Ultrasound waveform tomography with the second-order total-generalized-variation regularization

2016 ◽  
Author(s):  
Youzuo Lin ◽  
Lianjie Huang
Keyword(s):  
Second Order ◽  
Total Generalized Variation ◽  
Waveform Tomography ◽  
Generalized Variation

scholarly journals Second-order total generalized variation based model for restoring images with mixed Poisson — Gaussian noise

2021 ◽  
pp. 20-32
Author(s):  
Cong Pham ◽  
Thi Thu Thao Tran ◽  
Thanh Cong Nguyen ◽  
Duc Hoang Vo
Keyword(s):  
Gaussian Noise ◽  
High Efficiency ◽  
Gaussian Model ◽  
Second Order ◽  
Total Generalized Variation ◽  
Proposed Model ◽  
Total Variation Model ◽  
Alternating Minimization Algorithm ◽  
Generalized Variation ◽  
Noise Models

Introduction: A common problem in image restoration is image denoising. Among many noise models, the mixed Poisson-Gaussian model has recently aroused considerable interest. Purpose: Development of a model for denoising images corrupted by mixed Poisson-Gaussian noise, along with an algorithm for solving the resulting minimization problem. Results: We proposed a new total variation model for restoring an image with mixed Poisson-Gaussian noise, based on second-order total generalized variation. In order to solve this problem, an efficient alternating minimization algorithm is used. To illustrate its comparison with related methods, experimental results are presented, demonstrating the high efficiency of the proposed approach. Practical relevance: The proposed model allows you to remove mixed Poisson-Gaussian noise in digital images, preserving the edges. The presented numerical results demonstrate the competitive features of the proposed model.

Denoising optical coherence tomography using second order total generalized variation decomposition

2016 ◽  
Vol 24 ◽  
pp. 120-127 ◽  
Author(s):  
Jinming Duan ◽  
Wenqi Lu ◽  
Christopher Tench ◽  
Irene Gottlob ◽  
Frank Proudlock ◽  
...  
Keyword(s):  
Optical Coherence Tomography ◽  
Second Order ◽  
Optical Coherence ◽  
Total Generalized Variation ◽  
Generalized Variation

Second Order Total Generalized Variation for Image Zooming

2013 ◽  
Vol 42 (6) ◽  
pp. 732-736
Author(s):  
吴玉莲 WU Yu-lian ◽  
冯象初 FENG Xiang-chu ◽  
姜东焕 JIANG Dong-huan
Keyword(s):  
Second Order ◽  
Total Generalized Variation ◽  
Image Zooming ◽  
Generalized Variation

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.

scholarly journals Second order total generalized variation (TGV) for MRI

2010 ◽  
Vol 65 (2) ◽  
pp. 480-491 ◽  
Author(s):  
Florian Knoll ◽  
Kristian Bredies ◽  
Thomas Pock ◽  
Rudolf Stollberger
Keyword(s):  
Second Order ◽  
Total Generalized Variation ◽  
Generalized Variation

scholarly journals MR-Based Electrical Conductivity Imaging Using Second-Order Total Generalized Variation Regularization

2020 ◽  
Vol 10 (21) ◽  
pp. 7910
Author(s):  
Xiangdong Sun ◽  
Lijun Lu ◽  
Li Qi ◽  
Yingjie Mei ◽  
Xiaoyun Liu ◽  
...  
Keyword(s):  
Magnetic Resonance ◽  
Electrical Properties ◽  
Second Order ◽  
Noise Robustness ◽  
Laplacian Operator ◽  
Head Model ◽  
Essential Information ◽  
Total Generalized Variation ◽  
Conductivity Imaging ◽  
Generalized Variation

Electrical properties provide essential information for cancer detection and specific absorption rate (SAR) estimation. Magnetic resonance electrical properties tomography (MREPT) is an approach to retrieve the distribution of electrical properties. The conventional method suffers from the locally homogeneous assumption and amplification of noise. In this study, a novel approach was introduced to improve the accuracy and the noise robustness of conductivity imaging. The proposed approach reformulated the central equation of the gradient-based method to avoid the calculation of the Laplacian operator. The equation was regularized using the second-order total generalized variation, which formulates an objective function. The optimization problem was solved by the alternating direction method of multipliers (ADMM) method. The proposed method was validated by the simulation data of the cylindrical phantom and Ella head model, and the performance was compared with existing methods. The results demonstrated that the proposed method reconstructed an accurate conductivity image and alleviated the noise effects. Furthermore, phantom and healthy volunteer experiments were implemented at a 3 Tesla (T) magnetic resonance imaging (MRI) scanner. The results suggested that the developed method can provide solutions for improved conductivity reconstruction and show potential for clinical application.

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