Fast algorithm for total variation minimization

Sakurai, Masaru; Kiriyama, Satoshi; Goto, Tomio; Hirano, Satoshi

doi:10.1109/icip.2011.6115718

Cited by 17 publications

(19 citation statements)

References 7 publications

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“…Our experiments were performed on a PC with the Intel CPU 2.8 GHz and 8 GB RAM using MATLAB R2014a. Six different SRR methods were adopted for comparison, including the Bicubic method, the MFT method [23], the TV-based method [13], the TGV-based method [21], the TV4-based method [31], and the FTV4-based method [33]. Among the six methods, the Bicubic method was implemented by the function "imresize()" in the images toolbox of MATLAB; the MFT method used the scripts provided in [23]; other methods were taken by self-produced scripts according to [13,21,31,33].…”

Section: Methodsmentioning

confidence: 99%

“…In 2011, Sakurai et al proposed an extension of TV referred to as TV4 [31] in which both diagonal and back diagonal directional components are included in the typical TV model. TV4 can be defined as…”

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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Section: Methodsmentioning

confidence: 99%

Section: Four-directional Total Variationmentioning

confidence: 99%

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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“…The methods mentioned above merely contain gradient information in the vertical and horizontal directions, but ignores gradient in the diagonal and back-diagonal directions. 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.…”

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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“…Recently, some TV extensions emerged. Sakurai et al [4] proposed a four-directional total variation model to extend the vertical and horizontal gradient information in the TV regularization into four directions. Ren et al [5] proposed a fractional-order TV (FTV) model and tried to extend the integer-order TV model to the fractional order.…”

Section: Introductionmentioning

confidence: 99%

Image Deblurring under Impulse Noise via Total Generalized Variation and Non-Convex Shrinkage

Lin

Chen

et al. 2019

Algorithms

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Image deblurring under the background of impulse noise is a typically ill-posed inverse problem which attracted great attention in the fields of image processing and computer vision. The fast total variation deconvolution (FTVd) algorithm proved to be an effective way to solve this problem. However, it only considers sparsity of the first-order total variation, resulting in staircase artefacts. The L1 norm is adopted in the FTVd model to depict the sparsity of the impulse noise, while the L1 norm has limited capacity of depicting it. To overcome this limitation, we present a new algorithm based on the Lp-pseudo-norm and total generalized variation (TGV) regularization. The TGV regularization puts sparse constraints on both the first-order and second-order gradients of the image, effectively preserving the image edge while relieving undesirable artefacts. The Lp-pseudo-norm constraint is employed to replace the L1 norm constraint to depict the sparsity of the impulse noise more precisely. The alternating direction method of multipliers is adopted to solve the proposed model. In the numerical experiments, the proposed algorithm is compared with some state-of-the-art algorithms in terms of peak signal-to-noise ratio (PSNR), structural similarity (SSIM), signal-to-noise ratio (SNR), operation time, and visual effects to verify its superiority.

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Fast algorithm for total variation minimization

Cited by 17 publications

References 7 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

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

Image Deblurring under Impulse Noise via Total Generalized Variation and Non-Convex Shrinkage

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