Journal articles: 'Alternating direction methods of multipliers'

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Suzuki, Taiji. "STOCHASTIC ALTERNATING DIRECTION METHOD OF MULTIPLIERS FOR STRUCTURED REGULARIZATION." Journal of the Japanese Society of Computational Statistics 28, no. 1 (2015): 105–24. http://dx.doi.org/10.5183/jjscs.1502004_218.

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Hager, William W., and Hongchao Zhang. "Inexact alternating direction methods of multipliers for separable convex optimization." Computational Optimization and Applications 73, no. 1 (February 7, 2019): 201–35. http://dx.doi.org/10.1007/s10589-019-00072-2.

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Ma, Shiqian, Lingzhou Xue, and Hui Zou. "Alternating Direction Methods for Latent Variable Gaussian Graphical Model Selection." Neural Computation 25, no. 8 (August 2013): 2172–98. http://dx.doi.org/10.1162/neco_a_00379.

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Chandrasekaran, Parrilo, and Willsky ( 2012 ) proposed a convex optimization problem for graphical model selection in the presence of unobserved variables. This convex optimization problem aims to estimate an inverse covariance matrix that can be decomposed into a sparse matrix minus a low-rank matrix from sample data. Solving this convex optimization problem is very challenging, especially for large problems. In this letter, we propose two alternating direction methods for solving this problem. The first method is to apply the classic alternating direction method of multipliers to solve the problem as a consensus problem. The second method is a proximal gradient-based alternating-direction method of multipliers. Our methods take advantage of the special structure of the problem and thus can solve large problems very efficiently. A global convergence result is established for the proposed methods. Numerical results on both synthetic data and gene expression data show that our methods usually solve problems with 1 million variables in 1 to 2 minutes and are usually 5 to 35 times faster than a state-of-the-art Newton-CG proximal point algorithm.

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Yu, Siting, Jingjing Peng, Zengao Tang, and Zhenyun Peng. "Iterative methods to solve the constrained Sylvester equation." AIMS Mathematics 8, no. 9 (2023): 21531–53. http://dx.doi.org/10.3934/math.20231097.

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<abstract><p>In this paper, the multiple constraint least squares solution of the Sylvester equation $ AX+XB = C $ is discussed. The necessary and sufficient conditions for the existence of solutions to the considered matrix equation are given. Noting that the alternating direction method of multipliers (ADMM) is a one-step iterative method, a multi-step alternating direction method of multipliers (MSADMM) to solve the considered matrix equation is proposed and some convergence results of the proposed algorithm are proved. Problems that should be studied in the near future are listed. Numerical comparisons between MSADMM, ADMM and ADMM with Anderson acceleration (ACADMM) are included.</p></abstract>

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Li, Min, Li-Zhi Liao, and Xiaoming Yuan. "Inexact Alternating Direction Methods of Multipliers with Logarithmic–Quadratic Proximal Regularization." Journal of Optimization Theory and Applications 159, no. 2 (May 25, 2013): 412–36. http://dx.doi.org/10.1007/s10957-013-0334-4.

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Huang, Chunlin, and Dongbo Bu. "Predicting human contacts through alternating direction method of multipliers." International Journal of Modern Physics C 30, no. 07 (July 2019): 1940014. http://dx.doi.org/10.1142/s012918311940014x.

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Transmission of respiratory infectious diseases depends greatly on human close-proximity contacts, making thorough understanding of current and upcoming contacts essential for epidemic containment. Although different devices and software have been developed for contact data collection, there are few effective methods for contact prediction available in the near future as far as the authors know. In this study, we propose an approach to predict human contacts. We first extract human features together with their significances from the human contacts through alternating direction method of multipliers (ADMM), then predict future significances based on periodicity of contacts, and finally construct future contacts from human features and future significances. With the help of contact data collected in a Chinese University, we compare this approach with a trivial method of directly averaging known contacts. The comparison shows that our approach generates contacts deviating less from the true ones.

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Abeynanda, Hansi K., and G. H. J. Lanel. "A Study on Distributed Optimization over Large-Scale Networked Systems." Journal of Mathematics 2021 (April 29, 2021): 1–19. http://dx.doi.org/10.1155/2021/5540262.

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Distributed optimization is a very important concept with applications in control theory and many related fields, as it is high fault-tolerant and extremely scalable compared with centralized optimization. Centralized solution methods are not suitable for many application domains that consist of large number of networked systems. In general, these large-scale networked systems cooperatively find an optimal solution to a common global objective during the optimization process. Thus, it gives us an opportunity to analyze distributed optimization techniques that is demanded in most distributed optimization settings. This paper presents an analysis that provides an overview of decomposition methods as well as currently existing distributed methods and techniques that are employed in large-scale networked systems. A detailed analysis on gradient like methods, subgradient methods, and methods of multipliers including the alternating direction method of multipliers is presented. These methods are analyzed empirically by using numerical examples. Moreover, an example highlighting the fact that the gradient method fails to solve distributed problems in some circumstances is discussed under numerical results. A numerical implementation is used to demonstrate that the alternating direction method of multipliers can solve this particular problem, by revealing its robustness compared with the gradient method. Finally, we conclude the paper with possible future research directions.

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Chao, Miantao, Caozong Cheng, and Haibin Zhang. "A Linearized Alternating Direction Method of Multipliers with Substitution Procedure." Asia-Pacific Journal of Operational Research 32, no. 03 (June 2015): 1550011. http://dx.doi.org/10.1142/s0217595915500116.

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We consider the linearly constrained separable convex programming problem whose objective function is separable into m individual convex functions with non-overlapping variables. The alternating direction method of multipliers (ADMM) has been well studied in the literature for the special case m = 2, but the direct extension of ADMM for the general case m ≥ 2 is not necessarily convergent. In this paper, we propose a new linearized ADMM-based contraction type algorithms for the general case m ≥ 2. For the proposed algorithm, we prove its convergence via the analytic framework of contractive type methods and we derive a worst-case O(1/t) convergence rate in ergodic sense. Finally, numerical results are reported to demonstrate the effectiveness of the proposed algorithm.

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Wang, Si, Ting-Zhu Huang, Xi-le Zhao, and Jun Liu. "An Alternating Direction Method for Mixed Gaussian Plus Impulse Noise Removal." Abstract and Applied Analysis 2013 (2013): 1–11. http://dx.doi.org/10.1155/2013/850360.

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A combined total variation and high-order total variation model is proposed to restore blurred images corrupted by impulse noise or mixed Gaussian plus impulse noise. We attack the proposed scheme with an alternating direction method of multipliers (ADMM). Numerical experiments demonstrate the efficiency of the proposed method and the performance of the proposed method is competitive with the existing state-of-the-art methods.

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Liu, Yang, and Yazheng Dang. "Convergence Analysis of Multiblock Inertial ADMM for Nonconvex Consensus Problem." Journal of Mathematics 2023 (March 28, 2023): 1–12. http://dx.doi.org/10.1155/2023/4316267.

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The alternating direction method of multipliers (ADMM) is one of the most powerful and successful methods for solving various nonconvex consensus problem. The convergence of the conventional ADMM (i.e., 2-block) for convex objective functions has been stated for a long time. As an accelerated technique, the inertial effect was used by many authors to solve 2-block convex optimization problem. This paper combines the ADMM and the inertial effect to construct an inertial alternating direction method of multipliers (IADMM) to solve the multiblock nonconvex consensus problem and shows the convergence under some suitable conditions. Simulation experiment verifies the effectiveness and feasibility of the proposed method.

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Chao, Miantao, Yongxin Zhao, and Dongying Liang. "A Proximal Alternating Direction Method of Multipliers with a Substitution Procedure." Mathematical Problems in Engineering 2020 (April 27, 2020): 1–12. http://dx.doi.org/10.1155/2020/7876949.

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In this paper, we considers the separable convex programming problem with linear constraints. Its objective function is the sum of m individual blocks with nonoverlapping variables and each block consists of two functions: one is smooth convex and the other one is convex. For the general case m≥3, we present a gradient-based alternating direction method of multipliers with a substitution. For the proposed algorithm, we prove its convergence via the analytic framework of contractive-type methods and derive a worst-case O1/t convergence rate in nonergodic sense. Finally, some preliminary numerical results are reported to support the efficiency of the proposed algorithm.

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吉, 锋瑞. "New Numerical Methods for Robust Regularization Problem Based on Alternating Direction Method of Multipliers." Operations Research and Fuzziology 10, no. 02 (2020): 122–38. http://dx.doi.org/10.12677/orf.2020.102013.

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Chan, Raymond H., Min Tao, and Xiaoming Yuan. "Linearized Alternating Direction Method of Multipliers for Constrained Linear Least-Squares Problem." East Asian Journal on Applied Mathematics 2, no. 4 (November 2012): 326–41. http://dx.doi.org/10.4208/eajam.270812.161112a.

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Abstract.The alternating direction method of multipliers (ADMM) is applied to a constrained linear least-squares problem, where the objective function is a sum of two least-squares terms and there are box constraints. The original problem is decomposed into two easier least-squares subproblems at each iteration, and to speed up the inner iteration we linearize the relevant subproblem whenever it has no known closed-form solution. We prove the convergence of the resulting algorithm, and apply it to solve some image deblurring problems. Its efficiency is demonstrated, in comparison with Newton-type methods.

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Bílková, Zuzana, and Michal Šorel. "Projection methods for finding intersection of two convex sets and their use in signal processing problems." Electronic Imaging 2021, no. 10 (January 18, 2021): 226–1. http://dx.doi.org/10.2352/issn.2470-1173.2021.10.ipas-226.

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Finding a point in the intersection of two closed convex sets is a common problem in image processing and other areas. Projections onto convex sets (POCS) is a standard algorithm for finding such a point. Dykstra's projection algorithm is a well known alternative that finds the point in the intersection closest to a given point. Yet another lesser known alternative is the alternating direction method of multipliers (ADMM) that can be used for both purposes. In this paper we discuss the differences in the convergence of these algorithms in image processing problems. The ADMM applied to finding an arbitrary point in the intersection is much faster than POCS and any algorithm for finding the nearest point in the intersection.

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Jiang, Yaning, Xingju Cai, and Deren Han. "Solving policy design problems: Alternating direction method of multipliers-based methods for structured inverse variational inequalities." European Journal of Operational Research 280, no. 2 (January 2020): 417–27. http://dx.doi.org/10.1016/j.ejor.2019.05.044.

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Lv, Xin-Rong, Youming Li, and Yu-Cheng He. "Efficient Impulsive Noise Mitigation for OFDM Systems Using the Alternating Direction Method of Multipliers." Mathematical Problems in Engineering 2018 (June 7, 2018): 1–11. http://dx.doi.org/10.1155/2018/4968682.

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An efficient impulsive noise estimation algorithm based on alternating direction method of multipliers (ADMM) is proposed for OFDM systems using quadrature amplitude modulation (QAM). Firstly, we adopt the compressed sensing (CS) method based on the l1-norm optimization to estimate impulsive noise. Instead of the conventional methods that exploit only the received signal in null tones as constraint, we add the received signal of data tones and QAM constellations as constraints. Then a relaxation approach is introduced to convert the discrete constellations to the convex box constraints. After that a linear programming is used to solve the optimization problem. Finally, a framework of ADMM is developed to solve the problem in order to reduce the computation complexity. Simulation results for 4-QAM and 16-QAM demonstrate the practical advantages of the proposed algorithm over the other algorithms in bit error rate performance gains.

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Ding, Yanyun, and Yunhai Xiao. "Symmetric Gauss–Seidel Technique-Based Alternating Direction Methods of Multipliers for Transform Invariant Low-Rank Textures Problem." Journal of Mathematical Imaging and Vision 60, no. 8 (March 19, 2018): 1220–30. http://dx.doi.org/10.1007/s10851-018-0808-y.

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Shen, Hai-Long, and Xu Tang. "The PPADMM Method for Solving Quadratic Programming Problems." Mathematics 9, no. 9 (April 23, 2021): 941. http://dx.doi.org/10.3390/math9090941.

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In this paper, a preconditioned and proximal alternating direction method of multipliers (PPADMM) is established for iteratively solving the equality-constraint quadratic programming problems. Based on strictly matrix analysis, we prove that this method is asymptotically convergent. We also show the connection between this method with some existing methods, so it combines the advantages of the methods. Finally, the numerical examples show that the algorithm proposed is efficient, stable, and flexible for solving the quadratic programming problems with equality constraint.

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Wimalawarne, Kishan, Ryota Tomioka, and Masashi Sugiyama. "Theoretical and Experimental Analyses of Tensor-Based Regression and Classification." Neural Computation 28, no. 4 (April 2016): 686–715. http://dx.doi.org/10.1162/neco_a_00815.

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We theoretically and experimentally investigate tensor-based regression and classification. Our focus is regularization with various tensor norms, including the overlapped trace norm, the latent trace norm, and the scaled latent trace norm. We first give dual optimization methods using the alternating direction method of multipliers, which is computationally efficient when the number of training samples is moderate. We then theoretically derive an excess risk bound for each tensor norm and clarify their behavior. Finally, we perform extensive experiments using simulated and real data and demonstrate the superiority of tensor-based learning methods over vector- and matrix-based learning methods.

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Wang, Tao, Zihao Chen, Zhiwei Cheng, Xiaobo Deng, Junli Liang, and Jianchao Bai. "Joint design of mismatched filter and unimodular transmit waveform." Xibei Gongye Daxue Xuebao/Journal of Northwestern Polytechnical University 39, no. 6 (December 2021): 1349–55. http://dx.doi.org/10.1051/jnwpu/20213961349.

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To improve the receiver performance, unimodular transmit waveform and mismatched filter are jointly designed by using the alternating direction method of multipliers (ADMM). A series of auxiliary variables are introduced to decouple the variables in objective function and additional constrains. Denominator normalization(fractional programming technology) and step function are applied to obtain optimal solution from some subproblems. For given transmit waveform, same-length mismatched filter is designed in receiver. The low sidelobe level performance of the present methods are illustrated with the simulation results.

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Nagahara, Masaaki, Yu Iwai, and Noboru Sebe. "Projection onto the Set of Rank-Constrained Structured Matrices for Reduced-Order Controller Design." Algorithms 15, no. 9 (September 9, 2022): 322. http://dx.doi.org/10.3390/a15090322.

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In this paper, we propose an efficient numerical computation method of reduced-order controller design for linear time-invariant systems. The design problem is described by linear matrix inequalities (LMIs) with a rank constraint on a structured matrix, due to which the problem is non-convex. Instead of the heuristic method that approximates the matrix rank by the nuclear norm, we propose a numerical projection onto the rank-constrained set based on the alternating direction method of multipliers (ADMM). Then the controller is obtained by alternating projection between the rank-constrained set and the LMI set. We show the effectiveness of the proposed method compared with existing heuristic methods, by using 95 benchmark models from the COMPLeib library.

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Zhu, Jianguang, Kai Li, and Binbin Hao. "Image Restoration by a Mixed High-Order Total Variation and l1 Regularization Model." Mathematical Problems in Engineering 2018 (September 24, 2018): 1–13. http://dx.doi.org/10.1155/2018/6538610.

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Total variation regularization is well-known for recovering sharp edges; however, it usually produces staircase artifacts. In this paper, in order to overcome the shortcoming of total variation regularization, we propose a new variational model combining high-order total variation regularization and l1 regularization. The new model has separable structure which enables us to solve the involved subproblems more efficiently. We propose a fast alternating method by employing the fast iterative shrinkage-thresholding algorithm (FISTA) and the alternating direction method of multipliers (ADMM). Compared with some current state-of-the-art methods, numerical experiments show that our proposed model can significantly improve the quality of restored images and obtain higher SNR and SSIM values.

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Zhang, Yongxiang, Qiyuan Peng, Yu Yao, Xin Zhang, and Xuesong Zhou. "Solving cyclic train timetabling problem through model reformulation: Extended time-space network construct and Alternating Direction Method of Multipliers methods." Transportation Research Part B: Methodological 128 (October 2019): 344–79. http://dx.doi.org/10.1016/j.trb.2019.08.001.

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He, Jingfei, and Yatong Zhou. "Real-Time Data Recovery in Wireless Sensor Networks Using Spatiotemporal Correlation Based on Sparse Representation." Wireless Communications and Mobile Computing 2019 (May 20, 2019): 1–7. http://dx.doi.org/10.1155/2019/2310730.

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Due to data loss and sparse sampling methods utilized in WSNs to reduce energy consumption, reconstructing the raw sensed data from partial data is an indispensable operation. In this paper, a real-time data recovery method is proposed using the spatiotemporal correlation among WSN data. Specifically, by introducing the historical data, joint low-rank constraint and temporal stability are utilized to further exploit the data spatiotemporal correlation. Furthermore, an algorithm based on the alternating direction method of multipliers is described to solve the resultant optimization problem efficiently. The simulation results show that the proposed method outperforms the state-of-the-art methods for different types of signal in the network.

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Shi, Baoli, Zhi-Feng Pang, and Yu-Fei Yang. "Image Restoration Based on the Hybrid Total-Variation-Type Model." Abstract and Applied Analysis 2012 (2012): 1–30. http://dx.doi.org/10.1155/2012/376802.

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We propose a hybrid total-variation-type model for the image restoration problem based on combining advantages of the ROF model with the LLT model. Since twoL1-norm terms in the proposed model make it difficultly solved by using some classically numerical methods directly, we first employ the alternating direction method of multipliers (ADMM) to solve a general form of the proposed model. Then, based on the ADMM and the Moreau-Yosida decomposition theory, a more efficient method called the proximal point method (PPM) is proposed and the convergence of the proposed method is proved. Some numerical results demonstrate the viability and efficiency of the proposed model and methods.

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Stomberg, Gösta, Alexander Engelmann, and Timm Faulwasser. "A compendium of optimization algorithms for distributed linear-quadratic MPC." at - Automatisierungstechnik 70, no. 4 (March 25, 2022): 317–30. http://dx.doi.org/10.1515/auto-2021-0112.

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Abstract Model Predictive Control (MPC) for {networked, cyber-physical, multi-agent} systems requires numerical methods to solve optimal control problems while meeting communication and real-time requirements. This paper presents an introduction on six distributed optimization algorithms and compares their properties in the context of distributed MPC for linear systems with convex quadratic objectives and polytopic constraints. In particular, dual decomposition, the alternating direction method of multipliers, a distributed active set method, an essentially decentralized interior point method, and Jacobi iterations are discussed. Numerical examples illustrate the challenges, the prospect, and the limits of distributed MPC with inexact solutions.

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Liang, Peidong, Chentao Zhang, Habte Tadesse Likassa, and Jielong Guo. "New Robust Tensor PCA via Affine Transformations and L 2,1 Norms for Exact Tubal Low-Rank Recovery from Highly Corrupted and Correlated Images in Signal Processing." Mathematical Problems in Engineering 2022 (March 31, 2022): 1–14. http://dx.doi.org/10.1155/2022/3002348.

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In this latest work, the Newly Modified Robust Tensor Principal Component Analysis (New RTPCA) using affine transformation and L 2,1 norms is proposed to remove the outliers and heavy sparse noises in signal processing. This process is done by decomposing the original data matrix as the low-rank heavy sparse noises. The determination of the potential variables is casted as constrained convex optimization problem, and the Alternating Direction Method of Multipliers (ADMM) method is considered to reduce the computational loads in an iterative manner. The simulation results validate the effectiveness of the new method as compared with that of the state-of-the-art methods.

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Zhang, Benxin, Xiaolong Wang, Yi Li, and Zhibin Zhu. "A new difference of anisotropic and isotropic total variation regularization method for image restoration." Mathematical Biosciences and Engineering 20, no. 8 (2023): 14777–92. http://dx.doi.org/10.3934/mbe.2023661.

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<abstract><p>Total variation (TV) regularizer has diffusely emerged in image processing. In this paper, we propose a new nonconvex total variation regularization method based on the generalized Fischer-Burmeister function for image restoration. Since our model is nonconvex and nonsmooth, the specific difference of convex algorithms (DCA) are presented, in which the subproblem can be minimized by the alternating direction method of multipliers (ADMM). The algorithms have a low computational complexity in each iteration. Experiment results including image denoising and magnetic resonance imaging demonstrate that the proposed models produce more preferable results compared with state-of-the-art methods.</p></abstract>

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Wu, Jiangnan, Yongmei Zhao, Hongmei Zhang, Gang Hu, Hang Zeng, and Song Li. "Spatio-Temporal Traffic Data Tensor Restoration Method Based on Direction Weighting and P-Shrinkage Norm." Mathematical Problems in Engineering 2022 (October 13, 2022): 1–17. http://dx.doi.org/10.1155/2022/3304677.

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Due to the influence of data collection methods and external complex factors, missing traffic data is inevitable. However, complete traffic information is a necessary input for route planning and forecasting tasks. To reduce the impact of missing data problems, this paper uses the low-rank tensor completion framework based on T-SVD to complete the missing spatio-temporal traffic data, the aim is to recover a low-rank tensor from a tensor with partial observation terms, and the WLRTC-P model is proposed. We use the idea of direction weighting to solve the dependence of the original model on the data input direction, extract each direction correlation information of the tensor spatio-temporal traffic data, and use the p-shrinkage norm to replace the tensor average rank minimization problem, and the study shows that the p-shrinkage norm is tighter than the tensor nuclear norm and, finally, uses the alternating direction method of multipliers to solve this model. Experiments on two publicly available spatio-temporal traffic datasets verified the conjecture of data input direction’s influence on the completion accuracy, and compared with the existing classical model methods, WLRTC-P has high precision and generalization ability.

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Sun, Yun-Jia, Ting-Zhu Huang, Tian-Hui Ma, and Yong Chen. "Remote Sensing Image Stripe Detecting and Destriping Using the Joint Sparsity Constraint with Iterative Support Detection." Remote Sensing 11, no. 6 (March 13, 2019): 608. http://dx.doi.org/10.3390/rs11060608.

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Remote sensing images have been applied to a wide range of fields, but they are often degraded by various types of stripes, which affect the image visual quality and limit the subsequent processing tasks. Most existing destriping methods fail to exploit the stripe properties adequately, leading to suboptimal performance. Based on a full consideration of the stripe properties, we propose a new destriping model to achieve stripe detection and stripe removal simultaneously. In this model, we adopt the unidirectional total variation regularization to depict the directional property of stripes and the weighted ℓ 2 , 1 -norm regularization to depict the joint sparsity of stripes. Then, we combine the alternating direction method of multipliers and iterative support detection to solve the proposed model effectively. Comparison results on simulated and real data suggest that the proposed method can remove and detect stripes effectively while preserving image edges and details.

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Xi, Tengyan, Lihua Yuan, and Quanbin Sun. "A Combined Approach to Infrared Small-Target Detection with the Alternating Direction Method of Multipliers and an Improved Top-Hat Transformation." Sensors 22, no. 19 (September 27, 2022): 7327. http://dx.doi.org/10.3390/s22197327.

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In infrared small target detection, the infrared patch image (IPI)-model-based methods produce better results than other popular approaches (such as max-mean, top-hat, and human visual system) but in some extreme cases it suffers from long processing times and inconsistent performance. In order to overcome these issues, we propose a novel approach of dividing the traditional target detection process into two steps: suppression of background noise and elimination of clutter. The workflow consists of four steps: after importing the images, the second step applies the alternating direction multiplier method to preliminarily remove the background. Comparatively to the IPI model, this step does not require sliding patches, resulting in a significant reduction in processing time. To eliminate residual noise and clutter, the interim results from morphological filtering are then processed in step 3 through an improved new top-hat transformation, using a threefold structuring element. The final step is thresholding segmentation, which uses an adaptive threshold algorithm. Compared with IPI and the new top-hat methods, as well as some other widely used methods, our approach was able to detect infrared targets more efficiently (90% less computational time) and consistently (no sudden performance drop).

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Chen, Jie, Ryosuke Shimmura, and Joe Suzuki. "Efficient Proximal Gradient Algorithms for Joint Graphical Lasso." Entropy 23, no. 12 (December 2, 2021): 1623. http://dx.doi.org/10.3390/e23121623.

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We consider learning as an undirected graphical model from sparse data. While several efficient algorithms have been proposed for graphical lasso (GL), the alternating direction method of multipliers (ADMM) is the main approach taken concerning joint graphical lasso (JGL). We propose proximal gradient procedures with and without a backtracking option for the JGL. These procedures are first-order methods and relatively simple, and the subproblems are solved efficiently in closed form. We further show the boundedness for the solution of the JGL problem and the iterates in the algorithms. The numerical results indicate that the proposed algorithms can achieve high accuracy and precision, and their efficiency is competitive with state-of-the-art algorithms.

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Dai, Kun, Hong-Yi Yu, and Qing Li. "A Semisupervised Feature Selection with Support Vector Machine." Journal of Applied Mathematics 2013 (2013): 1–11. http://dx.doi.org/10.1155/2013/416320.

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Feature selection has proved to be a beneficial tool in learning problems with the main advantages of interpretation and generalization. Most existing feature selection methods do not achieve optimal classification performance, since they neglect the correlations among highly correlated features which all contribute to classification. In this paper, a novel semisupervised feature selection algorithm based on support vector machine (SVM) is proposed, termed SENFS. In order to solve SENFS, an efficient algorithm based on the alternating direction method of multipliers is then developed. One advantage of SENFS is that it encourages highly correlated features to be selected or removed together. Experimental results demonstrate the effectiveness of our feature selection method on simulation data and benchmark data sets.

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Xiao, Hua, Zhongliang Wang, Xueying Cui, Liping Wang, and Hongsheng Yang. "Hyperspectral Compressed Sensing Reconstruction Applying Multi-TV Collaboration." Journal of Sensors 2023 (April 6, 2023): 1–14. http://dx.doi.org/10.1155/2023/5186977.

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For hyperspectral images (HSI) compressed sensing reconstruction, the 3D total variation (3DTV) is a powerful regulation term encoding the spatial-spectral local smooth prior structure. The term is calculated by supposing the sparsity structure on a gradient map along the spatial and spectral direction. In some real scenes, however, the gradient maps along different directions of HSI are not always sparse. Actually, TV constraints established on the gradient map of the original HSI are more effective in most cases. In this paper, instead of imposing sparsity on gradient maps themselves directly, compressed sensing (CS) reconstruction for HSI is formulated as an optimization problem utilizing a novel regulation term named multi-TV (MTV), which combines the sparsity prior for the gradient map and the TV projection along with other directions of the gradient map. We also develop a workable utility algorithm based on the alternating direction method of multipliers (ADMM) to effectively deal with the optimization problem. The proposed MTV term can easily replace the conventional 3DTV term and be embedded into hyperspectral CS (HCS) reconstruction to improve its performance. Experimental results show that compared with similar state-of-the-art methods, the proposed MTV term can significantly improve reconstruction precision for HCS.

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Wu, Xiaoce, Bingyin Zhou, Qingyun Ren, and Wei Guo. "Multispectral image denoising using sparse and graph Laplacian Tucker decomposition." Computational Visual Media 6, no. 3 (July 20, 2020): 319–31. http://dx.doi.org/10.1007/s41095-020-0176-6.

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Abstract Multispectral image denoising is a basic problem whose results affect subsequent processes such as target detection and classification. Numerous approaches have been proposed, but there are still many challenges, particularly in using prior knowledge of multispectral images, which is crucial for solving the ill-posed problem of noise removal. This paper considers both non-local self-similarity in space and global correlation in spectrum. We propose a novel low-rank Tucker decomposition model for removing the noise, in which sparse and graph Laplacian regularization terms are employed to encode this prior knowledge. It can jointly learn a sparse and low-rank representation while preserving the local geometrical structure between spectral bands, so as to better capture simultaneously the correlation in spatial and spectral directions. We adopt the alternating direction method of multipliers to solve the resulting problem. Experiments demonstrate that the proposed method outperforms the state-of-the-art, such as cube-based and tensor-based methods, both quantitatively and qualitatively.

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Ding, Mingjun, Xiaodong Yang, Rui Hu, Zhitao Xiao, Jun Tong, and Jiangtao Xi. "On Matrix Completion-Based Channel Estimators for Massive MIMO Systems." Symmetry 11, no. 11 (November 6, 2019): 1377. http://dx.doi.org/10.3390/sym11111377.

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Large-scale symmetric arrays such as uniform linear arrays (ULA) have been widely used in wireless communications for improving spectrum efficiency and reliability. Channel state information (CSI) is critical for optimizing massive multiple-input multiple-output(MIMO)-based wireless communication systems. The acquisition of CSI for massive MIMO faces challenges such as training shortage and high computational complexity. For millimeter wave MIMO systems, the low-rankness of the channel can be utilized to address the challenge of training shortage. In this paper, we compared several channel estimation schemes based on matrix completion (MC) for symmetrical arrays. Performance and computational complexity are discussed and compared. By comparing the performance in different scenarios, we concluded that the generalized conditional gradient with alternating minimization (GCG-Alt) estimator provided a low-cost, robust solution, while the alternating direction method of multipliers (ADMM)-based hybrid methods achieved the best performance when the array response was perfectly known.

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Gao, Xuyang, Yibing Shi, Kai Du, Qi Zhu, and Wei Zhang. "Sparse Blind Deconvolution with Nonconvex Optimization for Ultrasonic NDT Application." Sensors 20, no. 23 (December 4, 2020): 6946. http://dx.doi.org/10.3390/s20236946.

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In the field of ultrasonic nondestructive testing (NDT), robust and accurate detection of defects is a challenging task because of the attenuation and noising of the ultrasonic wave from the structure. For determining the reflection characteristics representing the position and amplitude of ultrasonic detection signals, sparse blind deconvolution methods have been implemented to separate overlapping echoes when the ultrasonic transducer impulse response is unknown. This letter introduces the ℓ1/ℓ2 ratio regularization function to model the deconvolution as a nonconvex optimization problem. The initialization influences the accuracy of estimation and, for this purpose, the alternating direction method of multipliers (ADMM) combined with blind gain calibration is used to find the initial approximation to the real solution, given multiple observations in a joint sparsity case. The proximal alternating linearized minimization (PALM) algorithm is embedded in the iterate solution, in which the majorize-minimize (MM) approach accelerates convergence. Compared with conventional blind deconvolution algorithms, the proposed methods demonstrate the robustness and capability of separating overlapping echoes in the context of synthetic experiments.

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Han and Kan. "Blind Image Deblurring Based on Local Edges Selection." Applied Sciences 9, no. 16 (August 9, 2019): 3274. http://dx.doi.org/10.3390/app9163274.

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The edges of images are less sparse when images become blurred. Selecting effective image edges is a vital step in image deblurring, which can help us to build image deblurring models more accurately. While global edges selection methods tend to fail in capturing dense image structures, the edges are easy to be affected by noise and blur. In this paper, we propose an image deblurring method based on local edges selection. The local edges are selected by the difference between the bright channel and the dark channel. Then a novel image deblurring model including local edges regularization term is established. The obtaining of a clear image and blurring kernel is based on alternating iterations, in which the clear image is obtained by the alternating direction method of multipliers (ADMM). In the experiments, tests are carried out on gray value images, synthetic color images and natural color images. Compared with other state-of-the-art blind image deblurring methods, the visualization results and performance verify the effectiveness of our method.

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Zeng, Shuai, Shuangsheng Wang, and Yiming He. "Latency Aware Distributed ADMM over Networks." Journal of Physics: Conference Series 2050, no. 1 (October 1, 2021): 012004. http://dx.doi.org/10.1088/1742-6596/2050/1/012004.

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Abstract Methods based on the alternating direction method of multipliers (ADMM) has attracted academic attention because of its excellent convergence performance and potential application scenarios in many machine learning or optimization fields. However, classical distributed ADMM algorithm assumed ideal network communication, which do not consider the impact of network delay on computing performance. In this paper, based on the strategy of selecting bridges with lowest network latency and appropriate iterative process, we propose a latency aware distributed ADMM algorithm to alleviate the impact of network delay. The classical algorithm and proposed algorithm are tested and compared in real network scenarios. Experiments show that the proposed algorithm reduces the running time and improves the computing performance. Especially in networks with large delay, the effect is more obvious.

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Li, Fangda, Ankit Manerikar, Tanmay Prakash, and Avinash C. Kak. "A Splitting-Based Iterative Algorithm for GPU-Accelerated Statistical Dual-Energy X-Ray CT Reconstruction." Electronic Imaging 2020, no. 14 (January 26, 2020): 6–1. http://dx.doi.org/10.2352/issn.2470-1173.2020.14.coimg-a14.

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When dealing with material classification in baggage at airports, Dual-Energy Computed Tomography (DECT) allows characterization of any given material with coefficients based on two attenuative effects: Compton scattering and photoelectric absorption. However, straightforward projection-domain decomposition methods for this characterization often yield poor reconstructions due to the high dynamic range of material properties encountered in an actual luggage scan. Hence, for better reconstruction quality under a timing constraint, we propose a splitting-based, GPU-accelerated, statistical DECT reconstruction algorithm. Compared to prior art, our main contribution lies in the significant acceleration made possible by separating reconstruction and decomposition within an Alternating Direction Method of Multipliers (ADMM) framework. Experimental results, on both synthetic and real-world baggage phantoms, demonstrate a significant reduction in time required for convergence.

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Hammami, Dine El Houda, Saber Maraoui, and Kais Bouzrara. "Nonlinear distributed model predictive control with dual decomposition and event-based communication approach." Transactions of the Institute of Measurement and Control 42, no. 15 (July 6, 2020): 2929–40. http://dx.doi.org/10.1177/0142331220933437.

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This paper proposes a dual decomposition method for solving distributed model predictive control. This controller is designed for systems subject to communication constraints, in which nonlinear subsystems interconnected via dynamics and by constraints. The interconnections are relaxed by using gradient method, accelerated gradient and alternating direction methods of multipliers. Also, an event-based communication is proposed to handle the issue of communication constraints especially in embedded systems. In the proposed event-based communication strategy, each controller solves the optimization problem and communicate only if the prices are updated significantly, which can reduce the computation load and release the burden of the network while achieving global performance. Finally, the simulations study of the four-tank benchmark is presented to demonstrate the effectiveness of the proposed schemes.

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Li, Mingxuan, Shenkai Nong, Ting Nie, Chengshan Han, Liang Huang, and Lixin Qu. "A Novel Stripe Noise Removal Model for Infrared Images." Sensors 22, no. 8 (April 13, 2022): 2971. http://dx.doi.org/10.3390/s22082971.

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Infrared images often carry obvious streak noises due to the non-uniformity of the infrared detector and the readout circuit. These streak noises greatly affect the image quality, adding difficulty to subsequent image processing. Compared with current elimination algorithms for infrared stripe noises, our approach fully utilizes the difference between the stripe noise components and the actual information components, takes the gradient sparsity along the stripe direction and the global sparsity of the stripe noises as regular terms, and treats the sparsity of the components across the stripe direction as a fidelity term. On this basis, an adaptive edge-preserving operator (AEPO) based on edge contrast was proposed to protect the image edge and, thus, prevent the loss of edge details. The final solution was obtained by the alternating direction method of multipliers (ADMM). To verify the effectiveness of our approach, many real experiments were carried out to compare it with state-of-the-art methods in two aspects: subjective judgment and objective indices. Experimental results demonstrate the superiority of our approach.

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Wiegele, Angelika, and Shudian Zhao. "SDP-based bounds for graph partition via extended ADMM." Computational Optimization and Applications 82, no. 1 (March 17, 2022): 251–91. http://dx.doi.org/10.1007/s10589-022-00355-1.

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AbstractWe study two NP-complete graph partition problems, k-equipartition problems and graph partition problems with knapsack constraints (GPKC). We introduce tight SDP relaxations with nonnegativity constraints to get lower bounds, the SDP relaxations are solved by an extended alternating direction method of multipliers (ADMM). In this way, we obtain high quality lower bounds for k-equipartition on large instances up to $$n =1000$$ n = 1000 vertices within as few as 5 min and for GPKC problems up to $$n=500$$ n = 500 vertices within as little as 1 h. On the other hand, interior point methods fail to solve instances from $$n=300$$ n = 300 due to memory requirements. We also design heuristics to generate upper bounds from the SDP solutions, giving us tighter upper bounds than other methods proposed in the literature with low computational expense.

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Srivastav, Prateek Saurabh, Lan Chen, and Arfan Haider Wahla. "On the Performance of Efficient Channel Estimation Strategies for Hybrid Millimeter Wave MIMO System." Entropy 22, no. 10 (October 3, 2020): 1121. http://dx.doi.org/10.3390/e22101121.

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Millimeter wave (mmWave) relying upon the multiple output multiple input (MIMO) is a new potential candidate for fulfilling the huge emerging bandwidth requirements. Due to the short wavelength and the complicated hardware architecture of mmWave MIMO systems, the conventional estimation strategies based on the individual exploitation of sparsity or low rank properties are no longer efficient and hence more modern and advance estimation strategies are required to recapture the targeted channel matrix. Therefore, in this paper, we proposed a novel channel estimation strategy based on the symmetrical version of alternating direction methods of multipliers (S-ADMM), which exploits the sparsity and low rank property of channel altogether in a symmetrical manner. In S-ADMM, at each iteration, the Lagrange multipliers are updated twice which results symmetrical handling of all of the available variables in optimization problem. To validate the proposed algorithm, numerous computer simulations have been carried out which straightforwardly depicts that the S-ADMM performed well in terms of convergence as compared to other benchmark algorithms and also able to provide global optimal solutions for the strictly convex mmWave joint channel estimation optimization problem.

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Li, Xiaoyong, Xueru Bai, and Feng Zhou. "High-Resolution ISAR Imaging and Autofocusing via 2D-ADMM-Net." Remote Sensing 13, no. 12 (June 13, 2021): 2326. http://dx.doi.org/10.3390/rs13122326.

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A deep-learning architecture, dubbed as the 2D-ADMM-Net (2D-ADN), is proposed in this article. It provides effective high-resolution 2D inverse synthetic aperture radar (ISAR) imaging under scenarios of low SNRs and incomplete data, by combining model-based sparse reconstruction and data-driven deep learning. Firstly, mapping from ISAR images to their corresponding echoes in the wavenumber domain is derived. Then, a 2D alternating direction method of multipliers (ADMM) is unrolled and generalized to a deep network, where all adjustable parameters in the reconstruction layers, nonlinear transform layers, and multiplier update layers are learned by an end-to-end training through back-propagation. Since the optimal parameters of each layer are learned separately, 2D-ADN exhibits more representation flexibility and preferable reconstruction performance than model-driven methods. Simultaneously, it is able to better facilitate ISAR imaging with limited training samples than data-driven methods owing to its simple structure and small number of adjustable parameters. Additionally, benefiting from the good performance of 2D-ADN, a random phase error estimation method is proposed, through which well-focused imaging can be acquired. It is demonstrated by experiments that although trained by only a few simulated images, the 2D-ADN shows good adaptability to measured data and favorable imaging results with a clear background can be obtained in a short time.

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Feng, Xinxi, Le Han, and Le Dong. "Weighted Group Sparsity-Constrained Tensor Factorization for Hyperspectral Unmixing." Remote Sensing 14, no. 2 (January 14, 2022): 383. http://dx.doi.org/10.3390/rs14020383.

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Recently, unmixing methods based on nonnegative tensor factorization have played an important role in the decomposition of hyperspectral mixed pixels. According to the spatial prior knowledge, there are many regularizations designed to improve the performance of unmixing algorithms, such as the total variation (TV) regularization. However, these methods mostly ignore the similar characteristics among different spectral bands. To solve this problem, this paper proposes a group sparse regularization that uses the weighted constraint of the L2,1 norm, which can not only explore the similar characteristics of the hyperspectral image in the spectral dimension, but also keep the data smooth characteristics in the spatial dimension. In summary, a non-negative tensor factorization framework based on weighted group sparsity constraint is proposed for hyperspectral images. In addition, an effective alternating direction method of multipliers (ADMM) algorithm is used to solve the algorithm proposed in this paper. Compared with the existing popular methods, experiments conducted on three real datasets fully demonstrate the effectiveness and advancement of the proposed method.

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Yan, Fei, Siyuan Wu, Qiong Zhang, Yunqing Liu, and Haonan Sun. "Destriping of Remote Sensing Images by an Optimized Variational Model." Sensors 23, no. 17 (August 30, 2023): 7529. http://dx.doi.org/10.3390/s23177529.

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Satellite sensors often capture remote sensing images that contain various types of stripe noise. The presence of these stripes significantly reduces the quality of the remote images and severely affects their subsequent applications in other fields. Despite the existence of many stripe noise removal methods in the research, they often result in the loss of fine details during the destriping process, and some methods even generate artifacts. In this paper, we proposed a new unidirectional variational model to remove horizontal stripe noise. The proposed model fully considered the directional characteristics and structural sparsity of the stripe noise, as well as the prior features of the underlying image, to design different sparse constraints, and the ℓp quasinorm was introduced in these constraints to better describe these sparse characteristics, thus achieving a more excellent destriping effect. Moreover, we employed the fast alternating direction method of multipliers (ADMM) to solve the proposed non-convex model. This significantly improved the efficiency and robustness of the proposed method. The qualitative and quantitative results from simulated and real data experiments confirm that our method outperforms existing destriping approaches in terms of stripe noise removal and preservation of image details.

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Lam, Xin-Yee, Defeng Sun, and Kim-Chuan Toh. "Semi-proximal Augmented Lagrangian-Based Decomposition Methods for Primal Block-Angular Convex Composite Quadratic Conic Programming Problems." INFORMS Journal on Optimization 3, no. 3 (July 2021): 254–77. http://dx.doi.org/10.1287/ijoo.2019.0048.

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We first propose a semi-proximal augmented Lagrangian-based decomposition method to directly solve the primal form of a convex composite quadratic conic-programming problem with a primal block-angular structure. Using our algorithmic framework, we are able to naturally derive several well-known augmented Lagrangian-based decomposition methods for stochastic programming, such as the diagonal quadratic approximation method of Mulvey and Ruszczyński. Although it is natural to develop an augmented Lagrangian decomposition algorithm based on the primal problem, here, we demonstrate that it is, in fact, numerically more economical to solve the dual problem by an appropriately designed decomposition algorithm. In particular, we propose a semi-proximal symmetric Gauss–Seidel-based alternating direction method of multipliers (sGS-ADMM) for solving the corresponding dual problem. Numerical results show that our dual-based sGS-ADMM algorithm can very efficiently solve some very large instances of primal block-angular convex quadratic-programming problems. For example, one instance with more than 300,000 linear constraints and 12.5 million nonnegative variables is solved to the accuracy of 10-5 in the relative KKT residual in less than a minute on a modest desktop computer.

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LU, Lixuan, and Tao ZHANG. "Non-Blind Image Deblurring Method Using Shear High Order Total Variation Norm." Wuhan University Journal of Natural Sciences 26, no. 6 (December 2021): 495–506. http://dx.doi.org/10.1051/wujns/2021266495.

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In this paper, we propose a shear high-order gradient (SHOG) operator by combining the shear operator and high-order gradient (HOG) operator. Compared with the HOG operator, the proposed SHOG operator can incorporate more directionality and detect more abundant edge information. Based on the SHOG operator, we extend the total variation (TV) norm to shear high-order total variation (SHOTV), and then propose a SHOTV deblurring model. We also study some properties of the SHOG operator, and show that the SHOG matrices are Block Circulant with Circulant Blocks (BCCB) when the shear angle is [see formula in PDF]. The proposed model is solved efficiently by the alternating direction method of multipliers (ADMM). Experimental results demonstrate that the proposed method outperforms some state-of-the-art non-blind deblurring methods in both objective and perceptual quality.

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Tong, Guowei, Shi Liu, and Sha Liu. "Computationally efficient image reconstruction algorithm for electrical capacitance tomography." Transactions of the Institute of Measurement and Control 41, no. 3 (May 9, 2018): 631–46. http://dx.doi.org/10.1177/0142331218763013.

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The electrical capacitance tomography (ECT) is a visualization measurement method and can reconstruct the spatial permittivity distribution information in a measurement domain based on given capacitance values, in which the effectiveness of the image reconstruction algorithm plays a vital role in real-world engineering applications. Unlike common imaging methods, within the framework of the Tikhonov regularization methodology and the transform-domain sparsity method, a new cost function encapsulating the wavelet-based sparsity constraint is proposed to model the ECT imaging problem. An iteration scheme that integrates the superiorities of the alternating direction method of multipliers algorithm and splits a complicated optimization problem into several simpler sub-problems is developed to seek for the optimal solution of the proposed cost function. Numerical experiments validate that the proposed imaging algorithm is practicable and effective, and can improve the reconstruction accuracy and robustness.

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Journal articles on the topic 'Alternating direction methods of multipliers'

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