scholarly journals Combined total variation of first and fractional orders for Poisson noise removal in digital images

2021 ◽  
pp. 10-19
Author(s):  
Cong Pham ◽  
Thi Thu Tran ◽  
Minh Pham ◽  
Thanh Cong Nguyen
Keyword(s):  
Image Reconstruction ◽  
Image Restoration ◽  
Total Variation ◽  
Fractional Order ◽  
Optimization Problem ◽  
Poisson Noise ◽  
Experimental Results ◽  
First Order ◽  
Proposed Model ◽  
Total Variation Model

Introduction: Many methods have been proposed to handle the image restoration problem with Poisson noise. A popular approach to Poissonian image reconstruction is the one based on Total Variation. This method can provide significantly sharp edges and visually fine images, but it results in piecewise-constant regions in the resulting images. Purpose: Developing an adaptive total variation-based model for the reconstruction of images contaminated by Poisson noise, and an algorithm for solving the optimization problem. Results: We proposed an effective way to restore images degraded by Poisson noise. Using the Bayesian framework, we proposed an adaptive model based on a combination of first-order total variation and fractional order total variation. The first-order total variation model is efficient for suppressing the noise and preserving the keen edges simultaneously. However, the first-order total variation method usually causes artifact problems in the obtained results. To avoid this drawback, we can use high-order total variation models, one of which is the fractional-order total variation-based model for image restoration. In the fractional-order total variation model, the derivatives have an order greater than or equal to one. It leads to the convenience of computation with a compact discrete form. However, methods based on the fractional-order total variation may cause image blurring. Thus, the proposed model incorporates the advantages of two total variation regularization models, having a significant effect on the edge-preserving image restoration. In order to solve the considered optimization problem, the Split Bregman method is used. Experimental results are provided, demonstrating the effectiveness of the proposed method.  Practical relevance: The proposed method allows you to restore Poissonian images preserving their edges. The presented numerical simulation demonstrates the competitive performance of the model proposed for image reconstruction. Discussion: From the experimental results, we can see that the proposed algorithm is effective in suppressing noise and preserving the image edges. However, the weighted parameters in the proposed model were not automatically selected at each iteration of the proposed algorithm. This requires additional research.

scholarly journals An adaptive model combining a total variation filter and a fractional-order filter for image restoration

2019 ◽  
Vol 13 ◽  
pp. 174830181983305 ◽  
Author(s):  
Yafeng Yang ◽  
Donghong Zhao
Keyword(s):  
Image Restoration ◽  
Total Variation ◽  
Fractional Order ◽  
Gradient Algorithm ◽  
Remarkable Effect ◽  
Order Filter ◽  
Model Combining ◽  
Proposed Model ◽  
Primal Dual ◽  
Image Edges

In this paper, we propose a model that combines a total variation filter with a fractional-order filter, which can unite the advantages of the two filters, and has a remarkable effect in the protection of image edges and texture details; simultaneously, the proposed model can eliminate the staircase effect. In addition, the model improves the PSNR compared with the total variation filter and the fractional-order filter when removing noise. Zhu and Chan presented the primal-dual hybrid gradient algorithm and proved that it is effective for the total variation filter. On the basis of their work, we employ the primal-dual hybrid gradient algorithm to solve the combined model in this article. The final experimental results show that the new model and algorithm are effective for image restoration.

2D Wavelet Tree Ordering Based Localized Total Variation Model for Efficient Image Restoration

2022 ◽  
Author(s):  
K. Praveen Kumar ◽  
C. Venkata Narasimhulu ◽  
K. Satya Prasad
Keyword(s):  
Image Restoration ◽  
Total Variation ◽  
Good Condition ◽  
Window Size ◽  
Local Variation ◽  
Image Simulation ◽  
Regularization Algorithm ◽  
Total Variation Model ◽  
Degraded Image ◽  
Adjustment Scheme

The degraded image during the process of image analysis needs more number of iterations to restore it. These iterations take long waiting time and slow scanning, resulting in inefficient image restoration. A few numbers of measurements are enough to recuperate an image with good condition. Due to tree sparsity, a 2D wavelet tree reduces the number of coefficients and iterations to restore the degraded image. All the wavelet coefficients are extracted with overlaps as low and high sub-band space and ordered them such that they are decomposed in the tree ordering structured path. Some articles have addressed the problems with tree sparsity and total variation (TV), but few authors endorsed the benefits of tree sparsity. In this paper, a spatial variation regularization algorithm based on tree order is implemented to change the window size and variation estimators to reduce the loss of image information and to solve the problem of image smoothing operation. The acceptance rate of the tree-structured path relies on local variation estimators to regularize the performance parameters and update them to restore the image. For this, the Localized Total Variation (LTV) method is proposed and implemented on a 2D wavelet tree ordering structured path based on the proposed image smooth adjustment scheme. In the end, a reliable reordering algorithm proposed to reorder the set of pixels and to increase the reliability of the restored image. Simulation results clearly show that the proposed method improved the performance compared to existing methods of image restoration.

scholarly journals Fractional-Order Fusion Model for Low-Light Image Enhancement

Symmetry ◽  
2019 ◽  
Vol 11 (4) ◽  
pp. 574 ◽  
Author(s):  
Qiang Dai ◽  
Yi-Fei Pu ◽  
Ziaur Rahman ◽  
Muhammad Aamir
Keyword(s):  
Image Enhancement ◽  
Fractional Order ◽  
Input Image ◽  
Experimental Results ◽  
Fusion Model ◽  
Low Light ◽  
Visual Appearance ◽  
Light Image ◽  
Proposed Model ◽  
Detail Enhancement

In this paper, a novel fractional-order fusion model (FFM) is presented for low-light image enhancement. Existing image enhancement methods don’t adequately extract contents from low-light areas, suppress noise, and preserve naturalness. To solve these problems, the main contributions of this paper are using fractional-order mask and the fusion framework to enhance the low-light image. Firstly, the fractional mask is utilized to extract illumination from the input image. Secondly, image exposure adjusts to visible the dark regions. Finally, the fusion approach adopts the extracting of more hidden contents from dim areas. Depending on the experimental results, the fractional-order differential is much better for preserving the visual appearance as compared to traditional integer-order methods. The FFM works well for images having complex or normal low-light conditions. It also shows a trade-off among contrast improvement, detail enhancement, and preservation of the natural feel of the image. Experimental results reveal that the proposed model achieves promising results, and extracts more invisible contents in dark areas. The qualitative and quantitative comparison of several recent and advance state-of-the-art algorithms shows that the proposed model is robust and efficient.

scholarly journals Total Variation Regularization of Matrix-Valued Images

2007 ◽  
Vol 2007 ◽  
pp. 1-11 ◽  
Author(s):  
Oddvar Christiansen ◽  
Tin-Man Lee ◽  
Johan Lie ◽  
Usha Sinha ◽  
Tony F. Chan
Keyword(s):  
Total Variation ◽  
Diffusion Tensor ◽  
Natural Extension ◽  
Positive Definiteness ◽  
Total Variation Regularization ◽  
Diffusion Matrix ◽  
Proposed Model ◽  
Total Variation Model ◽  
Diffusion Tensor Images ◽  
Restoration Model

We generalize the total variation restoration model, introduced by Rudin, Osher, and Fatemi in 1992, to matrix-valued data, in particular, to diffusion tensor images (DTIs). Our model is a natural extension of the color total variation model proposed by Blomgren and Chan in 1998. We treat the diffusion matrixDimplicitly as the productD=LLT, and work with the elements ofLas variables, instead of working directly on the elements ofD. This ensures positive definiteness of the tensor during the regularization flow, which is essential when regularizing DTI. We perform numerical experiments on both synthetical data and 3D human brain DTI, and measure the quantitative behavior of the proposed model.

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