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admm algorithm for some regularized Perona-Malik equation and applications to image denoising

SIGNAL IMAGE AND VIDEO PROCESSING 2023年第3期17卷 609-617页

作者： Sniba, Farah Karami, Fahd Meskine, Driss Ecole Super Technol Essaouira BP 383 Essaouira El Jadida Essaouira Morocco

In this paper, we propose a new approach for solving the proposed variational model derived from Perona-Malik (PM) equation. This problem is the combination of P-M model and p-Laplacian operator. Our approach exploiting the different values of p (p near 1 or infinity) and using a variable contrast parameter. to adaptively control the scattering pattern in the restored image. Firstly, we present the variational model, and we prove the existence and uniqueness of the minimizer. To solve numerically our problem, we apply theadmmmethod to derive a robust scheme. Finally, we illustrate the effectiveness of our algorithm with various numerical tests which can compare favorably with some existing methods in the literature.

关键词： Perona-Malik model p-Laplacian operator admm algorithm Denoising image Staircase effect

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admm algorithm for Computational ghost imaging using Hadamard derivative pattern

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OPTICS COMMUNICATIONS 2024年 552卷

作者： Huang, Hong Han, Zhiguang Hainan Univ Sch Informat & Commun Engn Key Lab Marine Resource Utilizat South China Sea Haikou 570228 Peoples R China

Aiming at the problems of long reconstruction time, high sampling rate and poor imaging effect caused by traditional illumination speckle in ghost imaging reconstruction, this paper proposes to use ordered orthogonal Hadamard derived speckle as the illumination speckle series of ghost imaging to reduce the measurement times and improve the quality of reconstructed images. In addition, the alternate direction multiplier method is introduced into the image reconstruction algorithm to further improve the imaging performance of ghost imaging. Finally, the method used in this paper is evaluated objectively, and the evaluation results show that the combination of Hadamard derived speckle and alternating direction multiplication has better imaging effect, and can obtain high-quality reconstructed images under low sampling conditions. It is expected that this method can be applied to target detection and recognition, improve detection and recognition ability, and help users get more useful information.

关键词： Computational ghost imaging Hadamard derivative pattern admm algorithm Walsh measurement matrix Cake-cutting measurement matrix

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An improved robust admm algorithm for quantum state tomography

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QUANTUM INFORMATION PROCESSING 2016年第6期15卷 2343-2358页

作者： Li, Kezhi Zhang, Hui Kuang, Sen Meng, Fangfang Cong, Shuang Univ Sci & Technol China Dept Automat Hefei 230027 Peoples R China Univ London Imperial Coll Sci Technol & Med London England Hefei Uinv Hefei 230022 Peoples R China

In this paper, an improved adaptive weights alternating direction method of multipliers algorithm is developed to implement the optimization scheme for recovering the quantum state in nearly pure states. The proposed approach is superior to many existing methods because it exploits the low-rank property of density matrices, and it can deal with unexpected sparse outliers as well. The numerical experiments are provided to verify our statements by comparing the results to three different optimization algorithms, using both adaptive and fixed weights in the algorithm, in the cases of with and without external noise, respectively. The results indicate that the improved algorithm has better performances in both estimation accuracy and robustness to external noise. The further simulation results show that the successful recovery rate increases when more qubits are estimated, which in fact satisfies the compressive sensing theory and makes the proposed approach more promising.

关键词： Quantum state estimation Compressive sensing admm algorithm Adaptive weights

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Analysis of Distributed admm algorithm for Consensus Optimization in Presence of Node Error

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2019年第7期67卷 1774-1784页

作者： Majzoobi, Layla Lahouti, Farshad Shah-Mansouri, Vahid Univ Tehran Sch Elect & Comp Engn Tehran *** Iran CALTECH Dept Elect Engn Pasadena CA 91125 USA

Alternating direction method of multipliers (admm) is a popular convex optimization algorithm, which can be employed for solving distributed consensus optimization problems. In this setting, agents locally estimate the optimal solution of an optimization problem and exchange messages with their neighbors over a connected network. The distributed algorithms are typically exposed to different types of errors in practice, e.g., due to quantization or communication noise or loss. We here focus on analyzing the convergence of distributed admm for consensus optimization in the presence of additive random node error, in which case the nodes communicate a noisy version of their latest estimate of the solution to their neighbors in each iteration. We present analytical upper and lower bounds on the mean-squared steady-state error of the algorithm in case the local objective functions are strongly convex and have Lipschitz continuous gradients. In addition, we show that when the local objective functions are convex and the additive node error is bounded, the estimation error of the noisy admm for consensus optimization is also bounded. Numerical results are provided, which demonstrates the effectiveness of the presented analyses and shed light on the role of the system and network parameters on performance.

关键词： admm algorithm consensus optimization convergence node error steady-state error

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Activating demand side flexibility market in a fully decentralized P2P transactive energy trading framework using admm algorithm

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SUSTAINABLE CITIES AND SOCIETY 2024年 100卷

作者： Aminlou, Ali Mohammadi-Ivatloo, Behnam Zare, Kazem Razzaghi, Reza Anvari-Moghaddam, Amjad Univ Tabriz Fac Elect & Comp Engn Tabriz Iran LUT Univ Sch Energy Syst Dept Elect Engn Lappeenranta Finland Gebze Tech Univ Dept Elect Engn Gebze Turkiye Monash Univ Dept Elect & Comp Syst Engn Melbourne Australia Aalborg Univ Dept Energy AAU Energy DK-9220 Aalborg Denmark Univ Tabriz Fac Elect & Comp Engn 29 Bahman Bulvar Tabriz Iran

The communication network development and rising penetration of prosumers in distribution networks pave the way to emerge a fully decentralized energy transactions framework. Prosumers can share their excess energy production in a new market called the peer -to -peer (P2P) market. This paper proposes a decentralized P2P energy trading market that facilitates electrical energy trading between customers. In this new market, customers act as individual players and decide on their own willingness to maximize their social welfare by selling the extra energy production in the P2P market. Other participants can compensate for their energy deficiency in the P2P market at lower prices. In the decentralized framework, the participant's privacy is protected by sharing a limited amount of data between peers. The P2P market paved the way for another technology named the DSF market. The DSF market is activated by the distribution system operator (DSO) in the local P2P market framework. When congestion is detected in the following day, the DSO requests flexibility from the demand -side flexibility (DSF) and publishes a flexibility requirement table (FRT). Such market structure can incentivize customers to participate in DSF programs and help the main grid by mitigating congestion. This paper employed the alternating direction method of multipliers (admm) algorithm for solving the decentralized market. Numerical studies are carried out for several peers in a local community. Simulation results demonstrate that the customers participating in the P2P market supply 15.9% of their demand within the P2P market. Additionally, the findings indicate that customers exhibit a willingness to engage in the DSF program. Moreover, it is observed that 99% of the demand changes requested from the DSO in the FRT are adhered to by the peers.

关键词： Peer to Peer Energy transaction Energy communities admm algorithm Decentralized approach Demand side flexibility Flexibility improvement

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Fixing and extending some recent results on the admm algorithm

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NUMERICAL algorithmS 2021年第3期86卷 1303-1325页

作者： Banert, Sebastian Bot, Radu Ioan Csetnek, Ernoe Robert Lund Univ Dept Automat Control Fac Engn LTH Box 118 S-22100 Lund Sweden Univ Vienna Fac Math Oskar Morgenstern Pl 1 A-1090 Vienna Austria

We investigate the techniques and ideas used in Shefi and Teboulle (SIAM J Optim 24(1), 269-297, 2014) in the convergence analysis of two proximal admm algorithms for solving convex optimization problems involving compositions with linear operators. Besides this, we formulate a variant of the admm algorithm that is able to handle convex optimization problems involving an additional smooth function in its objective, and which is evaluated through its gradient. Moreover, in each iteration, we allow the use of variable metrics, while the investigations are carried out in the setting of infinite-dimensional Hilbert spaces. This algorithmic scheme is investigated from the point of view of its convergence properties.

关键词： admm algorithm Lagrangian Saddle points Variable metrics Positive semidefinite operators

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Recovery Performance of LpLq-admm algorithm under SαS impulse Noise 9

Recovery Performance of LpLq-ADMM Algorithm under SαS impul...

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IEEE-APS Topical Conference on Antennas and Propagation in Wireless Communications (APWC)

作者： Zhang, Chunjie Yang, Meng Hao, Dongbin Harbin Engn Univ Coll Informat & Commun Engn Harbin 150001 Heilongjiang Peoples R China

ISBN: (纸本)9781728105666

In the process of signal and image acquisition and transmission, there is not only the additive white Gaussian noise interference, but also the non-Gaussian noise interference. The performance of a standard reconstruction algorithm, known as compressed sensing, can be significantly reduced if it is used to recover the signal affected by non-Gaussian noise. In this paper, LpLq-admm algorithm (p is an element of (0,2), q is an element of (0,1)) based on alternating direction method of multipliers is proposed to improve the reconstruction accuracy and the robustness of signal and image restoration in impulsive S alpha S (symmetric alpha-stable) noise. Lp-norm is used as the loss function term to enhance the data restoration ability in S alpha S noise and Lq-norm is used as the generalized non convex penalty term to guarantee the sparsity of the signal. In order to efficiently solve the cost function model with minimum noncom/ex and nonsmooth, reduce the computational complexity of the objective function and improve the processing ability of high-dimensional data, in this paper, the alternating direction method of multipliers (admm) is used to solve the cost function model. The appropriate p and q values are selected via numerical simulation experiments to achieve the optimal reconstruction accuracy and robustness of sparse signals in S alpha S noise. The reconstruction probability of sparse signals and image recovery performance arc analyzed under the optimal p and q values. The simulation results show that LpLq-admm algorithm has great noise suppression ability to S alpha S noise, and its Peak Signal to Noise Ratio (PSNR) and signal recovery probability is higher than other recovery algorithms.

关键词： admm algorithm augmented Lagrange method compressed sensing quasi-norm S alpha S impulsive noise

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ANALYSIS OF DISTRIBUTED admm algorithm FOR CONSENSUS OPTIMIZATION IN PRESENCE OF ERROR 41

ANALYSIS OF DISTRIBUTED ADMM ALGORITHM FOR CONSENSUS OPTIMIZ...

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41st IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

作者： Majzoobi, Layla Lahouti, Farshad Univ Tehran Sch Elect Engn Tehran 14174 Iran CALTECH Dept Elect Engn Pasadena CA 91125 USA

ISBN: (纸本)9781479999880

admm is a popular algorithm for solving convex optimization problems. Applying this algorithm to distributed consensus optimization problem results in a fully distributed iterative solution which relies on processing at the nodes and communication between neighbors. Local computations usually suffer from different types of errors, due to e.g., observation or quantization noise, which can degrade the performance of the algorithm. In this work, we focus on analyzing the convergence behavior of distributed admm for consensus optimization in presence of additive node error. We specifically show that (a noisy) admm converges linearly under certain conditions and also examine the associated convergence point. Numerical results are provided which demonstrate the effectiveness of the presented analysis.

关键词： admm algorithm Consensus optimization Convergence

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MULTICORE IMPLEMENTATION OF LDPC DECODERS BASED ON admm algorithm 41

MULTICORE IMPLEMENTATION OF LDPC DECODERS BASED ON ADMM ALGO...

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41st IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

作者： Debbabi, Imen Khouja, Nadia Tlili, Fethi Le Gal, Bertrand Jego, Christophe Univ Carthage SUPCOM GRESCOM Lab Carthage Tunisia Univ Bordeaux Bordeaux INP IMS Lab Bordeaux France

ISBN: (纸本)9781479999880

Alternate direction method of multipliers (admm) technique has recently been proposed for LDPC decoding. Even though it improves the error rate performance compared with traditional message passing (MP) techniques, it shows a higher computation complexity. In this article, the admm decoding algorithm is first described. Then, its computation complexity is analyzed. Finally, an optimized version which benefits from the multi-core processors architecture as well as the admm algorithm's parallelism is presented. The optimized version of the admm decoder can achieve up to 30 Mbps for standardized LDPC codes on a laptop x86 processor. Therefore, it could guide an efficient GPU implementation for real-time and highthroughput decoding systems requiring correction performances beyond MP-Sum Product algorithm (SPA) capabilities.

关键词： LDPC decoding admm algorithm muti-core software optimization Forward Error Correction codes

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Positive-definite regularized estimation for high-dimensional covariance on scalar regression

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BIOMETRICS 2025年第1期81卷 ujaf017页

作者： He, Jie Qiu, Yumou Zhou, Xiao-Hua Nanjing Univ Aeronaut & Astronaut Sch Math Nanjing 211106 Peoples R China Peking Univ Sch Math Sci Beijing 100871 Peoples R China Peking Univ Ctr Stat Sci Beijing 100871 Peoples R China Peking Univ BICMR Beijing 100871 Peoples R China Peking Univ Dept Biostat Beijing 100871 Peoples R China

Covariance is an important measure of marginal dependence among variables. However, heterogeneity in subject covariances and regression models for high-dimensional covariance matrices is not well studied. Compared to regression analysis for conditional means, modeling high-dimensional covariances is much more challenging due to the large set of free parameters and the intrinsic positive-definite property that puts constraints on the regression parameters. In this paper, we propose a regularized estimation method for the regression coefficients of covariances under sufficient and necessary constraints for the positive definiteness of the conditional average covariance matrices given covariates. The proposed estimator satisfies the sparsity and positive-definite properties simultaneously. An alternating direction method of multipliers (admm) algorithm is proposed to solve the constrained and regularized optimization problem. We show the convergence of the proposed admm algorithm and derive the convergence rates of the proposed estimators for the regression coefficients and the heterogeneous covariances. The proposed method is evaluated by simulation studies, and its practical application is demonstrated by a case study on brain connectivity.

关键词： admm algorithm conditional average covariance matrix fMRI data high dimensionality positive-definiteness constraint regularization

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