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.

scholarly journals Edge-guided second-order total generalized variation for Gaussian noise removal from depth map

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Shuaihao Li ◽  
Bin Zhang ◽  
Xinfeng Yang ◽  
Weiping Zhu
Keyword(s):  
Gaussian Noise ◽  
Depth Map ◽  
Noise Removal ◽  
Second Order ◽  
Variational Model ◽  
High Quality ◽  
Edge Preserving ◽  
Total Generalized Variation ◽  
Primal Dual ◽  
Generalized Variation

Abstract Total generalized variation models have recently demonstrated high-quality denoising capacity for single image. In this paper, we present an accurate denoising method for depth map. Our method uses a weighted second-order total generalized variational model for Gaussian noise removal. By fusing an edge indicator function into the regularization term of the second-order total generalized variational model to guide the diffusion of gradients, our method aims to use the first or second derivative to enhance the intensity of the diffusion tensor. We use the first-order primal–dual algorithm to minimize the proposed energy function and achieve high-quality denoising and edge preserving result for depth maps with high -intensity noise. Extensive quantitative and qualitative evaluations in comparison to bench-mark datasets show that the proposed method provides significant higher accuracy and visual improvements than many state-of-the-art denoising algorithms.

New Hybrid Variational Recovery Model for Blurred Images with Multiplicative Noise

2013 ◽  
Vol 3 (4) ◽  
pp. 263-282 ◽  
Author(s):  
Yiqiu Dong ◽  
Tieyong Zeng
Keyword(s):  
Multiplicative Noise ◽  
Noise Removal ◽  
Variational Model ◽  
Convex Model ◽  
Split Bregman ◽  
New Approach ◽  
Uniqueness Of The Solution ◽  
Minimisation Problem ◽  
The Stability ◽  
Blurred Images

AbstractA new hybrid variational model for recovering blurred images in the presence of multiplicative noise is proposed. Inspired by previous work on multiplicative noise removal, an I-divergence technique is used to build a strictly convex model under a condition that ensures the uniqueness of the solution and the stability of the algorithm. A split-Bregman algorithm is adopted to solve the constrained minimisation problem in the new hybrid model efficiently. Numerical tests for simultaneous deblurring and denoising of the images subject to multiplicative noise are then reported. Comparison with other methods clearly demonstrates the good performance of our new approach.

scholarly journals Poisson Noise Removal Scheme Based on Fourth-Order PDE by Alternating Minimization Algorithm

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Weifeng Zhou ◽  
Qingguo Li
Keyword(s):  
Fourth Order ◽  
Noise Removal ◽  
Descent Method ◽  
Poisson Noise ◽  
Gradient Descent Method ◽  
Order Partial Differential Equation ◽  
Alternating Minimization ◽  
Minimization Algorithm ◽  
Tv Regularization ◽  
Alternating Minimization Algorithm

To overcome the staircasing effects introduced by the TV regularization in image restoration, this paper investigates a fourth-order partial differential equation (PDE) filter for removing Poisson noise. In consideration of the slow convergence property of the classical gradient descent method, we adopt the alternating minimization algorithm for realizing this scheme. Compared with the corresponding total variation based one, numerical simulations distinctly indicate the superiority of our proposed strategy in handling smooth regions of Poissonian images and improving the computational speed.

scholarly journals Median Filtering Using First-Order and Second-Order Neighborhood Pixels to Reduce Fixed Value Impulse Noise from Grayscale Digital Images

Electronics ◽  
2020 ◽  
Vol 9 (12) ◽  
pp. 2034
Author(s):  
Ali Salim Nasar Mursal ◽  
Haidi Ibrahim
Keyword(s):  
Impulse Noise ◽  
Digital Images ◽  
Noise Removal ◽  
Second Order ◽  
First Order ◽  
Information Preservation ◽  
Noisy Pixel ◽  
Detection Stage ◽  
The Difference ◽  
Two Stages

It is essential to restore digital images corrupted by noise to make them more useful. Many approaches have been proposed to restore images affected by fixed value impulse noise, but they still do not perform well at high noise density. This paper presents a new method to improve the detection and removal of fixed value impulse noise from digital images. The proposed method consists of two stages. The first stage is the noise detection stage, where the difference values between the pixels and their surrounding pixels are computed to decide whether they are noisy pixels or not. The second stage is the image denoising stage. In this stage, the original intensity value of the noisy pixels is estimated using only their first-order and second-order neighborhood pixels. These neighboring orders are based on the Euclidean distance between the noisy pixel and its neighboring pixels. The proposed method was evaluated by comparing it with some of the recent methods using 50 images at 18 noise densities. The experimental results confirm that the proposed method outperforms the existing filters, excelling in noise removal capability with structure and edge information preservation.

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.

Nonlinear Analysis of Visual Evoked Potentials Elicited by Color Stimulation

1997 ◽  
Vol 36 (04/05) ◽  
pp. 315-318 ◽  
Author(s):  
K. Momose ◽  
K. Komiya ◽  
A. Uchiyama
Keyword(s):  
Visual System ◽  
Evoked Potentials ◽  
Visual Evoked Potentials ◽  
Normal Subjects ◽  
Second Order ◽  
First Order ◽  
The Relationship ◽  
Perceived Color ◽  
Second Order Nonlinearity ◽  
Visual Evoked

Abstract:The relationship between chromatically modulated stimuli and visual evoked potentials (VEPs) was considered. VEPs of normal subjects elicited by chromatically modulated stimuli were measured under several color adaptations, and their binary kernels were estimated. Up to the second-order, binary kernels obtained from VEPs were so characteristic that the VEP-chromatic modulation system showed second-order nonlinearity. First-order binary kernels depended on the color of the stimulus and adaptation, whereas second-order kernels showed almost no difference. This result indicates that the waveforms of first-order binary kernels reflect perceived color (hue). This supports the suggestion that kernels of VEPs include color responses, and could be used as a probe with which to examine the color visual system.

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