scholarly journals Rician Noise Removal via a Learned Dictionary

2019 ◽  
Vol 2019 ◽  
pp. 1-13
Author(s):  
Jian Lu ◽  
Jiapeng Tian ◽  
Lixin Shen ◽  
Qingtang Jiang ◽  
Xueying Zeng ◽  
...  
Keyword(s):  
Image Processing ◽  
Noise Removal ◽  
Sparse Representations ◽  
Computational Results ◽  
Rician Noise ◽  
Noisy Image ◽  
Dual Algorithm ◽  
Proposed Model ◽  
Learned Dictionary ◽  
Primal Dual

This paper proposes a new effective model for denoising images with Rician noise. The sparse representations of images have been shown to be efficient approaches for image processing. Inspired by this, we learn a dictionary from the noisy image and then combine the MAP model with it for Rician noise removal. For solving the proposed model, the primal-dual algorithm is applied and its convergence is studied. The computational results show that the proposed method is promising in restoring images with Rician noise.

scholarly journals Anisotropic Diffusion Based Multiplicative Speckle Noise Removal

Sensors ◽  
2019 ◽  
Vol 19 (14) ◽  
pp. 3164 ◽  
Author(s):  
Mei Gao ◽  
Baosheng Kang ◽  
Xiangchu Feng ◽  
Wei Zhang ◽  
Wenjuan Zhang
Keyword(s):  
Standard Deviation ◽  
Anisotropic Diffusion ◽  
Additive Noise ◽  
Ground Truth ◽  
Speckle Noise ◽  
Noise Removal ◽  
Noisy Image ◽  
Stopping Criteria ◽  
Proposed Model ◽  
Optimal Values

Multiplicative speckle noise removal is a challenging task in image processing. Motivated by the performance of anisotropic diffusion in additive noise removal and the structure of the standard deviation of a compressed speckle noisy image, we address this problem with anisotropic diffusion theories. Firstly, an anisotropic diffusion model based on image statistics, including information on the gradient of the image, gray levels, and noise standard deviation of the image, is proposed. Although the proposed model can effectively remove multiplicative speckle noise, it does not consider the noise at the edge during the denoising process. Hence, we decompose the divergence term in order to make the diffusion at the edge occur along the boundaries rather than perpendicular to the boundaries, and improve the model to meet our requirements. Secondly, the iteration stopping criteria based on kurtosis and correlation in view of the lack of ground truth in real image experiments, is proposed. The optimal values of the parameters in the model are obtained by learning. To improve the denoising effect, post-processing is performed. Finally, the simulation results show that the proposed model can effectively remove the speckle noise and retain minute details of the images for the real ultrasound and RGB color images.

scholarly journals A new augmented Lagrangian primal dual algorithm for elastica regularization

2016 ◽  
Vol 10 (4) ◽  
pp. 325-338 ◽  
Author(s):  
Jianping Zhang ◽  
Ke Chen
Keyword(s):  
Image Processing ◽  
Image Segmentation ◽  
Numerical Experiments ◽  
Augmented Lagrangian ◽  
Splitting Methods ◽  
Dual Algorithm ◽  
Variational Models ◽  
Euler’S Elastica ◽  
Primal Dual ◽  
Restoration Problem

Regularization is a key element of variational models in image processing. To overcome the weakness of models based on total variation, various high order (typically second order) regularization models have been proposed and studied recently. Among these, Euler's elastica energy based regularizer is perhaps the most interesting in terms of both mathematical and physical justifications. More importantly its success has been proven in applications; however it has been a major challenge to develop fast and effective algorithms. In this paper we propose a new idea for deriving a primal dual algorithm, based on Legendre–Fenchel transformations, for representing the elastica regularizer. Combined with an augmented Lagrangian for-mulation, we are able to derive an equivalent unconstrained optimization that has fewer variables to work with than previous works based on splitting methods. We shall present our algorithms for both the image restoration problem and the image segmentation model. The idea applies to other models where the elastica regularizer is required. Numerical experiments show that the proposed method can produce highly competitive results with better efficiency.

scholarly journals Semi–definite programming for the nearest circulant semi–definite matrix problem

2021 ◽  
Vol 37 (1) ◽  
pp. 13-22
Author(s):  
SULIMAN AL-HOMIDAN
Keyword(s):  
Optimality Conditions ◽  
Original System ◽  
Data Matrix ◽  
Circulant Matrices ◽  
Computational Results ◽  
Matrix Problem ◽  
Dual Algorithm ◽  
Second Order Cone ◽  
Primal Dual ◽  
Paper Construct

"Positive semi–definite circulant matrices arise in many important applications. The problem arises in various applications where the data collected in a matrix do not maintain the specified structure as is expected in the original system. The task is to retrieve useful information while maintaining the underlying physical feasibility often necessitates search for a good structured approximation of the data matrix. This paper construct structured circulant positive semi–definite matrix that is nearest to a given data matrix. The problem is converted into a semi–definite programming problem as well as a problem comprising a semi–defined program and second-order cone problem. The duality and optimality conditions are obtained and the primal-dual algorithm is outlined. Some of the numerical issues involved will be addressed including unsymmetrical of the problem. Computational results are presented."

scholarly journals Distributed Primal-Dual Optimization for Online Multi-Task Learning

2020 ◽  
Vol 34 (04) ◽  
pp. 6631-6638
Author(s):  
Peng Yang ◽  
Ping Li
Keyword(s):  
Sequential Data ◽  
Dual Algorithm ◽  
Adversarial Learning ◽  
Task Learning ◽  
Proposed Model ◽  
Task Relatedness ◽  
Primal Dual ◽  
Bandwidth Constraint ◽  
Real World Datasets ◽  
Theoretical Results

Conventional online multi-task learning algorithms suffer from two critical limitations: 1) Heavy communication caused by delivering high velocity of sequential data to a central machine; 2) Expensive runtime complexity for building task relatedness. To address these issues, in this paper we consider a setting where multiple tasks are geographically located in different places, where one task can synchronize data with others to leverage knowledge of related tasks. Specifically, we propose an adaptive primal-dual algorithm, which not only captures task-specific noise in adversarial learning but also carries out a projection-free update with runtime efficiency. Moreover, our model is well-suited to decentralized periodic-connected tasks as it allows the energy-starved or bandwidth-constraint tasks to postpone the update. Theoretical results demonstrate the convergence guarantee of our distributed algorithm with an optimal regret. Empirical results confirm that the proposed model is highly effective on various real-world datasets.

scholarly journals A Convex Variational Model for Restoring SAR Images Corrupted by Multiplicative Noise

2020 ◽  
Vol 2020 ◽  
pp. 1-19
Author(s):  
Hanmei Yang ◽  
Jiachang Li ◽  
Lixin Shen ◽  
Jian Lu
Keyword(s):  
Multiplicative Noise ◽  
Variational Model ◽  
Total Variation Regularization ◽  
Dual Algorithm ◽  
Penalty Term ◽  
Mathematical Properties ◽  
Proposed Model ◽  
Primal Dual ◽  
Data Fidelity ◽  
Blurred Images

This paper studies a new convex variational model for denoising and deblurring images with multiplicative noise. Considering the statistical property of the multiplicative noise following Nakagami distribution, the denoising model consists of a data fidelity term, a quadratic penalty term, and a total variation regularization term. Here, the quadratic penalty term is mainly designed to guarantee the model to be strictly convex under a mild condition. Furthermore, the model is extended for the simultaneous denoising and deblurring case by introducing a blurring operator. We also study some mathematical properties of the proposed model. In addition, the model is solved by applying the primal-dual algorithm. The experimental results show that the proposed method is promising in restoring (blurred) images with multiplicative noise.

A modified Chambolle-Pock primal-dual algorithm for Poisson noise removal

CALCOLO ◽  
2020 ◽  
Vol 57 (3) ◽  
Author(s):  
Benxin Zhang ◽  
Zhibin Zhu ◽  
Zhijun Luo
Keyword(s):  
Noise Removal ◽  
Poisson Noise ◽  
Dual Algorithm ◽  
Primal Dual

ADAPTIVE SPARSE REPRESENTATION FOR MRI NOISE REMOVAL

2012 ◽  
Vol 24 (05) ◽  
pp. 383-394
Author(s):  
Mohammad Mahdi Khalilzadeh ◽  
Emad Fatemizadeh ◽  
Hamid Behnam
Keyword(s):  
Standard Deviation ◽  
Sparse Representation ◽  
Gaussian Noise ◽  
Noise Removal ◽  
Reconstruction Error ◽  
Local Error ◽  
Rician Noise ◽  
Learned Dictionary ◽  
Low Sensitivity ◽  
Simulated Images

Sparse representation is a powerful tool for image processing, including noise removal. It is an effective method for Gaussian noise removal by taking advantage of a fixed and learned dictionary. In this study, the variable distribution of Rician noise is reduced in magnetic resonance (MR) images by sparse representation based on reconstruction error sets. Standard deviation of Gaussian noise is used to find these errors locally. The proposed method represents two formulas for local error calculation using standard deviation of noise. The acquired results from the real and simulated images are comparable, and in some cases, better than the best Rician noise removal method due to the advantages of stability and low sensitivity to the parameters. Additionally, the devised algorithm acts automatically, because the proposed method includes the phase that estimates the noise properties.

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