Enhanced Collaborative Optimization Using Alternating Direction Method of Multipliers

Enhanced collaborative optimization (ECO) is a recently developed multidisciplinary design optimization (MDO) method in the family of collaborative optimization (CO). While ECO achieves better optimization performance than its predecessors, its formulation is much more complex and incurs higher computation and communication costs, mainly due to the use of linear models of nonlocal constraints (LMNC). Consequently, ECO is often not the most desirable MDO method for large-scale and/or highly coupled applications. In this paper, we propose a new method named “ECO-ADMM” by introducing the alternating direction method of multipliers (ADMM) to ECO. With the aid of Lagrangian multipliers, ECO-ADMM increases each discipline’s “awareness” of global constraint conditions and search history at a negligible cost of Lagrangian multipliers updating. We also propose a simplified version of ECO-ADMM which removes LMNC from the original ECO-ADMM. With case studies of two analytic test problems and an industrial vehicle suspension design problem, two main advantages of ECO-ADMM over ECO are observed. First, ECO-ADMM achieves faster convergence and better solutions than ECO in most cases where both methods have comparable settings. Second, in the cases where LMNC are removed, ECO-ADMM maintains a much higher level of optimization performance than ECO. Therefore, ECO-ADMM is expected to outperform ECO in most application scenarios, and its simplified version provides designers with the option of trading a reasonable level of performance for ease of implementation and lower computation and communication costs.     

Linearized Proximal Alternating Direction Method of Multipliers for Parallel Magnetic Resonance Imaging

In this study, we propose a linearized proximal alternating direction method with variable stepsize for solving total variation image reconstruction problems. Our method uses a linearized technique and the proximal function such that the closed form solutions of the subproblem can be easily derived. In the subproblem, we apply a variable stepsize, that is like Barzilai-Borwein stepsize, to accelerate the algorithm. Numerical results with parallel magnetic resonance imaging demonstrate the efficiency of the proposed algorithm.      

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.      

正则化超限学习机的多分块松弛交替方向乘子法

针对超限学习机在大数据环境下计算负担过重的问题,文中提出正则化超限学习机的多分块松弛交替方向乘子法及N-等分和N/2-等分情形的标量化实现.模型分块使算法具有高度的并行结构,与松弛技术结合提高算法的收敛速度.通过分析,建立算法收敛的充要条件,给出最优收敛率及最优参数.在基准数据集上仿真计算收敛率随分块数的变化关系,对比不同算法的收敛速率和GPU加速比.实验表明,文中算法具有较低的计算复杂度和较高的并行性.     

一种基于参考扫描的MRI相位伪影校正方法

基于参考扫描原理提出了一种MRI（Magnetic resonance imaging）相位伪影]1影的软件校正方法,首先进行一次不加频率编码梯度和相位编码梯度的参考扫描,将获得的回波链数据沿频率编码方向做傅里叶变换后求出各回波间的相位误差,由此建立相位误差补偿矩阵,对K空间数据进行校正,最后重建得到伪影校正后的图像。实验结果证明,该方法能有效消除MRI图像中的相位伪影,明显提高图像质量。     

DCNN深度特征与交替方向乘子的相关滤波跟踪

针对采用相关滤波的判别式目标跟踪遇到的瓶颈问题：由于目标快速移动引起边界效应，使得相关滤波器在学习与更新过程中可能会引入错误，最终错误的累积将导致跟踪失败。在采集深度学习特征与样本相似性度量的基础上，提出一种引入交替方向乘子方法的改进相关滤波目标跟踪算法，选择DCNN深度特征有效地表征待跟踪目标的初始状态，通过在线分类过程中样本相似性比对与半监督学习，辅助解决相关滤波器在学习过程中存在的自学习问题。所提目标跟踪算法特别适合训练样本为持续获得的、同时存储空间较小的机器学习过程，提高目标在快速运动与部分遮挡等复杂情况下的跟踪成功率，针对VOT2016标准测试视频的实验表明：当目标面临快速运动时，对比CN、SAMF、STC算法，所提DA-CFT跟踪算法将跟踪成功率分别由60.4%～73.4%、67.2%～82.9%、80.9%～88.1%提升至85.6%～91.0%。     

Improving Medical CT Image Blind Restoration Algorithm Based on Dictionary Learning by Alternating Direction Method of Multipliers

In this paper, the medical CT image blind restoration is translated into two sub problems, namely, image estimation based on dictionary learning and point spread function estimation. A blind restoration algorithm optimized by the alternating direction method of multipliers for medical CT images was proposed. At present, the existing methods of blind image restoration based on dictionary learning have the problem of low efficiency and precision. This paper aims to improve the effectiveness and accuracy of the algorithm and to improve the robustness of the algorithm. The local CT images are selected as training samples, and the K-SVD algorithm is used to construct the dictionary by iterative optimization, which is beneficial to improve the efficiency of the algorithm. Then, the orthogonal matching pursuit algorithm is employed to implement the dictionary update. Dictionary learning is accomplished by sparse representation of medical CT images. The alternating direction method of multipliers (ADMM) is used to solve the objective function and realize the local image restoration, so as to eliminate the influence of point spread function. Secondly, the local restoration image is used to estimate the point spread function, and the convex quadratic optimization method is used to solve the point spread function sub problems. Finally, the optimal estimation of point spread function is obtained by iterative method, and the global sharp image is obtained by the alternating direction method of multipliers. Experimental results show that, compared with the traditional adaptive dictionary restoration algorithm, the new algorithm improves the objective image quality metrics, such as peak signal to noise ratio, structural similarity, and universal image quality index. The new algorithm optimizes the restoration effect, improves the robustness of noise immunity and improves the computing efficiency.     

MR图像运动伪影的遗传算法校正

磁共振成像过程中,由于患者的生理运动或自主性运动会使扫描数据发生相位偏移,致使重建图像含有运动伪影,从而降低成像的质量,而且严重的伪影则会影响医生对病灶的精确定位。为了能有效地抑制运动伪影,利用遗传算法高度并行、随机和自适应全局寻优的特点,提出了基于遗传算法的运动伪影修正方法,即采用逐次修正扫描信号在K空间中已偏移的相位的方法来抑制伪影。基于遗传算法的修正方法,由于能有效校正扫描数据的相位偏移,因而可达到抑制运动伪影的目的。实验表明,该方法对由较小运动引起的伪影有很好的抑制作用,对含噪声及较大运动引起的伪影的抑制作用,与经典的迭代算法相比,也有很大地改善。     

The Unified Frame of Alternating Direction Method of Multipliers for Three Classes of Matrix Equations Arising in Control Theory

In this paper, the unified frame of alternating direction method of multipliers (ADMM) is proposed for solving three classes of matrix equations arising in control theory including the linear matrix equation, the generalized Sylvester matrix equation and the quadratic matrix equation. The convergence properties of ADMM and numerical results are presented. The numerical results show that ADMM tends to deliver higher quality solutions with less computing time on the tested problems.     

去除椒盐噪声的交替方向法

传统图像去噪法基于有用信息和噪声频率特性的差别实现去噪,实际中,有用信息和噪声在频带上往往存在重叠,因此,传统去噪法在抑制噪声的同时,往往损失了细节信息,使图像变模糊. 本文引入稀疏与低秩矩阵分解模型描述图像去噪问题,基于该模型,采用交替方向法（Alternating direction method,ADM）得到复原图像. 实验证明该方法比常用的中值滤波法更有效地抑制了椒盐噪声,同时更好地保持了原始图像的细节信息.     

Alternating Direction Method for Covariance Selection Models

The covariance selection problem captures many applications in various fields, and it has been well studied in the literature. Recently, an l ₁-norm penalized log-likelihood model has been developed for the covariance selection problem, and this novel model is capable of completing the model selection and parameter estimation simultaneously. With the rapidly increasing magnitude of data, it is urged to consider efficient numerical algorithms for large-scale cases of the l ₁-norm penalized log-likelihood model. For this purpose, this paper develops the alternating direction method (ADM). Some preliminary numerical results show that the ADM approach is very efficient for large-scale cases of the l ₁-norm penalized log-likelihood model.     

MRI快速序列的旋转伪影校正

磁共振扫描过程中病人的旋转运动会在图像上造成伪影,严重影响诊断效果,提出一种基于快速扫描的放置伪影校正算法以解决此问题,该算法首先提出K空间带状划分方法,通过放置数据带产生数据重叠;然后建立重叠区则化相似度判定准则,计算出旋转参数并校正数据带的位置信息;再根据K空间的厄米特区轭性质对校正后的不均匀数据补偿,并改进了Jackson网格化成像算法,使旋转伪影得抑制.实验结果表明,该算法可以有效地消除旋转伪影,且计算速度快、准确率高、受噪声影响小.     

Implementing the 3D Alternating Direction Method on the Hypercube

The paper considers computational domains structured as a 3D grid of cells. It presents a cell-to-hypercube map that is useful for implementing the alternating direction method. The map is shown to be perfectly load-balanced and to optimally preserve adjacencies between cells in the computational domain.     

基于重加权快速交替方向法的频谱感知

在认知无线电网络中,由于深衰落和低信噪比的影响,单个认知用户的宽带频谱检测性能较差,且算法复杂度较高。针对该问题,提出一种基于重加权快速交替方向法的频谱感知算法。利用目标函数的凸性,通过求导简化辅助变量的更新过程。对目标函数进行线性化处理,增加一个二次项,使待估变量更新时部分项线性化的增广拉格朗日函数成为严格凸函数,并使用迭代软阈值算法进行求解。在目标项中增加大权值抑制信号中的非零元素,获得接近于最小?0范数的解。实验结果表明,该算法能有效提高低信噪比环境下的检测概率和检测速度。     

稀疏子空间聚类的惩罚参数自调整交替方向法

稀疏子空间聚类是利用子空间并集中数据向量的稀疏表示,从而将数据划分到各自子空间,该类方法关键是求出最优稀疏解。文中采用交替方向法求稀疏解,交替方向法把复杂问题分解成简单的、有效求解的子问题,达到最优速度。在交替方向法求解过程中,通常惩罚因子是恒定不变的。文中提出一种惩罚因子参数自调整策略,根据每次迭代信息,调整惩罚因子参数。基于运动分割数据和Hopkins数据库实验,结果表明在迭代次数和运算时间上,稀疏子空间聚类的交替方向法及其惩罚参数自调整策略比传统算法有很大提高,而且对噪声数据也非常有效。     

改进的文档图像扭曲校正方法

由照相机拍摄的文档图像可能因扭曲变形导致OCR软件不能正确识别。为解决上述问题,采用图像分割技术进行单词及文本线检测,利用线性拟合得到单词的较低基线和较高基线,根据校正基线对单词进行旋转和垂直位移,得到校正后的图像。实验结果表明,该方法能快速有效地校正扭曲的文档图像,使校正后的图像在光学字符识别阶段的识别率有较大提高。     

基于递阶辨识与交替方向乘子法的深度图像增强

针对主流传感器采集的深度图像存在深度信息区域缺失、噪声等图像质量问题,提出一种基于SD全局优化模型的深度图像增强算法。采用非凸函数对SD全局优化模型平滑项进行建模,使其对异常值具有较强的鲁棒性。使用基于递阶辨识(HI)的交替方向乘子法求解SD全局优化模型,将目标函数分解成多个子目标函数,并对每个子目标函数通过HI思想进行逐个求解,降低求解复杂度。实验结果表明,该算法在加快收敛速度的同时,能有效去除图像噪声及抑制深度伪影。     

Multiplicative Denoising Based on Linearized Alternating Direction Method Using Discrepancy Function Constraint

The multiplicative noise (speckle) in coherent imaging systems such as synthetic aperture radar makes it difficult to interpret observed images. Recently, the total variation (TV) models have received much interest in removing the speckle due to the strong edge preserving ability and low computational cost of the TV regularizer. However, the classical methods have difficulties in two aspects: one is how to efficiently compute the solution of the models with special data-fidelity terms, the other is how to choose the regularization parameter since the variational models are rather sensitive to the parameter. In this paper, we propose a new linearized alternating direction method, which is able to handle the data-fidelity term efficiently, and meanwhile estimate the optimal value of the regularization parameter exactly based on a discrepancy function constraint. We further establish the global convergence of the proposed algorithm. Numerical experiments demonstrate that our methods overall outperform the current state-of-the-art methods for multiplicative noise removal.     

一种改进的多纹理方向空域错误隐藏算法

为了提高视频压缩码流传输过程中抗误码性能,提出一种改进的多纹理方向插值算法.该算法将丢失宏块多纹理区域自适应划分为若干子块,分别进行插值恢复;并结合一些现有算法的特点,对宏块不同纹理类型切换隐藏算法.实验结果表明,该算法不仅提高了方向插值的精确性,也避免了虚假边缘的产生,有效地提高了错误图像的掩盖效果.