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.

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。

基于同步ADMM算法含P2G-CCS的多园区综合能源系统优化调度

多园区综合能源微电网系统交互需要解决每个微电网之间的协调优化调度的问题,文中通过引入交互耦合功率变量解耦的方法,来求解园区内微电网之间交互的电功率,将集中求解的复杂问题转换为各微电网之间相互合作而且可以内部管理的优化问题,于是文中考虑采用同步式交替向乘子法(alternating direction method of multipliers,ADMM)分布式求解方法来实现各个园区微电网系统的成本关系分配,系统只需要求解分布式优化方案所需的信息,可以最大限度地降低运行成本,同时为了保证多园区微电网系统的低碳运行和降低环境成本,在考虑单个电热冷综合能源微电网系统的基础上,采用碳捕集设备和电转气装置以及配合阶梯碳交易机制的方法,更进一步降低系统碳排放;最后,通过仿真算例来验证所提方法和模型的有效性。

基于改进ADMM的含分布式光伏的配电网电压无功优化方法

由于所建立含分布式光伏(PV)的有源配电网电压无功优化模型是一个典型的非凸混合整数非线性优化模型,提出一种改进交替方向乘子法(ADMM)来求解含分布式光伏的配电网电压无功优化问题。首先以有载调压变压器和投切电容器组为例,建立一种新的广义可分解有源配电网电压无功优化模型,然后根据ADMM算法将有源配电网电压无功优化模型分解为2个子问题求解,并设计惩罚参数的自适应调节机制以加速收敛。在3个不同规模有源配电网算例上进行仿真测试,结果表明,所提出改进ADMM方法具有较好的收敛性和最优解。

非凸多分块优化的Bregman ADMM的收敛率研究

Wang等提出了求解带线性约束的多块可分非凸优化问题的带Bregman距离的交替方向乘子法(Bregman ADMM),并证明了其收敛性.该文将进一步研究求解带线性约束的多块可分非凸优化问题的Bregman ADMM的收敛率,以及算法产生的迭代点列有界的充分条件.在效益函数的Kurdyka-Lojasiewicz (KL)性质下,该文建立了值和迭代的收敛速率,证明了与目标函数相关的各种KL指数值可获得Bregman ADMM的三种不同收敛速度.更确切地说,该文证明了如下结果:如果效益函数的KL指数θ=0,那么由Bregman ADMM生成的序列经过有限次迭代后收敛;如果θ∈(0,1/2),那么Bregman ADMM是线性收敛的;如果θ∈(1/2,1),那么Bregman ADMM是次线性收敛的.

基于ADMM的SAR多运动目标成像方法

为提高合成孔径雷达(SAR)多运动目标同时聚焦性能和成像效率,利用多运动目标信号的多分量线性调频信号形式和稀疏先验知识,提出基于交替方向乘子法(ADMM)的SAR多运动目标成像方法。通过建立SAR多运动目标稀疏观测模型,将多运动目标成像问题建模为稀疏特征约束下的逆问题求解。基于自适应Chirplet分解方法对目标多普勒调频率进行估计,从而实现观测矩阵设计。为获得较高的动态响应范围和较低的旁瓣响应,采用ADMM对多运动目标进行稀疏重构,ADMM将复杂的凸优化问题分解为多个交替寻找最优解的子优化问题,从而实现多运动目标图像精确且高效重构。最后通过仿真实验和机载SAR实测数据验证所提算法在聚焦成像质量和工作效率方面优于其他成像方法。

基于ADMM的完全去中心化P2P能源交易机制

为研究完全去中心化的点对点(peer-to-peer,P2P)能源市场中产消者的最优清算问题,重点解决产消者内部的协作和在P2P市场中实现社会福利最大化的挑战,采用了一种新的平行、分布式的交替方向乘子法(alternating direction method of multipliers,ADMM),推导出P2P市场的交易机制。该方法考虑每个产消者的效用函数,并引入分布式发电机(distributed generator,DG)和电能存储系统(battery energy storage system,BESS)。算法中每个产消者通过迭代与其相邻的产消者同步交换少量信息,并优化以满足不同的需求。通过对6-peers系统的数值验证,证明了所提出方法的有效性。与基于池的交易机制相比,完全去中心化的P2P问题在单位时间内交易电量提升了160%,社会福利从-9.47元增加到32.43元。

基于同步型ADMM的含海上风电场电力系统分布鲁棒无功优化

大规模海上风电的出力具有很强的随机性和波动性,增大了电力系统无功电压控制的难度。为此,首先基于Kullback-Leibler散度衡量海上风电场风速的真实概率分布与参考概率分布间的距离,构建风速概率分布模糊集。然后,同时考虑输电网和海上风电场的运行约束,建立含海上风电场电力系统的分布鲁棒无功优化模型。为了在计算过程中保持输电网与海上风电场信息的私秘性,基于同步型的交替方向乘子法对输电网和海上风电场区域进行空间解耦,将原集中式优化模型分解为各区域对应的子模型并进行分布式迭代求解。其中,各区域的子模型为多层模型,通过在分布式算法中嵌入列与约束生成算法来迭代求解。最后,在含2个海上风电场的IEEE 39节点系统上进行算例分析。结果表明,所建立模型的决策结果能够在考虑海上风速不确定性的前提下,有效降低系统网损和电压偏差。

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.

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.

基于IR-ADMM组合技术对地震随机噪声的压制

稀疏表示是一种现行有效的随机噪声压制方法,常采用交替方向乘子法逐道分解地震信号,但实际应用中交替方向乘子法计算效率高但精度不足,难以满足高保真地震数据处理的要求。通过结合迭代重加权和交替方向乘子法2种算法,提出了一种新的基于迭代重加权交替方向乘子法的联合稀疏表示方法,兼具收敛速度快和重建精度高的优点。共偏移距道集地震数据具有水平同相轴结构,满足共稀疏性条件,将联合稀疏表示算法应用于共偏移距道集就能够利用信号的空间相干性,提高去噪算法性能。理论和实际资料试算结果表明,所提算法具有较好的应用效果。

基于低秩ADMM的超声图像复原方法

本文提出了一个超声图像复原模型,该模型融合了加权核范数最小化和数据保真度。加权核范数最小化能够自适应处理奇异值以保留图像细节,数据保真度则增强了图像复原效果。本研究采用交替方向乘子法(Alternating Direction Method of Multipliers,ADMM)高效求解,并通过实验结果验证了该方法的优越性。

Lowering the Error Floor of ADMM Penalized Decoder for LDPC Codes

Decoding by alternating direction method of multipliers(ADMM) is a promising linear programming decoder for low-density parity-check(LDPC) codes. In this paper, we propose a two-step scheme to lower the error floor of LDPC codes with ADMM penalized decoder.For the undetected errors that cannot be avoided at the decoder side, we modify the code structure slightly to eliminate low-weight code words. For the detected errors induced by small error-prone structures, we propose a post-processing method for the ADMM penalized decoder. Simulation results show that the error floor can be reduced significantly over three illustrated LDPC codes by the proposed two-step scheme.

基于自适应步长ADMM的柔性配电网光-储协同分布鲁棒优化配置

针对柔性配电网的显著分区特征以及光伏出力的不确定特性,提出了一种区域间分布式优化及区域内两阶段优化方法,建立了基于自适应步长交替方向乘子法的光-储协同分布鲁棒优化配置模型。基于耦合支路法将柔性互联装置解耦,通过一致性约束协调各区域间的边界条件,利用自适应步长交替方向乘子法进行全局迭代分布式优化。以最小化柔性配电网的投资运行总成本为优化目标,建立基于数据驱动的各子区域两阶段分布鲁棒优化模型,并提出一种交直流混合凸松弛方法处理非线性非凸模型以便快速求解。基于改进相对熵构建光伏典型出力场景的不确定概率分布模糊集,通过列与约束生成算法求解两阶段分布鲁棒优化模型。以改进的某实际293节点柔性配电网为算例验证所建模型的有效性。

联合协方差矩阵重构和ADMM的鲁棒波束形成

为解决传统波束形成器在干扰位置发生扰动和导向矢量失配时,造成自适应权重的不匹配,从而导致算法性能急剧下降,甚至期望信号相消的问题,提出一种联合协方差矩阵重构和交替方向乘子法(Alternating direction method of multipliers,ADMM)的鲁棒波束形成方法。对此,首先基于波束形成器最大输出功率准则,设计了求解最优导向矢量的优化模型。接着,根据Capon算法空间功率谱函数,利用定义的干扰范围对协方差矩阵进行重构,以展宽零陷并增强系统抗运动干扰能力。最后,关于导向矢量的二次不等式约束问题,本质为估计导向矢量和期望导向矢量间的差异,该方法利用ADMM对该二次规划问题进行迭代求解,并在每次迭代中获得导向矢量的具体解。另外,也分析了算法的复杂度。实验结果表明:对比现有的波束形成算法,在干扰处加宽了零陷,提高了波束的抗干扰性;结合复杂度也证明了其计算速度优于现有的算法,并且能够很好地校正失配导向矢量。本方法也为求解二次不等式约束问题和提高波束形成算法性能提供了一种思路和途径。

基于ADMM算法的机载太赫兹SAR成像高频振动补偿

太赫兹波具有频率高、波长短的特点,因此相对于传统的工作在微波波段的合成孔径雷达(Synthetic Aperture Radar,SAR),太赫兹SAR具有高成像分辨率,并在视频SAR、慢动目标检测等方面具有显著的优势。但与此同时,太赫兹SAR也对雷达平台的高频振动非常敏感。对于机载太赫兹SAR,由于气流和载机自身飞行特性的影响,载机存在高频振动,会造成回波信号的相位误差,并使成像结果出现鬼影目标和散焦现象,严重恶化成像质量。为了实现聚焦成像,需要对机载太赫兹SAR的进行高频振动补偿。不同于现有的将高频振动建模为多个简谐运动之和形式的算法,本文提出了一种基于交替方向乘子法(Alternating Direction Method of Multipliers,ADMM)的高频误差补偿方法,无须对高频振动进行建模,可以补偿更复杂的高频振动相位误差。首先通过对接收到的回波信号使用方位向快速傅里叶变换(Fast Fourier Transform,FFT)得到粗聚焦的图像,然后将振动补偿问题转化为图像的l1范数最小化问题,引入辅助变量构造目标函数并使用ADMM算法求解。在ADMM算法迭代过程的每次循环中,利用图像熵最小化准则对相位误差进行更新。最后利用估计得到的相位误差构造相位补偿信号,用于补偿太赫兹SAR回波信号的相位误差。对点目标和分布式场景的仿真实验结果验证了该方法的有效性,且在低信噪比条件下也能获得聚焦良好的图像。