Fast total variation based image restoration under mixed Poisson-Gaussian noise model

2018 ◽  
Author(s):  
Manu Ghulyani ◽  
Muthuvel Arigovindan
Keyword(s):  
Image Restoration ◽  
Total Variation ◽  
Gaussian Noise ◽  
Noise Model

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.

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 Directional TGV-Based Image Restoration under Poisson Noise

2021 ◽  
Vol 7 (6) ◽  
pp. 99
Author(s):  
Daniela di Serafino ◽  
Germana Landi ◽  
Marco Viola
Keyword(s):  
Computed Tomography ◽  
Image Restoration ◽  
Gaussian Noise ◽  
Computational Cost ◽  
Data Fitting ◽  
Poisson Noise ◽  
Glass Fibres ◽  
Leibler Divergence ◽  
Generalized Variation ◽  
Low Computational Cost

We are interested in the restoration of noisy and blurry images where the texture mainly follows a single direction (i.e., directional images). Problems of this type arise, for example, in microscopy or computed tomography for carbon or glass fibres. In order to deal with these problems, the Directional Total Generalized Variation (DTGV) was developed by Kongskov et al. in 2017 and 2019, in the case of impulse and Gaussian noise. In this article we focus on images corrupted by Poisson noise, extending the DTGV regularization to image restoration models where the data fitting term is the generalized Kullback–Leibler divergence. We also propose a technique for the identification of the main texture direction, which improves upon the techniques used in the aforementioned work about DTGV. We solve the problem by an ADMM algorithm with proven convergence and subproblems that can be solved exactly at a low computational cost. Numerical results on both phantom and real images demonstrate the effectiveness of our approach.

scholarly journals Revisiting the nonlinear Gaussian noise model for hybrid fiber spans

2021 ◽  
Vol 2 (1) ◽  
pp. 30-49
Author(s):  
Ioannis Roudas ◽  
Jaroslaw Kwapisz ◽  
Xin Jiang
Keyword(s):  
Gaussian Noise ◽  
Noise Model ◽  
Hybrid Fiber

Image Denoising via Bayesian Estimation of Statistical Parameter Using Generalized Gamma Density Prior in Gaussian Noise Model

2015 ◽  
Vol 14 (02) ◽  
pp. 1550017
Author(s):  
Pichid Kittisuwan
Keyword(s):  
Image Processing ◽  
Image Denoising ◽  
Gaussian Noise ◽  
Classical Problem ◽  
Statistical Parameter ◽  
Noise Model ◽  
Natural Image ◽  
Bayesian Techniques ◽  
Generalized Gamma ◽  
Gamma Density

The application of image processing in industry has shown remarkable success over the last decade, for example, in security and telecommunication systems. The denoising of natural image corrupted by Gaussian noise is a classical problem in image processing. So, image denoising is an indispensable step during image processing. This paper is concerned with dual-tree complex wavelet-based image denoising using Bayesian techniques. One of the cruxes of the Bayesian image denoising algorithms is to estimate the statistical parameter of the image. Here, we employ maximum a posteriori (MAP) estimation to calculate local observed variance with generalized Gamma density prior for local observed variance and Laplacian or Gaussian distribution for noisy wavelet coefficients. Evidently, our selection of prior distribution is motivated by efficient and flexible properties of generalized Gamma density. The experimental results show that the proposed method yields good denoising results.

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.

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