Hybrid Variational Model for Texture Image Restoration

2017 ◽  
Vol 7 (3) ◽  
pp. 629-642 ◽  
Author(s):  
Liyan Ma ◽  
Tieyong Zeng ◽  
Gongyan Li
Keyword(s):  
Image Quality ◽  
Image Restoration ◽  
Total Variation ◽  
Fractional Order ◽  
Gaussian Noise ◽  
Numerical Experiments ◽  
Computational Time ◽  
Variational Model ◽  
Texture Image

AbstractThe hybrid variational model for restoration of texture images corrupted by blur and Gaussian noise we consider combines total variation regularisation and a fractional-order regularisation, and is solved by an alternating minimisation direction algorithm. Numerical experiments demonstrate the advantage of this model over the adaptive fractional-order variational model in image quality and computational time.

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.

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 Efficient Iterative Regularization Method for Total Variation-Based Image Restoration

Electronics ◽  
2022 ◽  
Vol 11 (2) ◽  
pp. 258
Author(s):  
Ge Ma ◽  
Ziwei Yan ◽  
Zhifu Li ◽  
Zhijia Zhao
Keyword(s):  
Image Restoration ◽  
Total Variation ◽  
Regularization Method ◽  
Numerical Experiments ◽  
Optimization Problem ◽  
Split Bregman ◽  
Iterative Regularization ◽  
Tv Regularization ◽  
Fidelity Term ◽  
Restoration Effect

Total variation (TV) regularization has received much attention in image restoration applications because of its advantages in denoising and preserving details. A common approach to address TV-based image restoration is to design a specific algorithm for solving typical cost function, which consists of conventional ℓ2 fidelity term and TV regularization. In this work, a novel objective function and an efficient algorithm are proposed. Firstly, a pseudoinverse transform-based fidelity term is imposed on TV regularization, and a closely-related optimization problem is established. Then, the split Bregman framework is used to decouple the complex inverse problem into subproblems to reduce computational complexity. Finally, numerical experiments show that the proposed method can obtain satisfactory restoration results with fewer iterations. Combined with the restoration effect and efficiency, this method is superior to the competitive algorithm. Significantly, the proposed method has the advantage of a simple solving structure, which can be easily extended to other image processing applications.

scholarly journals A DENOISING OF BIOMEDICAL IMAGES

2015 ◽  
Vol XL-5/W6 ◽  
pp. 73-78 ◽  
Author(s):  
D. N. H. Thanh ◽  
S. D. Dvoenko
Keyword(s):  
Image Quality ◽  
Total Variation ◽  
Digital Image ◽  
Gaussian Noise ◽  
Digital Images ◽  
Poisson Noise ◽  
Biomedical Images ◽  
Biomedical Image ◽  
Digital Devices ◽  
Imaging Science

Today imaging science has an important development and has many applications in different fields of life. The researched object of imaging science is digital image that can be created by many digital devices. Biomedical image is one of types of digital images. One of the limits of using digital devices to create digital images is noise. Noise reduces the image quality. It appears in almost types of images, including biomedical images too. The type of noise in this case can be considered as combination of Gaussian and Poisson noises. In this paper we propose method to remove noise by using total variation. Our method is developed with the goal to combine two famous models: ROF for removing Gaussian noise and modified ROF for removing Poisson noise. As a result, our proposed method can be also applied to remove Gaussian or Poisson noise separately. The proposed method can be applied in two cases: with given parameters (generated noise for artificial images) or automatically evaluated parameters (unknown noise for real images).

scholarly journals POSITIVELY CONSTRAINED TOTAL VARIATION PENALIZED IMAGE RESTORATION

2011 ◽  
Vol 03 (01n02) ◽  
pp. 187-201 ◽  
Author(s):  
RAYMOND H. CHAN ◽  
HAI-XIA LIANG ◽  
JUN MA
Keyword(s):  
Image Processing ◽  
Image Restoration ◽  
Total Variation ◽  
Gaussian Noise ◽  
Impulsive Noise ◽  
Noise Model ◽  
Splitting Algorithm ◽  
New Approach ◽  
Tomographic Image Reconstruction ◽  
Noise Models

The total variation (TV) minimization models are widely used in image processing, mainly due to their remarkable ability in preserving edges. There are many methods for solving the TV model. These methods, however, seldom consider the positivity constraint one should impose on image-processing problems. In this paper we develop and implement a new approach for TV image restoration. Our method is based on the multiplicative iterative algorithm originally developed for tomographic image reconstruction. The advantages of our algorithm are that it is very easy to derive and implement under different image noise models and it respects the positivity constraint. Our method can be applied to various noise models commonly used in image restoration, such as the Gaussian noise model, the Poisson noise model, and the impulsive noise model. In the numerical tests, we apply our algorithm to deblur images corrupted by Gaussian noise. The results show that our method give better restored images than the forward–backward splitting algorithm.

scholarly journals A Novel Image-Restoration Method Based on High-Order Total Variation Regularization Term

Electronics ◽  
2019 ◽  
Vol 8 (8) ◽  
pp. 867 ◽  
Author(s):  
Jianhong Xiang ◽  
Pengfei Ye ◽  
Linyu Wang ◽  
Mingqi He
Keyword(s):  
Image Restoration ◽  
Total Variation ◽  
Regularization Parameter ◽  
Signal To Noise Ratio ◽  
High Order ◽  
Computational Time ◽  
Total Variation Regularization ◽  
Selection Scheme ◽  
Staircase Effect ◽  
Restoration Method

This paper presents two new models for solving image the deblurring problem in the presence of impulse noise. One involves a high-order total variation (TV) regularizer term in the corrected total variation L1 (CTVL1) model and is named high-order corrected TVL1 (HOCTVL1). This new model can not only suppress the defects of the staircase effect, but also improve the quality of image restoration. In most cases, the regularization parameter in the model is a fixed value, which may influence processing results. Aiming at this problem, the spatially adapted regularization parameter selection scheme is involved in HOCTVL1 model, and spatially adapted HOCTVL1 (SAHOCTVL1) model is proposed. When dealing with corrupted images, the regularization parameter in SAHOCTVL1 model can be updated automatically. Many numerical experiments are conducted in this paper and the results show that the two models can significantly improve the effects both in visual quality and signal-to-noise ratio (SNR) at the expense of a small increase in computational time. Compared to HOCTVL1 model, SAHOCTVL1 model can restore more texture details, though it may take more time.

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