scholarly journals Image Restoration using a Nonlinear Second-order Parabolic PDE-based Scheme

2017 ◽  
Vol 25 (1) ◽  
pp. 33-48 ◽  
Author(s):  
Tudor Barbu ◽  
Costică Moroşanu
Keyword(s):  
Image Restoration ◽  
Anisotropic Diffusion ◽  
Lagrange Equation ◽  
Second Order ◽  
Variational Model ◽  
Mathematical Treatment ◽  
Pde Model ◽  
Parabolic Pde ◽  
Diffusion Scheme ◽  
Conductance Parameter

AbstractA novel anisotropic diffusion-based image denoising and restoration approach is proposed in this paper. A variational model for image restoration is introduced first, then the corresponding Euler-Lagrange equation being determined. A nonlinear parabolic PDE model is then obtained from this equation. It is based on a novel edge-stopping function and conductance parameter. A serious mathematical treatment is performed on this second-order anisotropic diffusion scheme, its well-possedness being investigated. Then, a consistent explicit numerical approximation scheme based on the finite difference method is developed for the proposed PDE model.

scholarly journals Restoring Poissonian Images by a Combined First-Order and Second-Order Variation Approach

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Le Jiang ◽  
Jin Huang ◽  
Xiao-Guang Lv ◽  
Jun Liu
Keyword(s):  
Lagrange Equation ◽  
Noise Removal ◽  
Poisson Noise ◽  
Second Order ◽  
Variational Model ◽  
Gradient Descent Method ◽  
First Order ◽  
Order Variation ◽  
Imaging Science ◽  
Blurred Images

The restoration of blurred images corrupted by Poisson noise is an important topic in imaging science. The problem has recently received considerable attention in recent years. In this paper, we propose a combined first-order and second-order variation model to restore blurred images corrupted by Poisson noise. Our model can substantially reduce the staircase effect, while preserving edges in the restored images, since it combines advantages of the first-order and second-order total variation. We study the issues of existence and uniqueness of a minimizer for this variational model. Moreover, we employ a gradient descent method to solve the associated Euler-Lagrange equation. Numerical results demonstrate the validity and efficiency of the proposed method for Poisson noise removal problem.

A COMBINED FIRST-ORDER AND SECOND-ORDER VARIATION APPROACH FOR MULTIPLICATIVE NOISE REMOVAL

2014 ◽  
Vol 56 (2) ◽  
pp. 116-137
Author(s):  
LE JIANG ◽  
JIN HUANG ◽  
JUN LIU ◽  
XIAO-GUANG LV
Keyword(s):  
Multiplicative Noise ◽  
Lagrange Equation ◽  
Similarity Index ◽  
Structural Similarity ◽  
Noise Removal ◽  
Descent Method ◽  
Second Order ◽  
Variational Model ◽  
Gradient Descent Method ◽  
First Order

AbstractDenoising of images corrupted by multiplicative noise is an important task in various applications, such as laser imaging, synthetic aperture radar and ultrasound imaging. We propose a combined first-order and second-order variational model for removal of multiplicative noise. Our model substantially reduces the staircase effects while preserving edges in the restored images, since it combines advantages of the first-order and second-order total variation. The issues of existence and uniqueness of a minimizer for this variational model are analysed. Moreover, a gradient descent method is employed to solve the associated Euler–Lagrange equation, and several numerical experiments are given to show the efficiency of our model. In particular, a comparison with an existing model in terms of peak signal-to-noise ratio and structural similarity index is provided.

Defocus blurred image restoration by minimizing second-order central moment

2011 ◽  
Author(s):  
Sheng Zhong ◽  
Mingzhi Jin ◽  
Luxin Yan ◽  
Tianxu Zhang
Keyword(s):  
Image Restoration ◽  
Central Moment ◽  
Second Order ◽  
Blurred Image

Digital object restoration using generalized regression neural network deep learning—Taking Dunhuang mural restoration as an example

2020 ◽  
pp. 002072092092854
Author(s):  
Wenjing She
Keyword(s):  
Neural Network ◽  
Deep Learning ◽  
Image Restoration ◽  
Anisotropic Diffusion ◽  
Learning Algorithm ◽  
Diffusion Method ◽  
Generalized Regression Neural Network ◽  
Deep Learning Algorithm ◽  
Training Samples ◽  
Restoration Effect

In this research, Dunhuang murals is taken as the object of restoration, and the role of digital repair combined with deep learning algorithm in mural restoration is explored. First, the image restoration technology is described, as well as its advantages and disadvantages are analyzed. Second, the deep learning algorithm based on artificial neural network is described and analyzed. Finally, the deep learning algorithm is integrated into the digital repair technology, and a mural restoration method based on the generalized regression neural network is proposed. The morphological expansion method and anisotropic diffusion method are used to preprocess the image. The MATLAB software is used for the simulation analysis and evaluation of the image restoration effect. The results show that in the restoration of the original image, the accuracy of the digital image restoration technology is not high. The nontexture restoration technology is not applicable in the repair of large-scale texture areas. The predicted value of the mural restoration effect based on the generalized neural network is closer to the true value. The anisotropic diffusion method has a significant effect on the processing of image noise. In the image similarity rate, the different number of training samples and smoothing parameters are compared and analyzed. It is found that when the value of δ is small, the number of training samples should be increased to improve the accuracy of the prediction value. If the number of training samples is small, a larger value of δ is needed to get a better prediction effect, and the best restoration effect is obtained for the restored image. Through this study, it is found that this study has a good effect on the restoration model of Dunhuang murals. It provides experimental reference for the restoration of later murals.

scholarly journals Edge Enhancing Accelerated Diffusion Model for Speckle Denoising in Medical Imagery

2019 ◽  
Vol 29 ◽  
pp. 01009
Author(s):  
Arundhati Bagchi Misra ◽  
Chartese Jones ◽  
Hyeona Lim
Keyword(s):  
Medical Images ◽  
Lagrange Equation ◽  
Speckle Noise ◽  
Ultrasound Images ◽  
Total Variation Minimization ◽  
Pde Model ◽  
Medical Imagery ◽  
Wide Range ◽  
Automated Processing ◽  
Processing Techniques

Speckle noise occurs in a wide range of medical images due to sampling and digital degradation. Removing speckle noise from medical images is the key for further automated processing techniques like segmentation, and can help the clinicians with better diagnosis and therapy. We consider partial differential equation (PDE)-based denoising model which is a modified Euler-Lagrange equation derived from the total variation minimization functional with additional speckle noise constraints. The new PDE model is designed and optimized to rectify speckle noise and enhance edges present in medical imagery. Wealso develop the efficicient and stable discretization techniques for the corresponding speckle denoising model. The method is tested for several types of images including ultrasound images, and it is compared favorably to the conventional denoising model.

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