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.

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.

An Efficient Smoothing and Thresholding Image Segmentation Framework with Weighted Anisotropic-Isotropic Total Variation

In this paper,we design an efficient,multi-stage image segmentation framework that incorporates a weighted difference of anisotropic and isotropic total variation(AITV).The segmentation framework generally consists of two stages:smoothing and thresholding,thus referred to as smoothing-and-thresholding(SaT).In the first stage,a smoothed image is obtained by an AITV-regularized Mumford-Shah(MS)model,which can be solved efficiently by the alternating direction method of multipliers(ADMMs)with a closed-form solution of a proximal operator of the l_(1)-αl_(2) regularizer.The convergence of the ADMM algorithm is analyzed.In the second stage,we threshold the smoothed image by K-means clustering to obtain the final segmentation result.Numerical experiments demonstrate that the proposed segmentation framework is versatile for both grayscale and color images,effcient in producing high-quality segmentation results within a few seconds,and robust to input images that are corrupted with noise,blur,or both.We compare the AITV method with its original convex TV and nonconvex TVP(O<p<1)counterparts,showcasing the qualitative and quantitative advantages of our proposed method.

Fully Distributed Learning for Deep Random Vector Functional-Link Networks

In the contemporary era, the proliferation of information technology has led to an unprecedented surge in data generation, with this data being dispersed across a multitude of mobile devices. Facing these situations and the training of deep learning model that needs great computing power support, the distributed algorithm that can carry out multi-party joint modeling has attracted everyone’s attention. The distributed training mode relieves the huge pressure of centralized model on computer computing power and communication. However, most distributed algorithms currently work in a master-slave mode, often including a central server for coordination, which to some extent will cause communication pressure, data leakage, privacy violations and other issues. To solve these problems, a decentralized fully distributed algorithm based on deep random weight neural network is proposed. The algorithm decomposes the original objective function into several sub-problems under consistency constraints, combines the decentralized average consensus (DAC) and alternating direction method of multipliers (ADMM), and achieves the goal of joint modeling and training through local calculation and communication of each node. Finally, we compare the proposed decentralized algorithm with several centralized deep neural networks with random weights, and experimental results demonstrate the effectiveness of the proposed algorithm.

Image reconstruction based on total-variation minimization and alternating direction method in linear scan computed tomography

Linear scan computed tomography （LCT） is of great benefit to online industrial scanning and security inspection due to its characteristics of straight-line source trajectory and high scanning speed. However, in practical applications of LCT, there are challenges to image reconstruction due to limited-angle and insufficient data. In this paper, a new reconstruction algorithm based on total-variation （TV） minimization is developed to reconstruct images from limited-angle and insufficient data in LCT. The main idea of our approach is to reformulate a TV problem as a linear equality constrained problem where the objective function is separable, and then minimize its augmented Lagrangian function by using alternating direction method （ADM） to solve subproblems. The proposed method is robust and efficient in the task of reconstruction by showing the convergence of ADM. The numerical simulations and real data reconstructions show that the proposed reconstruction method brings reasonable performance and outperforms some previous ones when applied to an LCT imaging problem.

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.

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.

Alternating Direction Finite Volume Element Methods for Three-Dimensional Parabolic Equations

This paper presents alternating direction finite volume element methods for three-dimensional parabolic partial differential equations and gives four computational schemes, one is analogous to Douglas finite difference scheme with second-order splitting error, the other two schemes have third-order splitting error, and the last one is an extended LOD scheme. The L2 norm and H1 semi-norm error estimates are obtained for the first scheme and second one, respectively. Finally, two numerical examples are provided to illustrate the efficiency and accuracy of the methods.

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.

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.

Axisymmetric alternating direction explicit scheme for efficient coupled simulation of hydro-mechanical interaction in geotechnical engineering-Application to circular footing and deep tunnel in saturated ground

Explicit solution techniques have been widely used in geotechnical engineering for simulating the coupled hydro-mechanical(H-M) interaction of fluid flow and deformation induced by structures built above and under saturated ground, i.e. circular footing and deep tunnel. However, the technique is only conditionally stable and requires small time steps, portending its inefficiency for simulating large-scale H-M problems. To improve its efficiency, the unconditionally stable alternating direction explicit(ADE)scheme could be used to solve the flow problem. The standard ADE scheme, however, is only moderately accurate and is restricted to uniform grids and plane strain flow conditions. This paper aims to remove these drawbacks by developing a novel high-order ADE scheme capable of solving flow problems in nonuniform grids and under axisymmetric conditions. The new scheme is derived by performing a fourthorder finite difference(FD) approximation to the spatial derivatives of the axisymmetric fluid-diffusion equation in a non-uniform grid configuration. The implicit Crank-Nicolson technique is then applied to the resulting approximation, and the subsequent equation is split into two alternating direction sweeps,giving rise to a new axisymmetric ADE scheme. The pore pressure solutions from the new scheme are then sequentially coupled with an existing geomechanical simulator in the computer code fast Lagrangian analysis of continua(FLAC). This coupling procedure is called the sequentially-explicit coupling technique based on the fourth-order axisymmetric ADE scheme or SEA-4-AXI. Application of SEA-4-AXI for solving axisymmetric consolidation of a circular footing and of advancing tunnel in deep saturated ground shows that SEA-4-AXI reduces computer runtime up to 42%-50% that of FLAC’s basic scheme without numerical instability. In addition, it produces high numerical accuracy of the H-M solutions with average percentage difference of only 0.5%-1.8%.

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.

Multichannel Blind CT Image Restoration via Variable Splitting and Alternating Direction Method

Computed tomography(CT) blurring caused by point spread function leads to errors in quantification and visualization. In this paper, multichannel blind CT image restoration is proposed to overcome the effect of point spread function. The main advantage from multichannel blind CT image restoration is to exploit the diversity and redundancy of information in different acquisitions. The proposed approach is based on a variable splitting to obtain an equivalent constrained optimization formulation, which is addressed with the alternating direction method of multipliers and simply implemented in the Fourier domain. Numerical experiments illustrate that our method obtains a higher average gain value of at least 1.21 d B in terms of Q metric than the other methods, and it requires only 7 iterations of alternating minimization to obtain a fast convergence.

An Alternating Direction Nonmonotone Approximate Newton Algorithm for Inverse Problems

In this paper, an alternating direction nonmonotone approximate Newton algorithm (ADNAN) based on nonmonotone line search is developed for solving inverse problems. It is shown that ADNAN converges to a solution of the inverse problems and numerical results provide the effectiveness of the proposed algorithm.

Research on infrared dim and small target detection algorithm based on low-rank tensor recovery

In order to rapidly and accurately detect infrared small and dim targets in the infrared image of complex scene collected by virtual prototyping of space-based downward-looking multiband detection,an improved detection algorithm of infrared small and dim target is proposed in this paper.Firstly,the original infrared images are changed into a new infrared patch tensor mode through data reconstruction.Then,the infrared small and dim target detection problems are converted to low-rank tensor recovery problems based on tensor nuclear norm in accordance with patch tensor characteristics,and inverse variance weighted entropy is defined for self-adaptive adjustment of sparseness.Finally,the low-rank tensor recovery problem with noise is solved by alternating the direction method to obtain the sparse target image,and the final small target is worked out by a simple partitioning algorithm.The test results in various spacebased downward-looking complex scenes show that such method can restrain complex background well by virtue of rapid arithmetic speed with high detection probability and low false alarm rate.It is a kind of infrared small and dim target detection method with good performance.

Two-level Bregmanized method for image interpolation with graph regularized sparse coding

A two-level Bregmanized method with graph regularized sparse coding （TBGSC） is presented for image interpolation. The outer-level Bregman iterative procedure enforces the observation data constraints, while the inner-level Bregmanized method devotes to dictionary updating and sparse represention of small overlapping image patches. The introduced constraint of graph regularized sparse coding can capture local image features effectively, and consequently enables accurate reconstruction from highly undersampled partial data. Furthermore, modified sparse coding and simple dictionary updating applied in the inner minimization make the proposed algorithm converge within a relatively small number of iterations. Experimental results demonstrate that the proposed algorithm can effectively reconstruct images and it outperforms the current state-of-the-art approaches in terms of visual comparisons and quantitative measures.

MEC和区块链赋能无人机辅助的物联网资源优化

针对物联网设备部署在较偏远地区而导致的传输链路易受损或传输覆盖范围有限等问题,在此场景中引入无人机和移动边缘计算(mobile edge computing, MEC)技术,有效改善物联网设备能源供给,优化计算资源,同时提升通信覆盖范围,减少不必要的网络开销.另外,区块链技术的引入保证了数据计算卸载与交互过程中的安全性和可靠性,实现了数据共享.因此,面向无人机辅助的物联网系统提出一种融合MEC和区块链的资源分配决策方法,以实现MEC系统和区块链系统性能的最佳权衡为目标,综合考虑频谱资源和计算资源的分配,构建问题模型,并采用基于交替方向乘子(alternating direction method of multipliers, ADMM)法的分布式优化算法求解该优化问题.仿真结果表明,所提优化框架可以有效减少MEC系统的总能耗和区块链系统的计算时延.同时,所提方法具有良好的收敛性能,系统稳定性得到充分保证.

Two-stage ADMM-based distributed optimal reactive power control method for wind farms considering wake effects

Since the connection of small-scale wind farms to distribution networks,power grid voltage stability has been reduced with increasing wind penetration in recent years,owing to the variable reactive power consumption of wind generators.In this study,a two-stage reactive power optimization method based on the alternating direction method of multipliers(ADMM)algorithm is proposed for achieving optimal reactive power dispatch in wind farm-integrated distribution systems.Unlike existing optimal reactive power control methods,the proposed method enables distributed reactive power flow optimization with a two-stage optimization structure.Furthermore,under the partition concept,the consensus protocol is not needed to solve the optimization problems.In this method,the influence of the wake effect of each wind turbine is also considered in the control design.Simulation results for a mid-voltage distribution system based on MATLAB verified the effectiveness of the proposed method.

Active User and Data Detection for Uplink Grant-free NOMA Systems

This paper proposes some low complexity algorithms for active user detection(AUD),channel estimation(CE)and multi-user detection(MUD)in uplink non-orthogonal multiple access(NOMA)systems,including single-carrier and multi-carrier cases.In particular,we first propose a novel algorithm to estimate the active users and the channels for single-carrier based on complex alternating direction method of multipliers(ADMM),where fast decaying feature of non-zero components in sparse signal is considered.More importantly,the reliable estimated information is used for AUD,and the unreliable information will be further handled based on estimated symbol energy and total accurate or approximate number of active users.Then,the proposed algorithm for AUD in single-carrier model can be extended to multi-carrier case by exploiting the block sparse structure.Besides,we propose a low complexity MUD detection algorithm based on alternating minimization to estimate the active users’data,which avoids the Hessian matrix inverse.The convergence and the complexity of proposed algorithms are analyzed and discussed finally.Simulation results show that the proposed algorithms have better performance in terms of AUD,CE and MUD.Moreover,we can detect active users perfectly for multi-carrier NOMA system.