Fast alternating direction method of multipliers for total-variation-based image restoration

A novel algorithm, i.e. the fast alternating direction method of multipliers （ADMM）, is applied to solve the classical total-variation （ TV ）-based model for image reconstruction. First, the TV-based model is reformulated as a linear equality constrained problem where the objective function is separable. Then, by introducing the augmented Lagrangian function, the two variables are alternatively minimized by the Gauss-Seidel idea. Finally, the dual variable is updated. Because the approach makes full use of the special structure of the problem and decomposes the original problem into several low-dimensional sub-problems, the per iteration computational complexity of the approach is dominated by two fast Fourier transforms. Elementary experimental results indicate that the proposed approach is more stable and efficient compared with some state-of-the-art algorithms.

Reconstruction of electrical capacitance tomography images based on fast linearized alternating direction method of multipliers for two-phase flow system

Electrical capacitance tomography(ECT)has been applied to two-phase flow measurement in recent years.Image reconstruction algorithms play an important role in the successful applications of ECT.To solve the ill-posed and nonlinear inverse problem of ECT image reconstruction,a new ECT image reconstruction method based on fast linearized alternating direction method of multipliers(FLADMM)is proposed in this paper.On the basis of theoretical analysis of compressed sensing(CS),the data acquisition of ECT is regarded as a linear measurement process of permittivity distribution signal of pipe section.A new measurement matrix is designed and L1 regularization method is used to convert ECT inverse problem to a convex relaxation problem which contains prior knowledge.A new fast alternating direction method of multipliers which contained linearized idea is employed to minimize the objective function.Simulation data and experimental results indicate that compared with other methods,the quality and speed of reconstructed images are markedly improved.Also,the dynamic experimental results indicate that the proposed algorithm can ful fill the real-time requirement of ECT systems in the application.

Nested Alternating Direction Method of Multipliers to Low-Rank and Sparse-Column Matrices Recovery

The task of dividing corrupted-data into their respective subspaces can be well illustrated,both theoretically and numerically,by recovering low-rank and sparse-column components of a given matrix.Generally,it can be characterized as a matrix and a 2,1-norm involved convex minimization problem.However,solving the resulting problem is full of challenges due to the non-smoothness of the objective function.One of the earliest solvers is an 3-block alternating direction method of multipliers(ADMM)which updates each variable in a Gauss-Seidel manner.In this paper,we present three variants of ADMM for the 3-block separable minimization problem.More preciously,whenever one variable is derived,the resulting problems can be regarded as a convex minimization with 2 blocks,and can be solved immediately using the standard ADMM.If the inner iteration loops only once,the iterative scheme reduces to the ADMM with updates in a Gauss-Seidel manner.If the solution from the inner iteration is assumed to be exact,the convergence can be deduced easily in the literature.The performance comparisons with a couple of recently designed solvers illustrate that the proposed methods are effective and competitive.

Distributed MPC for Reconfigurable Architecture Systems via Alternating Direction Method of Multipliers

This paper investigates the distributed model predictive control(MPC)problem of linear systems where the network topology is changeable by the way of inserting new subsystems,disconnecting existing subsystems,or merely modifying the couplings between different subsystems.To equip live systems with a quick response ability when modifying network topology,while keeping a satisfactory dynamic performance,a novel reconfiguration control scheme based on the alternating direction method of multipliers(ADMM)is presented.In this scheme,the local controllers directly influenced by the structure realignment are redesigned in the reconfiguration control.Meanwhile,by employing the powerful ADMM algorithm,the iterative formulas for solving the reconfigured optimization problem are obtained,which significantly accelerate the computation speed and ensure a timely output of the reconfigured optimal control response.Ultimately,the presented reconfiguration scheme is applied to the level control of a benchmark four-tank plant to illustrate its effectiveness and main characteristics.

Distributed Alternating Direction Method of Multipliers for Multi-Objective Optimization

In this paper, a distributed algorithm is proposed to solve a kind of multi-objective optimization problem based on the alternating direction method of multipliers. Compared with the centralized algorithms, this algorithm does not need a central node. Therefore, it has the characteristics of low communication burden and high privacy. In addition, numerical experiments are provided to validate the effectiveness of the proposed algorithm.

Application of Linearized Alternating Direction Multiplier Method in Dictionary Learning

The Alternating Direction Multiplier Method (ADMM) is widely used in various fields, and different variables are customized in the literature for different application scenarios [1] [2] [3] [4]. Among them, the linearized alternating direction multiplier method (LADMM) has received extensive attention because of its effectiveness and ease of implementation. This paper mainly discusses the application of ADMM in dictionary learning (non-convex problem). Many numerical experiments show that to achieve higher convergence accuracy, the convergence speed of ADMM is slower, especially near the optimal solution. Therefore, we introduce the linearized alternating direction multiplier method (LADMM) to accelerate the convergence speed of ADMM. Specifically, the problem is solved by linearizing the quadratic term of the subproblem, and the convergence of the algorithm is proved. Finally, there is a brief summary of the full text.

Full-vectorial finite-difference beam propagation method based on the modified alternating direction implicit method

A modified alternating direction implicit algorithm is proposed to solve the full-vectorial finite-difference beam propagation method formulation based on H fields. The cross-coupling terms are neglected in the first sub-step, but evaluated and doubly used in the second sub-step. The order of two sub-steps is reversed for each transverse magnetic field component so that the cross-coupling terms are always expressed in implicit form, thus the calculation is very efficient and stable. Moreover, an improved six-point finite-difference scheme with high accuracy independent of specific structures of waveguide is also constructed to approximate the cross-coupling terms along the transverse directions. The imaginary-distance procedure is used to assess the validity and utility of the present method. The field patterns and the normalized propagation constants of the fundamental mode for a buried rectangular waveguide and a rib waveguide are presented. Solutions are in excellent agreement with the benchmark results from the modal transverse resonance method.

Impact Force Localization and Reconstruction via ADMM-based Sparse Regularization Method

In practice,simultaneous impact localization and time history reconstruction can hardly be achieved,due to the illposed and under-determined problems induced by the constrained and harsh measuring conditions.Although l_(1) regularization can be used to obtain sparse solutions,it tends to underestimate solution amplitudes as a biased estimator.To address this issue,a novel impact force identification method with l_(p) regularization is proposed in this paper,using the alternating direction method of multipliers(ADMM).By decomposing the complex primal problem into sub-problems solvable in parallel via proximal operators,ADMM can address the challenge effectively.To mitigate the sensitivity to regularization parameters,an adaptive regularization parameter is derived based on the K-sparsity strategy.Then,an ADMM-based sparse regularization method is developed,which is capable of handling l_(p) regularization with arbitrary p values using adaptively-updated parameters.The effectiveness and performance of the proposed method are validated on an aircraft skin-like composite structure.Additionally,an investigation into the optimal p value for achieving high-accuracy solutions via l_(p) regularization is conducted.It turns out that l_(0.6)regularization consistently yields sparser and more accurate solutions for impact force identification compared to the classic l_(1) regularization method.The impact force identification method proposed in this paper can simultaneously reconstruct impact time history with high accuracy and accurately localize the impact using an under-determined sensor configuration.

Stochastic Accelerated Alternating Direction Method of Multipliers for Hedging Communication Noise in Combined Heat and Power Dispatch

Combined heat and power dispatch(CHPD)opens a new window for increasing operational flexibility and reducing wind power curtailment.Electric power and district heating systems are independently controlled by different system operators;therefore,a decentralized solution paradigm is necessary for CHPD,in which only minor boundary information is required to be exchanged via a communication network.However,a nonideal communication environment with noise could lead to divergence or incorrect solutions of decentralized algorithms.To bridge this gap,this paper proposes a stochastic accelerated alternating direction method of multipliers(SA-ADMM)for hedging communication noise in CHPD.This algorithm provides a general framework to address more types of constraint sets and separable objective functions than the existing stochastic ADMM.Different from the single noise sources considered in the existing stochastic approximation methods,communication noise from multiple sources is addressed in both the local calculation and the variable update stages.Case studies of two test systems validate the effectiveness and robustness of the proposed SAADMM.

A New Stopping Criterion for Eckstein and Bertsekas’s Generalized Alternating Direction Method of Multipliers

In this paper,we propose a new stopping criterion for Eckstein and Bertsekas’s generalized alternating direction method of multipliers.The stopping criterion is easy to verify,and the computational cost is much less than the classical stopping criterion in the highly influential paper by Boyd et al.(Found Trends Mach Learn 3(1):1–122,2011).

A Bregman-style Partially Symmetric Alternating Direction Method of Multipliers for Nonconvex Multi-block Optimization

The alternating direction method of multipliers(ADMM)is one of the most successful and powerful methods for separable minimization optimization.Based on the idea of symmetric ADMM in two-block optimization,we add an updating formula for the Lagrange multiplier without restricting its position for multiblock one.Then,combining with the Bregman distance,in this work,a Bregman-style partially symmetric ADMM is presented for nonconvex multi-block optimization with linear constraints,and the Lagrange multiplier is updated twice with different relaxation factors in the iteration scheme.Under the suitable conditions,the global convergence,strong convergence and convergence rate of the presented method are analyzed and obtained.Finally,some preliminary numerical results are reported to support the correctness of the theoretical assertions,and these show that the presented method is numerically effective.

A Symmetric Linearized Alternating Direction Method of Multipliers for a Class of Stochastic Optimization Problems

Alternating direction method of multipliers(ADMM)receives much attention in the recent years due to various demands from machine learning and big data related optimization.In 2013,Ouyang et al.extend the ADMM to the stochastic setting for solving some stochastic optimization problems,inspired by the structural risk minimization principle.In this paper,we consider a stochastic variant of symmetric ADMM,named symmetric stochastic linearized ADMM(SSL-ADMM).In particular,using the framework of variational inequality,we analyze the convergence properties of SSL-ADMM.Moreover,we show that,with high probability,SSL-ADMM has O((ln N)·N^(-1/2))constraint violation bound and objective error bound for convex problems,and has O((ln N)^(2)·N^(-1))constraint violation bound and objective error bound for strongly convex problems,where N is the iteration number.Symmetric ADMM can improve the algorithmic performance compared to classical ADMM,numerical experiments for statistical machine learning show that such an improvement is also present in the stochastic setting.

面向光伏集群的配电网模型⁃数据联合驱动无功/电压控制

传统配电网的无功/电压控制(VVC)方法,难以兼顾控制决策的全局最优性与实时响应能力,分布式光伏(DPV)的分散化、高比例并网导致该矛盾日益突出。结合模型优化的寻优能力与深度强化学习的在线决策效率,提出了面向光伏(PV)集群的配电网模型-数据联合驱动VVC策略。首先,考虑日前优化调度与日内实时控制的运行特征,结合DPV集群划分,构建了配电网分布式两阶段VVC框架;然后,以系统运行网损最低为目标,建立了配电网分布式日前VVC模型,并提出了基于Nesterov加速梯度的分布式求解算法;其次,以日前决策为输入量,建立了基于部分可观马尔可夫博弈的配电网实时VVC模型,并提出了基于迭代终止惩罚函数的改进多智能体深度确定性策略梯度算法;最后,基于MATLAB/PyCharm软件平台进行了算例分析,验证了所提方法的全局趋优性以及实时响应能力,提高了PV高比例接入配电网运行的经济性和安全性。

基于NSST与稀疏先验的遥感图像去模糊方法

针对遥感图像的模糊问题,设计一种基于非下采样剪切波变换与稀疏先验的图像复原算法.首先,利用遥感图像在非下采样剪切波分解下的高频图像的稀疏特性设置先验条件构造图像复原模型;其次,采用交替方向乘子法求解模型;再次,采用软阈值方法对高频图像进行约束处理,在低频图像进行导向滤波处理,以最大可能保留图像的细节信息;最后,将高频图像与低频图像进行重构,对重构后的图像采用卷积神经网络进行深度去噪,最终复原出清晰的图像.将该去模糊算法与H-PNP,GSR,L2TV算法进行实验对比.实验结果表明,该算法能有效去除遥感图像中的模糊和噪声,保留图像的边缘细节,客观评价指标均高于其他3种对比实验算法.

基于分数阶全变分和低秩正则化的彩色图像去模糊方法

针对现有的彩色图像去模糊过程中存在色彩失衡、阶梯效应和伪影等现象,提出了一种基于分数阶全变分和低秩正则的图像去模糊优化方法。首先,将传统的RGB彩色图像转换到YCbCr颜色空间,利用其亮度通道特征解决色彩失衡问题;其次,利用分数阶全变分的特征消除图像恢复任务中出现的阶梯效应,并且引入加权核范数低秩正则进一步抑制伪影及噪声;最后,利用交替方向乘子法设计出高效的求解方法,通过迭代优化得到纯净图像的最优估计。对彩色图像测试的实验结果表明,所提出的方法对图像去模糊任务取得较好的视觉恢复效果,客观评价指标良好。

基于复合正则化的稀疏SAR成像方法研究

随着高分辨率对地观测要求的不断提高,合成孔径雷达(Synthetic Aperture Radar,SAR)的应用将越来越广泛。针对高分辨率SAR成像存在数据量大、存储难度高、计算时间长等问题,目前常用的解决方法是在SAR成像模型中引入压缩感知(Compressed Sensing,CS)的方法降低采样率和数据量。通常使用单一的正则化作为约束条件,可以抑制点目标旁瓣,实现点目标特征增强,但是观测场景中可能存在多种目标类型,因此使用单一正则化约束难以满足多种特征增强的要求。本文提出了一种基于复合正则化的稀疏高分辨SAR成像方法,通过压缩感知降低数据量,并使用多种正则化的线性组合作为约束条件,增强观测场景中不同类型目标的特征,实现复杂场景中高分辨率对地观测的要求。该方法在稀疏SAR成像模型中引入非凸正则化和全变分(Total Variation,TV)正则化作为约束条件,减小稀疏重构误差、增强区域目标的特征,降低噪声对成像结果的影响,提高成像质量;采用改进的交替方向乘子法(Alternating Direction Method of Multipliers,ADMM)实现复合正则化约束的求解,减少计算时间、快速重构图像;使用方位距离解耦算子代替观测矩阵及其共轭转置,进一步降低计算复杂度。仿真和实测数据实验表明,本文所提算法可以对点目标和区域目标进行特征增强,减小计算复杂度,提高收敛性能,实现快速高分辨的图像重构。

考虑异步通信的配电-气网分布式有功-无功协同优化

配电-气网(EGDN)中新能源大量并网和燃气运输过程中管网压力变化均可能导致配电网的电压波动增大。文中提出一种考虑异步通信的EGDN有功-无功协同优化方法。首先,研究EGDN中各元件的有功-无功特性;其次,根据EGDN能量运输过程中无功需求特性,建立EGDN无功供需模型;然后,考虑EGDN无功平衡和网络运行约束,以最小化电网电压波动、网损和EGDN购电/气成本为目标,建立EGDN无功电压优化控制模型;最后,为保障EGDN中各能源主体信息的安全性与私密性,考虑配电网与配气网信息采集传输情况存在差异,可能存在通信延迟和信息丢包情况,采用异步交替方向乘子法对模型进行求解。通过对改进的IEEE 33节点系统和7节点配气网构成的EGDN系统进行仿真,结果表明,所提方法可有效缓解EGDN电压波动问题,减小网损并降低系统总运行成本。

求解不可分离非凸非光滑问题的线性惯性ADMM算法

针对目标函数中包含耦合函数H(x,y)的非凸非光滑极小化问题,提出了一种线性惯性交替乘子方向法(Linear Inertial Alternating Direction Method of Multipliers,LIADMM)。为了方便子问题的求解,对目标函数中的耦合函数H(x,y)进行线性化处理,并在x-子问题中引入惯性效应。在适当的假设条件下,建立了算法的全局收敛性;同时引入满足Kurdyka-Lojasiewicz不等式的辅助函数,验证了算法的强收敛性。通过两个数值实验表明,引入惯性效应的算法比没有惯性效应的算法收敛性能更好。

基于压缩感知的缺失机械振动信号重构新方法

针对工业机械设备实时监测中不可控因素导致的振动信号数据缺失问题,提出一种基于自适应二次临近项交替方向乘子算法(adaptive quadratic proximity-alternating direction method of multipliers, AQ-ADMM)的压缩感知缺失信号重构方法。AQ-ADMM算法在经典交替方向乘子算法算法迭代过程中添加二次临近项,且能够自适应选取惩罚参数。首先在数据中心建立信号参考数据库用于构造初始字典,然后将K-奇异值分解(K-singular value decomposition, K-SVD)字典学习算法和AQ-ADMM算法结合重构缺失信号。对仿真信号和两种真实轴承信号数据集添加高斯白噪声后作为样本,试验结果表明当信号压缩率在50%~70%时,所提方法性能指标明显优于其它传统方法,在重构信号的同时实现了对含缺失数据机械振动信号的快速精确修复。

基于自适应深度先验的高光谱图像超分辨率

为了解决现有的高光谱超分辨率方法依赖于手工先验和数据驱动先验会导致参数选择困难或可解释性差的问题,采用一种基于自适应深度先验正则的高光谱图像超分辨率方法,进行了理论分析和实验验证。首先设计基于卷积神经网络的多阶段特征提取网络,提取退化图像的空间和光谱信息;其次将提取到的空-谱先验输入基于transformer模型的特征融合模块;然后自适应交互空域和谱域的互补信息,以捕获图像的全局先验特征;最后在退化模型中插入深度先验正则项,将超分辨率问题表述为一个优化问题,其解可以通过交替方向乘子法获得并降低求解复杂度。结果表明,所提出算法在信噪比均为35 dB时,重建信噪比分别达到了34.16 dB和29.35 dB,比次优算法高出2.78 dB和2.17 dB,重建的高分辨率高光谱图像与其固有结构具有较高的一致性。该研究为综合利用手工先验和数据驱动先验增强高光谱图像空间分辨率提供了参考。