Variation' (TV) by Rudin, Osher and Fatemi [16] in slightly different ways.…”

Section: Introductionmentioning

confidence: 99%

ADMM-TGV image restoration for scientific applications with unbiased parameter choice

Zietlow,

Lindner

2023

Preprint

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Image restoration via Alternating Direction Method of Multipliers (ADMM) has gained large interest within the last decade. Solving standard problems of Gaussian and Poisson noise, the set of ‘Total Variation’ (TV) based regularizers proved to be efficient and versatile. In the last few years the ‘Total Generalized Variation’ (TGV) approach combined TV regularizers of different orders adaptively to better suit local regions in the image. This improved the technique significantly. The approach solved the staircase problem inherent of the first order TV while keeping the beneficial edge preservation. The iterative minimization for the augmented Lagrangian of TGV problems requires four important parameters, two penalty parameters ρ and η and two regularization parameters λ0 and λ1. The choice of penalty parameters decides on the convergence speed, the regularization parameters decide on the impact of the respective regularizer and are determined by the noise level in the image. For scientific applications of such algorithms, an automated and thus objective method to determine these parameters is essential to receive unbiased results independent of the user. Obviously, both sets of parameters are to be well-chosen to achieve optimal results, too. In this paper a method is proposed to adaptively chose optimal ρ and η values for the iteration to converge faster, based on the primal and dual residuals arising from the opti-mality conditions of the augmented Lagrangian. Further, we show how to choose λ0 and λ1 based on the inherent noise in the image.

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A nonconvex $$\hbox{TV}_q-l_1$$ regularization model and the ADMM based algorithm

Cited by 7 publications

References 52 publications

Robust mean shift filter for mixed Gaussian and impulsive noise reduction in color digital images

Robust mean shift filter for mixed Gaussian and impulsive noise reduction in color digital images

Proximal linearized alternating direction method of multipliers algorithm for nonconvex image restoration with impulse noise

ADMM-TGV image restoration for scientific applications with unbiased parameter choice

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