A Coordinate Descent Method for Total Variation Minimization

Deng, Hong; Ren, Dongwei; Xiao, Gang; Zhang, David; Zuo, Wangmeng

doi:10.1155/2017/3012910

Cited by 3 publications

(2 citation statements)

References 60 publications

(72 reference statements)

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“…During the past several decades, many techniques have been developed to restore the corrupted image, such as the blind denoising method [ 9 , 10 ] and total-variation denoising method [ 11 , 12 ]. Among the traditional denoising methods, the standard median filter is one of the most popular nonlinear filters for the removal of salt-and-pepper noise in terms of its good denoising capability and computational efficiency [ 13 ].…”

Section: Introductionmentioning

confidence: 99%

A two-stage filter for removing salt-and-pepper noise using noise detector based on characteristic difference parameter and adaptive directional mean filter

Nie

2018

PLoS ONE

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In this paper, a two-stage filter for removing salt-and-pepper noise using noise detector based on characteristic difference parameter and adaptive directional mean filter is proposed. The first stage firstly detects the noise corrupted pixels by combining characteristic difference parameter and gray level extreme, then develops an improved adaptive median filter to firstly restore them. The second stage introduces a restoration scheme to further restore the noise corrupted pixels, which firstly divides them into two types and then applies different restoration skills for the pixels based on the classification result. One type of pixels is restored by the mean filter and the other type of pixels is restored by the proposed adaptive directional mean filter. The new filter firstly adaptively selects the optimal filtering window and direction template, then replaces the gray level of noise corrupted pixel by the mean value of pixels on the optimal template. Experimental results show that the proposed filter outperforms many existing main filters in terms of noise suppression and detail preservation.

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Section: Introductionmentioning

confidence: 99%

A two-stage filter for removing salt-and-pepper noise using noise detector based on characteristic difference parameter and adaptive directional mean filter

Nie

2018

PLoS ONE

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“…For example, in [9], a BCDtype method, block coordinate gradient projection (BCGP) method, is analyzed, in which at each sub-iteration, the exact minimization with respect to a certain block of variables is replaced or updated through a single step of the gradient projection method. We also note that, in [36], a FOTV-regularized BCD method, incorporated with the augmented Lagrangian method (ALM), is recommended to solve the problem of image restoration. More recently, a convergent, BCD-based regularization method is proposed and analyzed for linear inverse problems with forward operators having a distinct tensor product form [78].…”

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confidence: 99%

A variational method for Abel inversion tomography with mixed Poisson-Laplace-Gaussian noise

Kong

Wei

2022

IPI

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<p style='text-indent:20px;'>Abel inversion tomography plays an important role in dynamic experiments, while most known studies are started with a single Gaussian assumption. This paper proposes a mixed Poisson-Laplace-Gaussian distribution to characterize the noise in charge-coupled-device (CCD) sensed radiographic data, and develops a multi-convex optimization model to address the reconstruction problem. The proposed model is derived by incorporating varying amplitude Gaussian approximation and expectation maximization algorithm into an infimal convolution process. To solve it numerically, variable splitting and augmented Lagrangian method are integrated into a block coordinate descent framework, in which anisotropic diffusion and additive operator splitting are employed to gain edge preserving and computation efficiency. Supplementarily, a space of functions of adaptive bounded Hessian is introduced to prove the existence and uniqueness of solution to a higher-order regularized, quadratic subproblem. Moreover, a simplified algorithm with higher order regularizer is derived for Poisson noise removal. To illustrate the performance of the proposed algorithms, numerical tests on synthesized and real digital data are performed.</p>

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Analysing Mission-critical Cyber-physical Systems with AND/OR Graphs and MaxSAT

Barrère

Hankin

2021

ACM Trans. Cyber-Phys. Syst.

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Cyber-Physical Systems (CPS) often involve complex networks of interconnected software and hardware components that are logically combined to achieve a common goal or mission; for example, keeping a plane in the air or providing energy to a city. Failures in these components may jeopardise the mission of the system. Therefore, identifying the minimal set of critical CPS components that is most likely to fail, and prevent the global system from accomplishing its mission, becomes essential to ensure reliability. In this article, we present a novel approach to identifying the Most Likely Mission-critical Component Set (MLMCS) using AND/OR dependency graphs enriched with independent failure probabilities. We address the MLMCS problem as a Maximum Satisfiability (MaxSAT) problem. We translate probabilities into a negative logarithmic space to linearise the problem within MaxSAT. The experimental results conducted with our open source tool LDA4CPS indicate that the approach is both effective and efficient. We also present a case study on complex aircraft systems that shows the feasibility of our approach and its applicability to mission-critical cyber-physical systems. Finally, we present two MLMCS-based security applications focused on system hardening and forensic investigations.

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A Coordinate Descent Method for Total Variation Minimization

Cited by 3 publications

References 60 publications

A two-stage filter for removing salt-and-pepper noise using noise detector based on characteristic difference parameter and adaptive directional mean filter

A two-stage filter for removing salt-and-pepper noise using noise detector based on characteristic difference parameter and adaptive directional mean filter

A variational method for Abel inversion tomography with mixed Poisson-Laplace-Gaussian noise

Analysing Mission-critical Cyber-physical Systems with AND/OR Graphs and MaxSAT

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