Deblurring Poisson noisy images by total variation with overlapping group sparsity

Lv, Xiao-Guang; Jiang, Le; Liu, Jun

doi:10.1016/j.amc.2016.03.029

Cited by 23 publications

(15 citation statements)

References 63 publications

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“…For this purpose, in the case of Gaussian noise we have selected the methods proposed by Cuesta et al [38], fractional-order total variation using proximity algorithm (FTV-PA) [57], R-NL [58], Adaptive Regularization with the Structure Tensor [59]., the full fractional anisotropic diffusion (FFAD) [60] and overlapping group sparsity (OLGS) [40] for comparative analysis. For the case of Poisson noise, comparison is performed with the methods such as fourth-order partial differential equation filter (FOPDEF) [12], TV-Poi [61], OGS-ADM [62], Framelet based (BPID-FR) [63], spatially adaptive (RLSATV) [64] and sparse based (TV-L0) [65]. The work of TV-Poi and OGS-ADM is based on the TV and overlapping group sparsity based prior for Poisson noise image deblurring.…”

Section: Comparative Analysismentioning

confidence: 99%

A Framework for Image Denoising Using First and Second Order Fractional Overlapping Group Sparsity (HF-OLGS) Regularizer

2019

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Denoising images subjected to Gaussian and Poisson noise has attracted attention in many areas of image processing. This paper introduces an image denoising framework using higher order fractional overlapping group sparsity prior to sparser image representation constraint. The proposed prior has a capability of avoiding staircase effects in both edges and oscillatory patterns (textures). We adopt the alternating direction method of multipliers for optimizing the proposed objective function by converting it into a constrained optimization problem using variable splitting approach. Finally, we conduct experiments on various degraded images and compare our results with those of several state-of-the-art methods. The numerical results show that the proposed fractional order image denoising framework improves the peak signal to noise ratio of an image by preserving the textures and eliminating the staircases effects. This leads to visually pleasant restored images which exhibit a higher value of Structural SIMilarity score when compared to that of other methods. INDEX TERMS Image denoising, fractional-order, Gaussian and Poisson noise, overlapping group sparsity, alternating direction method of multipliers.

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Section: Comparative Analysismentioning

confidence: 99%

A Framework for Image Denoising Using First and Second Order Fractional Overlapping Group Sparsity (HF-OLGS) Regularizer

2019

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“…The mixture model could better suppress the staircase effect and preserve the details in image edges. Recently, overlapping group sparsity has been applied to figure out Cauchy noise [23], Poisson noise [24], and speckle noise [25], demonstrating its effectiveness. The methods mentioned above merely contain gradient information in the vertical and horizontal directions, but ignores gradient in the diagonal and back-diagonal directions.…”

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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“…First, Rudin et al proposed a nonlinear TV model for denoising of the image as follows 3 :

\min_{u} : ‖ \nabla u ‖_{2} + \frac{μ}{2} ‖ u - u_{0} ‖_{2}^{2},

where μ is the regularization parameter and

normalΨ false(false| normal\nabla u false| false) = false‖ normal\nabla u {false‖}_{2}

is the TV regularizer. Based on this idea, several researchers worked in deblurring process 5‐8 and denoising–deblurring processes 9,10 . The other regularization term that we mentioned here is the Mumford–Shah regularizing functional 2 .…”

Section: Introductionmentioning

confidence: 99%

“…where is the regularization parameter and Ψ(|(u|) = ||(u|| 2 is the TV regularizer. Based on this idea, several researchers worked in deblurring process [5][6][7][8] and denoising-deblurring processes. 9,10 The other regularization term that we mentioned here is the Mumford-Shah regularizing functional.…”

Section: Introductionmentioning

confidence: 99%

Image deblurring using adaptive fractional‐order shock filter

Irandoust‐pakchin

Babapour

Lakestani

2020

Math Methods in App Sciences

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In this paper, a novel image enhancement model based on shock filter for image deblurring is proposed in three cases. For the weight of shock filter, the fractional‐order derivative of initial blurry image is used. This fractional‐order weight can be adjusted adaptively according to the gradient of blurred image. Compared with the traditional integer‐order shock filter, the proposed model creates less staircase effect, whereas the enhancement and deblurring of the resulted images are efficiently good. Stability properties of the proposed method are studied theoretically, and also to show the validity of stability studies results, some numerical experiments are presented. The three cases of proposed method are compared with together and with other methods. Different test images are used to show the validity of these cases. Numerical experiments confirm the efficiency of these cases.

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Deblurring Poisson noisy images by total variation with overlapping group sparsity

Cited by 23 publications

References 63 publications

A Framework for Image Denoising Using First and Second Order Fractional Overlapping Group Sparsity (HF-OLGS) Regularizer

A Framework for Image Denoising Using First and Second Order Fractional Overlapping Group Sparsity (HF-OLGS) Regularizer

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

Image deblurring using adaptive fractional‐order shock filter

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