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To automatic detect and characterize paper impurities with computer vision, we present a novel two parts evaluation procedure with feature representations using Alternating Direction Method of Multipliers (ADMM) sparse codes. The method is based on an offline training step to obtain sparse coefficients and codebooks via learning extracted features with ADMM optimization, followed by an online detection step to use linear SVM classifier to assess defective paper samples from no-defective ones. Our approach bridges the gap between paper impurities evaluation and sparse feature representations, taking advantages of existing ADMM algorithms to handle sparse codes problem. We compare different feature descriptors and sparse code methods to implement the procedure and experimentally validate it on a dataset of 11 paper classes. Experiment results show that the proposed method is competitive and effective in terms of evaluation accuracy and speed. [ABSTRACT FROM AUTHOR]

In recent years, using the low-rank structure of the data to recover the matrix has become one of the hot issues in image processing. However, it usually leads to a suboptimal solution because current convex relaxations of the rank function (e.g., nuclear norm, etc.) reduce the rank components excessively and treat each rank component equally. To solve this problem, many nonconvex relaxations have been proposed, but their convergence properties are generally not easy to guarantee. In this paper, we construct a novel double nonconvex nonsmooth model by combining the truncated Schatten-p norm and the Schatten-p norm for the first time, called N-DNNR. It ignores the effect of large singular values on the matrix rank through the truncated Schatten-p norm and approximates the rank function by the Schatten-p norm. The alternating directional multiplier method (ADMM) is introduced to solve the N-DNNR model, which is more robust than other state-of-the-art algorithms and guarantees global convergence. In particular, updating the variable X is a nonconvex optimization problem, and we solve it by the approximate gradient algorithm (PG) and the weighted singular value threshold operator (WSVF), which has a closed-form solution. Finally, experimental results on synthetic data and real images show that the N-DNNR model has stronger generalization and recovery capabilities than the TSPN model. [ABSTRACT FROM AUTHOR]

The "dual carbon" goal has made it a mainstream trend for new energy stations (NESs) and energy storage stations (ESSs) to jointly participate in market regulation. This paper proposes a multiple time scale distributed optimization method for NESs and ESSs based on the alternate direction multiplier method (ADMM). By first considering the uncertainty of new energy output and the volatility of electricity market prices, a multi time scale revenue model is constructed for day-ahead, intraday, and real-time markets. Then, the objective function is built by maximizing the comprehensive market revenues and is simplified using the synergistic effect of NESs and ESSs. Next, the simplified objective function is solved by the ADMM, and the revenues are maximized while each energy meets the relevant constraints. Lastly, the 33-node network topology is used to illustrate the feasibility of the proposed method. The simulation results show that after optimization, the output of NESs and ESSs can coordinate work in day-ahead, intraday, and real-time markets, while the abandonment power of wind and light is significantly improved. [ABSTRACT FROM AUTHOR]

Image data often suffer from evident degradation like corruptions and missing values due to the defects of image acquisition equipment. Low-Rank Matrix Recovery (LRMR) is an effective technique to address this issue based on the low-rank prior of images. Moreover, smoothness is another prior widely existing in natural images, and thus there have been plenty of research focusing on simultaneously utilizing the two priors for improving the performance of image recovery. However, these studies either involve a hyper parameter to balance regularizers designed for both priors that is hard to be well tuned, or can not fully utilize both efficiently. In this paper, we propose the Modified Correlated Total Variation (MCTV) regularization that is a new regularizer used to simultaneously fully characterize both priors in a parameter free way. Subsequently, within the framework of two most studied LRMR tasks: Robust Principle Component Analysis (RPCA) and Matrix Completion (MC), we construct two models dubbed MCTV-RPCA and MCTV-MC. Besides, we also design optimization algorithms for both problems based on Alternating Direction Method of Multipliers (ADMM), which are further proven to have global convergence theories. Lots of experiments on applications to image denoising and inpainting reveal the superior performance of our approach over many state of the art competing ones. [ABSTRACT FROM AUTHOR]

This paper introduces a dynamic consensus-based economic dispatch (ED) algorithm utilizing the Alternating Direction Method of Multipliers (ADMM) to optimize real-time pricing and generation/demand decisions within a decentralized energy management framework. The increasing complexity of modern energy markets, driven by the proliferation of Distributed Energy Resources (DER) and variable demands from hybrid electric vehicles, necessitates a departure from traditional centralized dispatch methods. This research proposes a novel ADMM-based solution tailored for non-responsive and responsive demand units that integrates demand response mechanisms to adaptively manage real-time fluctuations while enhancing security and privacy through distributed data management. The testing of the algorithm on the IEEE 39 bus system under various load conditions over 24 h demonstrated the algorithm's effectiveness in handling traditional and renewable energy sources, particularly highlighting the economic benefits of shifting controllable loads to periods of low-cost renewable availability. The findings underscore the algorithm's potential to reduce energy costs, enhance energy efficiency, and offer a scalable solution across diverse grid systems, contributing significantly to advancing global energy policy and sustainable management practices. [ABSTRACT FROM AUTHOR]

This paper studies a statistical learning model where the model coefficients have a pre-determined non-overlapping group sparsity structure. We consider a combination of a loss function and a regularizer to recover the desired group sparsity patterns, which can embrace many existing works. We analyze directional stationary solutions of the proposed formulation, obtaining a sufficient condition for a directional stationary solution to achieve optimality and establishing a bound of the distance from the solution to a reference point. We develop an efficient algorithm that adopts an alternating direction method of multiplier (ADMM), showing that the iterates converge to a directional stationary solution under certain conditions. In the numerical experiment, we implement the algorithm for generalized linear models with convex and nonconvex group regularizers to evaluate the model performance on various data types, noise levels, and sparsity settings. [ABSTRACT FROM AUTHOR]

Recently, discriminative correlation filters (DCF) have been successfully applied for visual tracking. However, traditional DCF trackers tend to separately solve boundary effect and temporal degradation problems in the tracking process. In this paper, a variational online learning correlation filter (VOLCF) is proposed for visual tracking to improve the robustness and accuracy of the tracking process. Unlike previous methods, which use only first-order temporal constraints, this approach leads to overfitting and filter degradation. First, beyond the standard filter training requirement, our proposed VOLCF method introduces a model confidence term, which leverages the temporal information of adjacent frames during filter training. Second, to ensure the consistency of the temporal and spatial characteristics of the video sequence, the model introduces Kullback–Leibler (KL) divergence to obtain the second-order information of the filter. In contrast to traditional target tracking models that rely solely on first-order feature information, this approach facilitates the acquisition of a generalized connection between the previous and current filters. As a result, it incorporates joint-regulated filter updating. Through quantitative and qualitative analyses of the experiment, it proves that the VOLCF model has excellent tracking performance. [ABSTRACT FROM AUTHOR]

Sizing and configuring community-shared energy storage according to the actual demand of community users is important for the development of user-side energy storage. To solve this problem, this paper first proposes a community energy storage cooperative sharing mode containing multiple transaction types and then establishes a sizing and configuration model of community-shared energy storage based on a cooperative game among community users and energy storage operators, in which the loss caused by the capacity decay of energy storage is quantified by a dynamic power loss cost factor. To improve the solving efficiency, a distributed and cooperating solving method based on ADMM is used to solve the sizing and configuration model. On this basis, the bilateral Shapley method is used to allocate the total annual cost according to the marginal expected cost brought by each user. Compared with existing strategies, this paper calculates the economic benefits of community-shared energy storage based on several typical days of each year and quantifies the capacity decay of energy storage by a dynamic power loss cost factor which increases year by year to be closer to the real situation. Finally, the simulation verifies that the model proposed in this paper can be used for the sizing and configuration of community-shared energy storage. Compared with the original annual cost, the total annual cost of the community is reduced by 3.92%, and the annual operation cost of the community which equals annual electricity purchasing cost minus annual electricity selling income plus annual power loss cost is reduced by 25.6%. [ABSTRACT FROM AUTHOR]

Efficient and low-carbon energy utilization is a crucial aspect of promoting green and sustainable development. Multi-energy microgrids, which incorporate multiple interchangeable energy types, offer effective solutions for low-carbon and efficient energy consumption. This study aims to investigate the sharing of energy and carbon in multiple multi-energy microgrids (MMEMs) to enhance their economic impact, low-carbon attributes, and the efficient utilization of renewable energy. In this paper, an energy–carbon co-sharing operation model is established, incorporating carbon capture systems (CCSs) and two-stage power-to-gas (P2G) devices within the MMEMs to actualize low-carbon operation. Furthermore, based on cooperative game theory, this paper establishes an energy–carbon co-sharing Nash negotiation model and negotiates based on the energy–carbon contribution of each subject in the cooperation as bargaining power so as to maximize both the benefits of the MMEM alliance and the distribution of the cooperation benefits. The case study results show that the overall benefits of the alliance can be increased through Nash negotiation. Energy–carbon co-sharing can effectively increase the renewable energy consumption rate of 8.34%, 8.78%, and 8.83% for each multi-energy microgrid, and the overall carbon emission reduction rate reaches 17.81%. Meanwhile, the distribution of the benefits according to the energy–carbon co-sharing contribution capacity of each entity is fairer. [ABSTRACT FROM AUTHOR]

The distributed alternating direction method of multipliers (ADMM) is an effective algorithm for solving large-scale optimization problems. However, its high communication cost limits its scalability. An asynchronous lazy ADMM algorithm based on hierarchical sparse allreduce communication mode (HSAC-ALADMM) is proposed to reduce the communication cost of the distributed ADMM: firstly, this paper proposes a lazily aggregate parameters strategy to filter the transmission parameters of the distributed ADMM, which reduces the payload of the node per iteration. Secondly, a hierarchical sparse allreduce communication mode is tailored for sparse data to aggregate the filtered transmission parameters effectively. Finally, a Calculator-Communicator-Manager framework is designed to implement the proposed algorithm, which combines the asynchronous communication protocol and the allreduce communication mode effectively. It separates the calculation and communication by multithreading, thus improving the efficiency of system calculation and communication. Experimental results for the L1-regularized logistic regression problem with public datasets show that the HSAC-ALADMM algorithm is faster than existing asynchronous ADMM algorithms. Compared with existing sparse allreduce algorithms, the hierarchical sparse allreduce algorithm proposed in this paper makes better use of the characteristics of sparse data to reduce system time in multi-core cluster. [ABSTRACT FROM AUTHOR]

Multi-frame image super-resolution reconstruction focuses on obtaining a high-resolution (HR) image from a low-resolution image. Since the super-resolution problem is ill-posed, it is frequent to use regularization techniques. However, the choice of these regularization terms is not always direct. Generally, every term should contain some prior knowledge over the image, that is why it plays an important role in increasing the quality of the restored HR image. In this paper, we propose a total variable-order variation based-regularization to provide a natural-looking and an effective reconstruction of the desired HR image. We also present some existence and uniqueness results of our proposed model. The alternating direction method of multipliers algorithm is employed to implement the numerical simulations. Experimental results reveal that the proposed approach can reconstruct and recover high-quality results visually and quantitatively. [ABSTRACT FROM AUTHOR]

Longitudinal data, measurements taken from the same subjects over time, appear routinely in many scientific fields, such as biomedical science, public health, ecology and environmental sciences. With the rapid development of information technology, modern longitudinal data are becoming massive in volume and high dimensional, hence often require distributed analysis in real-world applications. Standard divide-and-conquer techniques do not apply directly to longitudinal big data due to within-subject dependence. In this paper, we focus on developing a distributed algorithm to support quantile regression (QR) analysis of longitudinal big data, which currently remains an open and challenging issue. We employ weighted quantile regression (WQR) to accommodate the correlation in longitudinal big data, and parallelize the WQR estimation process with a two-stage algorithm to support distributed computing. Based on weights estimated in the first stage by the Newton–Raphson algorithm, the second stage solves the WQR problem using the multi-block alternating direction method of multipliers (ADMM). Simulation studies show that, compared to traditional non-distributed algorithms, our proposed method has favorable estimation accuracy and is computationally more efficient in both non-distributed and distributed environments. Further, we also analyze an air quality data set to illustrate the practical performance of this method. [ABSTRACT FROM AUTHOR]

The issue of underwater image haze removal is investigated in this paper. The exponential attenuation phenomenon in the underwater light propagation process causes the low contrast, color distortion, and blurred edges problems of underwater images and consequently limits the application of the vision-based underwater technology. To overcome these problems, an adaptive color correction method is proposed for underwater single image haze removal. First of all, the estimated transmission map by image blurriness is adopted in the image formation model to remove the haze of underwater images. Secondly, the alternating direction method of multipliers and the histogram displacement in the Lab color space are used to improve the uniform brightness and to correct the color distortion of the restored underwater images. Finally, both qualitative and quantitative experimental results show that the proposed method can produce better restoration results in different underwater scenes compared to other state-of-the-art underwater image restoration methods. [ABSTRACT FROM AUTHOR]

Rooftop solar and batteries, along with other distributed energy resources (DERs), add a new demand-side flexibility, which, when harnessed, will enable distribution operators to more efficiently manage their constrained networks. This paper presents network-aware coordination (NAC), an approach for coordinating DER within unbalanced distribution network constraints, which utilizes the alternating direction method of multipliers (ADMMs) to solve a distributed receding-horizon OPF. As far as we are aware, this paper is the first to report on the practical implementation and performance of an ADMM-based technique solving a significant network problem in live operations. We present real-world trial results of NAC coordinating 31 residential batteries on a constrained feeder within Tasmania’s 11-kV distribution network. The batteries are coordinated to manage the network’s constraints during periods of high feeder demand, decreasing the need for expensive conventional network management, in this case a diesel generator. We achieve a 34% reduction in diesel over seven peaks with 31 batteries capable of meeting 10% of peak demand. Supplementary simulations indicate the potential for a 74% diesel reduction if battery numbers were increased to 100. We find that compared to uncoordinated battery response, the NAC achieves 13% lower total costs over the trial period. [ABSTRACT FROM AUTHOR]

The integration of deep neural networks into sparse synthetic aperture radar (SAR) imaging is explored to enhance SAR imaging performance and reduce the system's sampling rate. However, the scarcity of training samples and mismatches between the training data and the SAR system pose significant challenges to the method's further development. In this paper, we propose a novel SAR imaging approach based on deep image prior powered by RED (DeepRED), enabling unsupervised SAR imaging without the need for additional training data. Initially, DeepRED is introduced as the regularization technique within the sparse SAR imaging model. Subsequently, variable splitting and the alternating direction method of multipliers (ADMM) are employed to solve the imaging model, alternately updating the magnitude and phase of the SAR image. Additionally, the SAR echo simulation operator is utilized as an observation model to enhance computational efficiency. Through simulations and real data experiments, we demonstrate that our method maintains imaging quality and system downsampling rate on par with deep-neural-network-based sparse SAR imaging but without the requirement for training data. [ABSTRACT FROM AUTHOR]

This paper develops a novel copula denoising optimization solution for separating Poisson noise from images, or removing mixtures of Poisson and Gaussian noise. The proposed approach is elaborated in two steps: first, a spatial bilateral total variation (BTV) regularization is used to reduce Gaussian noise; second, a learning copula procedure is employed to separate the Poisson noise from the ideal image. This leads to capture different image features while significantly reducing the noise. Analytically, we include results on the approximation of the Poisson component as well as the resolution of the proposed optimization model. In addition, to resolve the BTV minimization problem, we proposed an alternating direction method of multipliers algorithm. Finally, numerical results are provided to remove noise while preserving important details and features, along with convincing comparisons to demonstrate the performance of the proposed approach. We show, in particular, that using a large database can improve the robustness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

This paper discusses a consensus-based alternating direction method of multipliers (ADMMs) approach for solving the dynamic dc optimal power flow (DC-OPF) problem with demand response in a distributed manner. In smart grid, emerging techniques together with distributed nature of data and information, significantly increase the complexity of power systems operation and stimulate the needs for distributed optimization. In this paper, the distributed DC-OPF approach solves local OPF problems of individual subsystems in parallel, which are coordinated via global consensus variables (i.e., phase angles on boundary buses of adjacent subsystems). Three distributed DC-OPF algorithms are discussed with different convergence performance and/or communication requirement. All three distributed algorithms can effectively handle prevailing constraints for the transmission network, generating units, and demand response in individual subsystems, while the global convergence can be guaranteed. In particular, based on the traditional distributed ADMM approach, a fully decentralized algorithm without the central controller is proposed in Algorithm 2 with a new communication strategy, in which only limited information on boundary buses are exchanged among adjacent subsystems. In addition, the accelerated ADMM is discussed in Algorithm 3 for improving the convergence performance. In recognizing distributed OPF approaches in literature, one major research focus on this paper is to quantify the impact of key parameters and subsystem partitioning strategies on the convergence performance and the data traffic via numerical case studies. A general guidance for subsystem partitioning is proposed and verified via large-scale power systems. [ABSTRACT FROM PUBLISHER]

This paper focuses on a high-dimensional semi-parametric regression model in which a partially linear model is used for the parametric part and the B-spline basis function approach is used to estimate the unknown function for the non-parametric part. Within the framework of this model, the constrained least squares estimation is investigated, and the alternating-direction multiplier method (ADMM) is used to solve the model. The convergence is proved under certain conditions. Finally, numerical simulations are performed and applied to workers' wage data from CPS85. The results show that the ADMM algorithm is very effective in solving high-dimensional partially linear models. [ABSTRACT FROM AUTHOR]

This paper considers large-scale linear ill-posed inverse problems whose solutions can be represented as sums of smooth and piecewise constant components. To solve such problems we consider regularizers consisting of two terms that must be balanced. Namely, a Tikhonov term guarantees the smoothness of the smooth solution component, while a total-variation (TV) regularizer promotes blockiness of the non-smooth solution component. A scalar parameter allows to balance between these two terms and, hence, to appropriately separate and regularize the smooth and non-smooth components of the solution. This paper proposes an efficient algorithm to solve this regularization problem by the alternating direction method of multipliers (ADMM). Furthermore, a novel algorithm for automatic choice of the balancing parameter is introduced, using robust statistics. The proposed approach is supported by some theoretical analysis, and numerical experiments concerned with different inverse problems are presented to validate the choice of the balancing parameter. [ABSTRACT FROM AUTHOR]

In a wind farm, the interactions between turbines caused by wakes can significantly reduce the power output of the wind farm. Cooperative control among the turbines has the potential to improve the power output. However, existing centralized power optimization methods are computationally expensive and does not scale well for large wind farms, limiting their practical use in real-time control for time-varying wind conditions and turbine configuration (with adding or maintaining of turbines). To address this problem, this paper proposes a fully distributed power optimization method for wind farms using alternating direction method of multipliers (ADMM). The proposed method allows the wind farm power output to be optimized in fully distributed manner with turbine-to-turbine message passing over a mesh network, guarantees the implemented control actions satisfy the control constraints of all turbines, and provably converges to a stationary point of the wind farm power optimization problem. Simulation results demonstrate that the proposed method can significantly reduce the computation time with hardly sacrificing the power gain compared with centralized method and thus is computationally efficient for real-time power optimization of large wind farms. [ABSTRACT FROM AUTHOR]

Quantile regression offers a powerful means of understanding the comprehensive relationship between response variables and predictors. By formulating prior domain knowledge and assumptions as constraints on parameters, the estimation efficiency can be enhanced. This paper studies some methods based on multi-block ADMM (Alternating Direction Method of Multipliers) to fit general penalized quantile regression models with linear constraints on regression coefficients. Different formulations for handling linear constraints and general penalties are explored and compared. Among these formulations, the most efficient one is identified, which provides an explicit expression for each parameter during iterations and eliminates the nested-loop in existing algorithms. Furthermore, this work addresses the challenges posed by big data by developing a parallel ADMM algorithm suitable for distributed data storage. The algorithm's convergence and a robust stopping criterion are established. To demonstrate the excellent performance of the proposed algorithms, extensive numerical experiments and a real data example are presented. These empirical validations showcase the effectiveness of the methods in handling complex datasets. The details of theoretical proofs and different algorithm variations are provided in the Appendix. [ABSTRACT FROM AUTHOR]

Variational regularization, renowned for its sound theoretical foundations and impressive performance, is widely used in image restoration. The traditional regularization models typically use a predefined regularizer to promote smoothness in the solution. However, these models do not explicitly take into account any external information that should be preserved in the restoration. In this paper, we introduce a novel guided regularization model to enhance the efficacy of traditional regularization. Our model incorporates an external guidance regularizer, utilizing a guidance image to bolster the quality of restoration. By integrating this external information into the regularization process, the model is better equipped to preserve specific features or attributes indicated by the guidance image, leading to more accurate and aesthetically pleasing restored images. Furthermore, we demonstrate the convexity of the model and prove the existence and uniqueness of the solution. The alternating direction method of multipliers (ADMM) algorithm is employed to numerically solve the proposed model. In the experimental evaluation, the proposed model is applied to image denoising and deblurring tasks. The experiments successfully validate the proposed model and algorithm. Compared with several state-of-the-art models, the proposed model demonstrates the best performance in terms of peak signal-to-noise ratio (PSNR) and structural similarity index (SSIM). • A novel guided regularization model is proposed, which aims to incorporate additional guidance into regularization process. • We demonstrate the convexity of the model and prove the existence and uniqueness of the solution. • The proposed guided regularization model is applied to image denoising and deblurring tasks, yielding satisfactory results. [ABSTRACT FROM AUTHOR]

The rapid technological advances of cellular technologies will revolutionize network automation in industrial internet of things (IIoT). In this paper, we investigate the two-timescale resource allocation problem in IIoT networks with hybrid energy supply, where temporal variations of energy harvesting (EH), electricity price, channel state, and data arrival exhibit different granularity. The formulated problem consists of energy management at a large timescale, as well as rate control, channel selection, and power allocation at a small timescale. To address this challenge, we develop an online solution to guarantee bounded performance deviation with only causal information. Specifically, Lyapunov optimization is leveraged to transform the long-term stochastic optimization problem into a series of short-term deterministic optimization problems. Then, a low-complexity rate control algorithm is developed based on alternating direction method of multipliers (ADMM), which accelerates the convergence speed via the decomposition-coordination approach. Next, the joint channel selection and power allocation problem is transformed into a one-to-many matching problem, and solved by the proposed price-based matching with quota restriction. Finally, the proposed algorithm is verified through simulations under various system configurations. [ABSTRACT FROM AUTHOR]

In this paper, we study the non-convex regularization problem based on magnetic resonance imaging (MRI) reconstruction. In order to achieve high quality and fast reconstruction of MRI images, we use the non-convex Cauchy total variation (CauchyTV) as the regularization term for MRI reconstruction, and an effective alternating direction method of multipliers is selected to solve the new model. The CauchyTV model can effectively improve the fitting performance and reduce aliasing artifacts. The experimental results show that the performance of the CauchyTV model is better than the other typical TV regularization methods. [ABSTRACT FROM AUTHOR]

In this paper, we propose a novel convex variational model for image restoration with multiplicative noise. To preserve the edges in the restored image, our model incorporates a total variation regularizer. Additionally, we impose an equality constraint on the data fidelity term, which simplifies the model selection process and promotes sparsity in the solution. We adopt the alternating direction method of multipliers (ADMM) method to solve the model efficiently. To validate the effectiveness of our model, we conduct numerical experiments on both real and synthetic noise images, and compare its performance with existing methods. The experimental results demonstrate the superiority of our model in terms of PSNR and visual quality. [ABSTRACT FROM AUTHOR]

The ratio of |$\ell _{1}$| and |$\ell _{2}$| norms, denoted as |$\ell _{1}/\ell _{2}$|⁠ , has presented prominent performance in promoting sparsity. By adding partial support information to the standard |$\ell _{1}/\ell _{2}$| minimization, in this paper, we introduce a novel model, i.e. the weighted |$\ell _{1}/\ell _{2}$| minimization, to recover sparse signals from the linear measurements. The restricted isometry property based conditions for sparse signal recovery in both noiseless and noisy cases through the weighted |$\ell _{1}/\ell _{2}$| minimization are established. And we show that the proposed conditions are weaker than the analogous conditions for standard |$\ell _{1}/\ell _{2}$| minimization when the accuracy of the partial support information is at least |$50\%$|⁠. Moreover, we develop effective algorithms and illustrate our results via extensive numerical experiments on synthetic data in both noiseless and noisy cases. [ABSTRACT FROM AUTHOR]

Sparse Gaussian graphical models have been extensively applied to detect the conditional independence structures from fully observed data. However, datasets with missing observations are quite common in many practical fields. In this paper, we propose a robust Gaussian graphical model with the covariance matrix being estimated from the partially observed data. We prove that the inverse of the Karush–Kuhn–Tucker mapping associated with the proposed model satisfies the calmness condition automatically. We also apply a linearly convergent alternating direction method of multipliers to find the solution to the proposed model. The numerical performance is evaluated on both the synthetic data and real data sets. [ABSTRACT FROM AUTHOR]

Over the last ten years, there has been a significant interest in employing nonnegative matrix factorization (NMF) to reduce dimensionality to enable a more efficient clustering analysis in machine learning. This technique has been applied in various image processing applications within the fields of computer vision and sensor-based systems. Many algorithms exist to solve the NMF problem. Among these algorithms, the alternating direction method of multipliers (ADMM) and its variants are one of the most popular methods used in practice. In this paper, we propose a block-active ADMM method to minimize the NMF problem with general Bregman divergences. The subproblems in the ADMM are solved iteratively by a block-coordinate-descent-type (BCD-type) method. In particular, each block is chosen directly based on the stationary condition. As a result, we are able to use much fewer auxiliary variables and the proposed algorithm converges faster than the previously proposed algorithms. From the theoretical point of view, the proposed algorithm is proved to converge to a stationary point sublinearly. We also conduct a series of numerical experiments to demonstrate the superiority of the proposed algorithm. [ABSTRACT FROM AUTHOR]

The traditional robust principal component analysis (RPCA) model aims to decompose the original matrix into low-rank and sparse components and uses the nuclear norm to describe the low-rank prior information of the natural image. In addition to low-rankness, it has been found in many recent studies that local smoothness is also crucial prior in low-level vision. In this paper, we propose a new RPCA model based on weight nuclear norm and modified second-order total variation regularization (WMSTV-RPCA for short), which exploits both the global low-rankness and local smoothness of the matrix. Extensive experimental results show, both qualitatively and quantitatively, that the proposed WMSTV-RPCA can more effectively remove noise, and model dynamic scenes compared with the competing methods. [ABSTRACT FROM AUTHOR]

Different from the existing works that focus on transceiver design of over-the-air computation (AirComp) over static networks, we in this paper consider an unmanned aerial vehicle (UAV) aided AirComp system, where the UAV as a flying base station aggregates data from mobile sensors. The trajectory design of the UAV provides an additional degree of freedom to improve the performance of AirComp. We aim to minimize the time-averaged mean-squared error (MSE) of AirComp by jointly optimizing the UAV trajectory, receive normalizing factors, and sensors’ transmit power. To this end, we first propose a novel and equivalent problem transformation by introducing intermediate variables. This reformulation leads to a convex subproblem when fixing any other two blocks of variables, thereby enabling efficient algorithm design based on the principle of block coordinate descent and alternating direction method of multipliers (ADMM) techniques. In particular, we derive the optimal closed-form solutions for normalizing factors and intermediate variables optimization subproblems. We also recast the convex trajectory design subproblem into an ADMM form and obtain the closed-form expressions for each variable updating. Simulation results show that the proposed algorithm achieves a smaller time-averaged MSE while reducing the simulation time by orders of magnitude compared to state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]

In this paper we study nonconvex and nonsmooth multi-block optimization over Euclidean embedded (smooth) Riemannian submanifolds with coupled linear constraints. Such optimization problems naturally arise from machine learning, statistical learning, compressive sensing, image processing, and tensor PCA, among others. By utilizing the embedding structure, we develop an ADMM-like primal-dual approach based on decoupled solvable subroutines such as linearized proximal mappings, where the duality is with respect to the embedded Euclidean spaces. First, we introduce the optimality conditions for the afore-mentioned optimization models. Then, the notion of ϵ -stationary solutions is introduced as a result. The main part of the paper is to show that the proposed algorithms possess an iteration complexity of O (1 / ϵ 2) to reach an ϵ -stationary solution. For prohibitively large-size tensor or machine learning models, we present a sampling-based stochastic algorithm with the same iteration complexity bound in expectation. In case the subproblems are not analytically solvable, a feasible curvilinear line-search variant of the algorithm based on retraction operators is proposed. Finally, we show specifically how the algorithms can be implemented to solve a variety of practical problems such as the NP-hard maximum bisection problem, the ℓ q regularized sparse tensor principal component analysis and the community detection problem. Our preliminary numerical results show great potentials of the proposed methods. [ABSTRACT FROM AUTHOR]

Alternating direction method of multipliers (ADMM) is a widely used tool for machine learning in distri-buted settings where a machine learning model is trained over distributed data sources through an interactive process of local computation and message passing. Such an iterative process could cause privacy concerns of data owners. The goal of this paper is to provide differential privacy for ADMM-based distributed machine learning. Prior approaches on differentially private ADMM exhibit low utility under high privacy guarantee and assume the objective functions of the learning problems to be smooth and strongly convex. To address these concerns, we propose a novel differentially private ADMM-based distributed learning algorithm called DP-ADMM, which combines an approximate augmented Lagrangian function with time-varying Gaussian noise addition in the iterative process to achieve higher utility for general objective functions under the same differential privacy guarantee. We also apply the moments accountant method to analyze the end-to-end privacy loss. The theoretical analysis shows that the DP-ADMM can be applied to a wider class of distributed learning problems, is provably convergent, and offers an explicit utility-privacy tradeoff. To our knowledge, this is the first paper to provide explicit convergence and utility properties for differentially private ADMM-based distributed learning algorithms. The evaluation results demonstrate that our approach can achieve good convergence and model accuracy under high end-to-end differential privacy guarantee. [ABSTRACT FROM AUTHOR]

The light field information would be captured through light field cameras and in different directions regarding 3D image view recordings. In this paper, in order to increase the spatio-angular super-resolution quality and to decrease the reconstruction error regarding the light field information, we use a graph-based light field super-resolution strategy. Accordingly, in order to apply the complementary data in the light field views, we use a graph regularizer for the total recovery of the information and an edge-preserving technique that represents an isometry between curves in the 2D manifold and 5D space of the RGB image views. Moreover, the reconstruction of the light field information is based on applying the alternating direction method of multipliers (ADMM) algorithm. Accordingly, a recent enhanced ADMM model has been used in this paper which is denominated as “Plug-and-Play” and permits the user to plug an image reconstruction technique and a denoising methodology as the first and second sub-problems respectively. On that account, we would be able to resolve the light field super-resolution problem considering the graph-based light field structure as the first sub-problem and the edge-preserving technique as the denoising methodology. Consequently, by applying the proposed super-resolution strategy, the super-resolved light field outcome would be more favorable in terms of visual quality and reconstruction errors in comparison with other state-of-the-art methodologies. [ABSTRACT FROM AUTHOR]

The interconnection of power and natural gas systems can improve the flexibility of system operation and the capacity of renewable energy consumption. It is necessary to consider the interaction between both, and carry out collaborative optimization of energy flow. For space-time related line packs, this paper studies the optimal multi-energy flow (OMEF) model of an integrated electricity-gas system, taking into account the dynamic characteristics of a natural gas system. Besides, in order to avoid the problem of large data collection in centralized algorithms and consider the characteristics of decentralized autonomous decision-making for each subsystem, this paper proposes a decentralized algorithm for the OMEF problem. This algorithm transforms the original non-convex OMEF problem into an iterative convex programming problem through penalty convex-concave procedure (PCCP), and then, uses the alternating direction method of multipliers (ADMM) algorithm at each iteration of PCCP to develop a decentralized collaborative optimization of power flow and natural gas flow. Finally, numerical simulations verify the effectiveness and accuracy of the algorithm proposed in this paper, and analyze the effects of dynamic characteristics of networks on system operation. [ABSTRACT FROM AUTHOR]

This paper presents a robust statistical approach to distributed power system state estimation (DPSSE) under bad data based on iterative reweight least squares (IRWLS) method and an improved alternating direction method of multipliers (ADMM) framework. In particular, the Hampel’s redescending and the Schweppe–Huber generalized M-estimators (SHGM) are studied for mitigating the adverse effect of outliers with large magnitude. Moreover, a new robust weight smoothing scheme is proposed for improving the numerical stability and convergence speed of the algorithm. The proposed approach is further extended to recursive monitoring of measurement devices and inpainting of missing data by utilizing prior information provided in previous state estimation. The resultant algorithm is solved using the Levenberg–Marquardt (LM) solver, which helps to maintain numerical stability under unexpected adverse situations. Experimental results show that the proposed approach outperforms conventional approaches using the ADMM with L1 outlier detection in state estimation accuracy and convergence speed. Moreover, it maintains numerical stability and good performance under missing data. As state estimation will be performed more frequently in future smart grid due to the increased penetration of renewables, the proposed methods and investigations offer much insight in addressing the missing data and outlier problems in DPSSE. [ABSTRACT FROM AUTHOR]

This paper focuses on power distribution systems with inverter-interfaced renewable energy sources (RESs), and develops a distributed control framework to steer the RES output powers to solutions of ac optimal power flow (OPF) problems. The design of the distributed control algorithm is based on suitable linear approximation of the ac power-flow equations, and leverages the so-called alternating direction method of multipliers (ADMM). Convergence of the RES-inverter output powers to solutions of the approximate ac OPF problem is established under suitable conditions on the mismatches between the commanded setpoints and actual RES output powers. Overall, since the proposed scheme can be cast as an ADMM with inexact primal and dual updates, the convergence results can be applied to more general distributed optimization settings. [ABSTRACT FROM AUTHOR]

The number of devices connected to the Internet of Things (IoT) is growing at an enormous rate globally. In the next generation networks, distributed fog computing deployments at the network edge can provide computing resources to the users, especially for latency-sensitive applications. Further, the heterogeneous needs of the fifth generation (5G) networks demand the virtualization of network functions, termed as network function virtualization (NFV). Therefore, an integrated NFV and fog computing resource allocation framework for IoT is of prime importance. Accordingly, in this paper, we model the interactions between the data service operators (DSOs) and the authorized data service subscribers (ADSSs) as an equilibrium problem with equilibrium constraints (EPEC), and utilize the alternating direction method of multipliers (ADMM) as a large-scale optimization tool to obtain solutions. This results in the optimization of resource pricing for the DSOs and the amount of resources to be purchased by the ADSSs. Moreover, we propose a many-to-many matching based model to allocate the fog node (FN) resources according to the VNF resource requirements of the ADSSs. Simulation results show the effectiveness of our proposed approach in achieving efficient resource allocation in NFV enabled IoT fog computing. [ABSTRACT FROM AUTHOR]

In clinical medical applications, sparse-view computed tomography (CT) imaging is an effective method for reducing radiation doses. The iterative reconstruction method is usually adopted for sparse-view CT. In the process of optimizing the iterative model, the approach of directly solving the quadratic penalty function of the objective function can be expected to perform poorly. Compared with the direct solution method, the alternating direction method of multipliers (ADMM) algorithm can avoid the ill-posed problem associated with the quadratic penalty function. However, the regularization items, sparsity transform, and parameters in the traditional ADMM iterative model need to be manually adjusted. In this paper, we propose a data-driven ADMM reconstruction method that can automatically optimize the above terms that are difficult to choose within an iterative framework. The main contribution of this paper is that a modified U-net represents the sparse transformation, and the prior information and related parameters are automatically trained by the network. Based on a comparison with other state-of-the-art reconstruction algorithms, the qualitative and quantitative results show the effectiveness of our method for sparse-view CT image reconstruction. The experimental results show that the proposed method performs well in streak artifact elimination and detail structure preservation. The proposed network can deal with a wide range of noise levels and has exceptional performance in low-dose reconstruction tasks. [ABSTRACT FROM AUTHOR]

This paper presents synchronous as well as asynchronous formulations of the alternating direction method of multipliers (ADMM) for solving continuous‐time nonlinear distributed model predictive control (DMPC) problems. It is shown that the optimal control problems of certain system classes can be transformed to fit the consensus‐based ADMM variant problem formulation. The arising subproblems are solved locally on the agent level while the consensus step is solved centrally by a coordinator. Furthermore, the convergence of the synchronous and asynchronous ADMM algorithms to their respective first‐order optimality conditions is presented in a continuous‐time setting. The algorithm is applied to different example systems for which the convergence behavior and influence of the individual algorithmic parameters are investigated. The computation time of the agents remains unaffected by the system size and thus demonstrates the applicability to high‐scaled systems. Moreover, results show that the asynchronous algorithm performs better in terms of execution time when compared to its synchronous counterpart. [ABSTRACT FROM AUTHOR]

In this paper, we address the image denoising problem in presence of speckle degradation typically arising in ultra-sound images. Variational methods and Convolutional Neural Networks (CNNs) are considered well-established methods for specific noise types, such as Gaussian and Poisson noise. Nonetheless, the advances achieved by these two classes of strategies are limited when tackling the de-speckle problem. In fact, variational methods for speckle removal typically amounts to solve a non-convex functional with the related issues from the convergence viewpoint; on the other hand, the lack of large datasets of noise-free ultra-sound images has not allowed the extension of the state-of-the-art CNN denoiser methods to the case of speckle degradation. Here, we aim at combining the classical variational methods with the predictive properties of CNNs by considering a weighted total variation regularized model; the local weights are obtained as the output of a statistically inspired neural network that is trained on a small and composite dataset of natural and synthetic images. The resulting non-convex variational model, which is minimized by means of the Alternating Direction Method of Multipliers (ADMM) is proven to converge to a stationary point. Numerical tests show the effectiveness of our approach for the denoising of natural and satellite images. • An hybrid strategy for the despeckling problem combining convolutional neural networks and variational methods is proposed. • The proposed neural architecture is statistically-inspired and not requires the training on a large data-set of images. • A proof of convergence to a stationary point for the alternating direction method is given. [ABSTRACT FROM AUTHOR]

In this paper, a unified optimization model for medical image fusion based on tensor decomposition and the non-subsampled shearlet transform (NSST) is proposed. The model is based on the NSST method and the tensor decomposition method to fuse the high-frequency (HF) and low-frequency (LF) parts of two source images to obtain a mixed-frequency fused image. In general, we integrate low-frequency and high-frequency information from the perspective of tensor decomposition (TD) fusion. Due to the structural differences between the high-frequency and low-frequency representations, potential information loss may occur in the fused images. To address this issue, we introduce a joint static and dynamic guidance (JSDG) technique to complement the HF/LF information. To improve the result of the fused images, we combine the alternating direction method of multipliers (ADMM) algorithm with the gradient descent method for parameter optimization. Finally, the fused images are reconstructed by applying the inverse NSST to the fused high-frequency and low-frequency bands. Extensive experiments confirm the superiority of our proposed TDFusion over other comparison methods. [ABSTRACT FROM AUTHOR]

This paper proposes a distributed empirical likelihood (DEL) method for performing an integrative analysis of multiple data sources with the flexibility of handling either homogeneous or heterogeneous data. The proposed DEL method does not require pooling individual data sets into a centralized operational platform, so the privacy of subject-level information in individual data sources is protected. The DEL method is shown to be almost surely equal to the centralized empirical likelihood approach that would be adopted if individual data sets were combined and stored at one place. We establish the large-sample properties and algorithm convergence of the DEL method. We also illustrate the numerical performance of the DEL method using simulation studies and a real-data example, in which the DEL method is clearly advantageous over the classical meta-estimation method when analyzing unbalanced data sets. [ABSTRACT FROM AUTHOR]

Over the past few years, deep learning methods have emerged as powerful image denoising tools. Among them, unsupervised deep learning without external training data is more practical and challenging. Reducing noisy overfitting is challenging due to single-image unsupervised learning is prone to overfitting. In this paper, we propose a method named drop-DIP combing Deep Image Prior (DIP) with drop-out for the first time to solve the above problems. In our method, we construct new network training pairs by performing drop-out training on the Bernoulli sampling of the input and output, and then construct a regularization term by using the corrected bias of the output and the generated prior. Finally, update the parameters through the Alternating Direction Method of Multipliers (ADMM) algorithm. Experiments demonstrate that drop-DIP can alleviate the overfitting difficulty in DIP, facilitate the early stopping of the network, and is applicable to different noise models. Furthermore, our method has good performance on Peak Signal to Noise Ratio (PSNR), Structural Similarity (SSIM), and Learned Perceptual Image Patch Similarity (LPIPS) metrics validated by two different datasets. [ABSTRACT FROM AUTHOR]