A New Fast Algorithm for Constrained Four-Directional Total Variation Image Denoising Problem

Liao, Fan; Coatrieux, Jean Louis; Wu, Jiasong; Hu, Shu

doi:10.1155/2015/815132

Cited by 10 publications

(6 citation statements)

References 28 publications

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“…Further, based on TV4, Liao et al improved the boundary conditions and provided a complete mathematical proof for both anisotropic and isotropic cases [32]:…”

Section: Four-directional Total Variationmentioning

confidence: 99%

“…In contrast, the TV method can only minimize horizontal and vertical gradients, reducing image noise in the horizontal and vertical directions, whereas the four-direction gradient regularization approach can reduce noise in the 45 • and 135 • directions, thereby improving the quality of image reconstruction [31,32]. Based on the four-direction TV (TV4) proposed by Sakurai et al [31], Wu et al presented a four-directional fractional-order TV (FTV4) [33], which applies the fractional-order difference operator to alleviate the staircase artifacts in TV4 and improve its denoising ability.…”

Section: Introductionmentioning

confidence: 99%

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Infrared Image Super-Resolution Reconstruction Based on Quaternion Fractional Order Total Variation with Lp Quasinorm

et al. 2018

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Featured Application: This paper proposes a new super-resolution reconstruction method for infrared images, which makes a contribution to the research in infrared image processing and image reconstruction.Abstract: Owing to the limitations of the imaging principle as well as the properties of imaging systems, infrared images often have some drawbacks, including low resolution, a lack of detail, and indistinct edges. Therefore, it is essential to improve infrared image quality. Considering the information of neighbors, a description of sparse edges, and by avoiding staircase artifacts, a new super-resolution reconstruction (SRR) method is proposed for infrared images, which is based on fractional order total variation (FTV) with quaternion total variation and the L p quasinorm. Our proposed method improves the sparsity exploitation of FTV, and efficiently preserves image structures. Furthermore, we adopt the plug-and-play alternating direction method of multipliers (ADMM) and the fast Fourier transform (FFT) theory for the proposed method to improve the efficiency and robustness of our algorithm; in addition, an accelerated step is adopted. Our experimental results show that the proposed method leads to excellent performances in terms of an objective evaluation and the subjective visual effect.

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“…Further, based on TV4, Liao et al improved the boundary conditions and provided a complete mathematical proof for both anisotropic and isotropic cases [32]:…”

Section: Four-directional Total Variationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Infrared Image Super-Resolution Reconstruction Based on Quaternion Fractional Order Total Variation with Lp Quasinorm

et al. 2018

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“…The impact of single direction constraint over a limited angle tomographic image taken from both x and y directions also showed that the directional information plays an important role in feature preservation in the image taken from a limited view angle ( Zhang et al, 2021 ). There have been alternative modified gradient based total variation algorithms ( Zhang et al, 2021 ; Sakurai et al, 2011 ; Fan Liao & Shu, 2015 ; Huang et al, 2016 ; Huang et al, 2018 ; Hu & Jacob, 2012 ; Zhou & Fan, 2021 ). Sakurai et al proposed a faster four directional TV algorithm that brings two additional partial terms to the horizontal and vertical directional terms in classical TV ( Sakurai et al, 2011 ).…”

Section: Introductionmentioning

confidence: 99%

A nonlinear total variation based computed tomography (CT) image reconstruction method using gradient reinforcement

Ertas

2024

PeerJ

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Compressed sensing-based reconstruction algorithms have been proven to be more successful than analytical or iterative methods for sparse computed tomography (CT) imaging by narrowing down the solution set thanks to its ability to seek a sparser solution. Total variation (TV), one of the most popular sparsifiers, exploits spatial continuity of features by restricting variation between two neighboring pixels in each direction as using partial derivatives. When the number of projections is much fewer than the one in conventional CT, which results in much less sampling rate than the minimum required one, TV may not provide satisfactory results. In this study, a new regularizer is proposed which seeks for a sparser solution by reinforcing the gradient of TV and empowering the spatial continuity of features. The experiments are done by using both analitical phantom and real human CT images and the results are compared with conventional, four-directional, and directional TV algorithms by using contrast-to-noise ratio (CNR), signal-to-noise ratio (SNR) and Structural Similarity Index (SSIM) metrics. Both quantitative and visual evaluations show that the proposed method is promising for sparse CT image reconstruction by reducing the background noise while preserving the features and edges.

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“…Four-directional total variation (TV4) [26] can make full use of the neighbor gradient information of each pixel. A new four-directional total variation model proposed by Liao et al [27] takes gradient information in the diagonal and back-diagonal directions into account. They solved the optimization problem with gradient projection (GP) and also given a complete mathematical proof for the first time.…”

Section: Introductionmentioning

confidence: 99%

Four-Directional Total Variation With Overlapping Group Sparsity for Image Denosing

Zhou

Fan

2021

IEEE Access

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In this paper, a new model combining four-directional total variation with overlapping group sparsity is proposed, which not only suppresses the staircase effects introduced by traditional total variation, but also fully utilizes the gradient neighborhood information on each pixel of the image. In order to decrease the computation time of image denoising, the alternating direction method of multipliers (ADMM) is adopted to divide the complex optimization problem into separate subproblems that are easy to solve. At the same time, two-dimensional Fast Fourier Transform (FFT) and majorization-minimization (MM) are used to solve the subproblems alternatively. Then, the proposed new model is compared with other state-of-the-art models. Experiments show that the new model is robust in denoising. The new model not only excavates the gradient information of the four directions on the image to remove the noise more effectively, but also better in preserving image features, further reducing staircase artifacts. INDEX TERMS Image denoising; Four-directional total variation; Overlapping group sparsity; ADMM.

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A New Fast Algorithm for Constrained Four-Directional Total Variation Image Denoising Problem

Cited by 10 publications

References 28 publications

Infrared Image Super-Resolution Reconstruction Based on Quaternion Fractional Order Total Variation with Lp Quasinorm

Infrared Image Super-Resolution Reconstruction Based on Quaternion Fractional Order Total Variation with Lp Quasinorm

A nonlinear total variation based computed tomography (CT) image reconstruction method using gradient reinforcement

Four-Directional Total Variation With Overlapping Group Sparsity for Image Denosing

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