Block Coordinate Descent Method Research Articles

Spreading code optimization for low-earth orbit satellites via mixed-integer convex programming

Optimizing the correlation properties of spreading codes is critical for minimizing inter-channel interference in satellite navigation systems. By improving the codes’ correlation sidelobes, we can enhance navigation performance while minimizing the required spreading code lengths. In the case of low-earth orbit (LEO) satellite navigation, shorter code lengths (on the order of a hundred) are preferred due to their ability to achieve fast signal acquisition. Additionally, the relatively high signal-to-noise ratio in LEO systems reduces the need for longer spreading codes to mitigate inter-channel interference. In this work, we propose a two-stage block coordinate descent (BCD) method which optimizes the codes’ correlation properties while enforcing the autocorrelation sidelobe zero property. In each iteration of the BCD method, we solve a mixed-integer convex program over a block of 25 binary variables. Our method is applicable to spreading code families of arbitrary sizes and lengths, and we demonstrate its effectiveness for a problem with 66 length-127 codes and a problem with 130 length-257 codes.

Vehicle Selection and Resource Allocation for Federated Learning-Assisted Vehicular Network

To exploit the massive amounts of onboard data in vehicular networks while protecting data privacy and security, federated learning (FL) is regarded as a promising technology to support enormous vehicular applications. Despite that FL has great potential to improve the architecture of intelligent vehicular networks, the mobility of the vehicles and the dynamic nature of wireless channels make the integration of FL and vehicular networks more challenging. In this paper, we propose a vehicle mobility- and channel dynamic-aware FL (MADCA-FL) scheme to fit vehicular networks and enhance learning performances. This novel scheme enables the RSU to select appropriate vehicles and weightedly average the local models. Afterward, MADCA-FL formulates a problem to maximize the model accuracy while assuring the latency and energy restrictions, by jointly optimizing the computation and communication resources. With a mixed- integer non-linear programming structure, the problem is NP-hard. Firstly, we utilize the successive convex approximation algorithm to handle the non-convexity, and then apply the Lagrange multiplier method and the block coordinate descent method to obtain the optimal solution. Extensive experiments are conducted to confirm the effectiveness of our proposed scheme.

Wasserstein distance regularized graph neural networks

Distribution shift widely exists in graph representation learning and often reduces model performance. This work investigates how to improve the performance of a graph neural network (GNN) in a single graph by controlling distribution shift between embedding spaces. Specifically, we provide an upper error-bound estimation, which quantitatively analyzes how distribution shift affects GNNs' performance in a single graph. Considering that there is no natural domain division in a single graph, we propose PW-GNN to simultaneously learn discriminative embedding and reduce distribution shift. PW-GNN measures distribution discrepancy using the distance between test embeddings and prototypes, and transfers minimizing distribution shift to minimizing the power of Wasserstein distance, which is introduced into GNNs as a regularizer. A series of theoretical analyses are carried out to demonstrate the effectiveness of PW-GNN. Besides, a low-complexity training algorithm is designed by exploring entropy-regularized strategy and block coordinate descent method. Extensive numerical experiments are conducted on different datasets with both biased and unbiased splits. We empirically test our model equipped with four backbone models. Results show that PW-GNN outperforms state-of-the-art baselines and mitigates up to 8% of negative effects off distribution shift on backbones.

Robust condition identification against label noise in industrial processes based on trusted connection dictionary learning

In the era of big data, the pervasive use of artificial intelligence (AI) technology has revolutionized various industries. AI-powered systems, particularly those utilizing data-driven interpretable and reliable methods for accurate condition identification, have emerged as a crucial factor in achieving intelligent industrial systems. However, in real industrial sites, the labels of offline data often contain incorrect labels, i.e. label noise, due to human error, sensor failure, and other sources, which reduces the accuracy of the model and affects the performance and safety of the industrial system. To tackle the challenge of precarious performance caused by label noise, this paper proposes a robust method called Trusted Connection Dictionary Learning (TCDL) which effectively mitigates the adverse effects of label noise through interpretable constraints and guarantees the trustworthiness of the model for industrial applications. Specifically, to address the issue of data structure and label inconsistency arising from label noise, this paper presents a dynamic graph model that jointly optimizes data features and label information to obtain consistent representations of them. Subsequently, to effectively fit the labeled data, TCDL leverages the label information from the nearest neighbors through the optimized graph structure and facilitates the self-correction of label noise, leading to robust representations of process features and a reliable condition classifier. Finally, a novel iterative optimization algorithm that combines the Block Coordinate Descent (BCD) method and the Alternating Direction Multiplier Method (ADMM) is also developed to ensure the convergence of the algorithm. Due to simple constraints, it can obtain accurately optimized variables with few iterations. Numerical simulations and industrial experiments demonstrate the superiority of the proposed method compared to some state-of-the-art methods.

More communication-efficient distributed sparse learning

In a modern distributed learning framework, the speeds of intra-worker calculation and inter-worker communication may differ by 1,000 times. It is advisable to perform expensive calculations on worker machines and communicate as few rounds as possible. In this paper, we propose three novel distributed sparse learning algorithms (EDSL-ET, EDSL-IBCD, and EDSL-IBCD-ET) in high dimensions, which are efficient in both computation and communication. Algorithm EDSL-ET utilizes the Topk sparse technique to reduce communication costs and adopts error feedback to guarantee convergence. Algorithm EDSL-IBCD greatly reduces communication costs by introducing an independent block coordinate descent method. Algorithm EDSL-IBCD-ET takes advantage of EDSL-ET and EDSL-IBCD algorithms for extra-high dimensional feature learning, which is the best one whether in communication, computation, and stability. We give theoretical guarantees of the three algorithms under mild conditions, which match the performance of the centralized algorithm. Extensive experiments on simulated and real data validate our theoretical analysis and demonstrate that the proposed algorithms perform well with just a few rounds of communications.

Randomized progressive iterative approximation for B-spline curve and surface fittings

For large-scale data fitting, the least-squares progressive iterative approximation is a widely used method in many applied domains because of its intuitive geometric meaning and efficiency. In this work, we present a randomized progressive iterative approximation (RPIA) for the B-spline curve and surface fittings. In each iteration, RPIA locally adjusts the control points according to a random criterion of index selections. The difference for each control point is computed concerning the randomized block coordinate descent method. From geometric and algebraic aspects, the illustrations of RPIA are provided. We prove that RPIA constructs a series of fitting curves (resp., surfaces), whose limit curve (resp., surface) can converge in expectation to the least-squares fitting result of the given data points. Numerical experiments are given to confirm our results and show the benefits of RPIA.

Joint trajectory, transmission time and power optimization for multi-UAV data collecting system

Unmanned aerial vehicles (UAVs) have been generally applied in the field of communication due to their small size, flexible mobility, and convenient deployment. As a mobile base station, the UAV node can quickly establish a line-of-sight link with the ground node, thereby improving communication performance. In this paper, we study a multi-UAV assisted data collecting system. Specifically, in the case of limited system energy consumption, UAV flight energy consumption and ground node data transmission energy consumption are considered as an general limitation, and considering the channel interference between nodes, a multi-UAV assisted data collection model is studied. An non-convex problem that maximizes the minimum amount of data collected from ground nodes is further formulated. Since the original optimization problem is non-convex that difficult to solve directly, the problem is first decomposed into four sub-problems, and then the solution of each sub-problem is obtained by using successive convex approximation and block coordinate descent method. Finally, based on the solution of the four subproblems, an iterative algorithm for joint optimization of data transmission planning, transmission power, UAV trajectory and mission time is proposed. Simulation experiments show that the proposed algorithm can obtain more transmission data than the baseline algorithms.

Multi-UAV-assisted Internet of Remote Things communication within satellite–aerial–terrestrial integrated network

Due to the limited transmission capabilities of terrestrial intelligent devices within the Internet of Remote Things (IoRT), this paper proposes an optimization scheme aimed at enhancing data transmission rate while ensuring communication reliability. This scheme focuses on multi-unmanned aerial vehicle (UAV)-assisted IoRT data communication within the satellite–aerial–terrestrial integrated network (SATIN), which is one of the key technologies for the sixth generation (6G) networks. To optimize the system’s data transmission rate, we introduce a multi-dimensional coverage and power optimization (CPO) algorithm, rooted in the block coordinate descent (BCD) method. This algorithm concurrently optimizes various parameters, including the number and deployment of UAVs, the correlation between IoRT devices and UAVs, and the transmission power of both devices and UAVs. To ensure comprehensive coverage of a large-scale randomly distributed array of terrestrial devices, combined with machine learning algorithm, we present the Dynamic Deployment based on K-means (DDK) algorithm. Additionally, we address the non-convexity challenge in resource allocation for transmission power through variable substitution and the successive convex approximation technique (SCA). Simulation results substantiate the remarkable efficacy of our CPO algorithm, showcasing a maximum 240% improvement in the uplink transmission rate of IoRT data compared to conventional methods.

Energy Efficient Resource Allocation for Uplink RIS-Aided Millimeter-Wave Networks With NOMA

In this paper, energy efficiency (EE) is maximized for the reconfigurable intelligent surface (RIS) aided millimeter-Wave (mmWave) networks with non-orthogonal multiple access (NOMA) and multiple mobile devices. To this end, we first propose the EE optimization, under the constraints of maximum power, minimal rate of devices and constant modulus of beamforming (BF) vectors. Then, the joint resource allocation scheme of power allocation (PA) and BF is designed. Specifically, given PA, an effective iterative algorithm based on the majorizationminimization, concave-convex procedure and block coordinate descent (BCD) is presented to obtain closed-form solutions of suboptimal passive BF (PBF) and analog BF (ABF) for each iteration. Then, given PBF and ABF, an effective iterative algorithm based on the successive convex approximation, BCD and Dinkelbach methods is derived to achieve suboptimal closedform PA for each iteration. By incorporating these two algorithms into the BCD method, a joint optimization algorithm for EE maximization is presented. As a result, joint resource allocation of PA, PBF and ABF is attained. Besides, the convergence and complexity of the algorithms are analyzed. For comparison, the benchmark scheme based on the multidimensional search method and artificial bee colony algorithm is also presented. Simulation results show that the proposed joint scheme is effective and higher EE can be obtained with lower complexity.

Low-Light Enhancement Method Based on a Retinex Model for Structure Preservation

Enhancing low-light image visibility is a critical task in computer vision since it helps to improve input for high-level algorithms. High-quality images typically have clear structural information. In previous studies, due to the lack of proper structural guidance, restored images had some problems, such as unclear structural areas and overexposed or underexposed local areas. To address the above problems, in this paper, we introduce a coefficient of variation (COV) with excellent performance in maintaining structural information, and then we propose a low-light image enhancement method that utilizes the COV to extract structural information from images. First, we apply a traditional retinex model to estimate both reflectance and illumination. Second, we use the COV to indicate the degree of dispersion of the input sample, which enables us to obtain a robust structure-distinguishing weight map for low-light images. The weight map is adaptively divided to obtain a structural weight map, which is then used to enhance the gradient image. This process is applied before the reflectance layer of the retinex model. Finally, the result is obtained by using the block coordinate descent method. According to extensive experiments, outstanding results can be achieved by our proposed method in terms of both subjective and objective evaluation metrics in comparison with other state-of-the-art methods. The source code is available at our website <xref ref-type="fn" rid="fn1" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">¹</xref> <fn id="fn1" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><label>¹</label> <uri>https://github.com/bbxavi/spcv22</uri> </fn> .

Robust Tensor Completion via Capped Frobenius Norm.

Tensor completion (TC) refers to restoring the missing entries in a given tensor by making use of the low-rank structure. Most existing algorithms have excellent performance in Gaussian noise or impulsive noise scenarios. Generally speaking, the Frobenius-norm-based methods achieve excellent performance in additive Gaussian noise, while their recovery severely degrades in impulsive noise. Although the algorithms using the lp -norm ( ) or its variants can attain high restoration accuracy in the presence of gross errors, they are inferior to the Frobenius-norm-based methods when the noise is Gaussian-distributed. Therefore, an approach that is able to perform well in both Gaussian noise and impulsive noise is desired. In this work, we use a capped Frobenius norm to restrain outliers, which corresponds to a form of the truncated least-squares loss function. The upper bound of our capped Frobenius norm is automatically updated using normalized median absolute deviation during iterations. Therefore, it achieves better performance than the lp -norm with outlier-contaminated observations and attains comparable accuracy to the Frobenius norm without tuning parameter in Gaussian noise. We then adopt the half-quadratic theory to convert the nonconvex problem into a tractable multivariable problem, that is, convex optimization with respect to (w.r.t.) each individual variable. To address the resultant task, we exploit the proximal block coordinate descent (PBCD) method and then establish the convergence of the suggested algorithm. Specifically, the objective function value is guaranteed to be convergent while the variable sequence has a subsequence converging to a critical point. Experimental results based on real-world images and videos exhibit the superiority of the devised approach over several state-of-the-art algorithms in terms of recovery performance. MATLAB code is available at https://github.com/Li-X-P/Code-of-Robust-Tensor-Completion.

Fourier Domain Robust Denoising Decomposition and Adaptive Patch MRI Reconstruction.

The sparsity of the Fourier transform domain has been applied to magnetic resonance imaging (MRI) reconstruction in k -space. Although unsupervised adaptive patch optimization methods have shown promise compared to data-driven-based supervised methods, the following challenges exist in MRI reconstruction: 1) in previous k -space MRI reconstruction tasks, MRI with noise interference in the acquisition process is rarely considered. 2) Differences in transform domains should be resolved to achieve the high-quality reconstruction of low undersampled MRI data. 3) Robust patch dictionary learning problems are usually nonconvex and NP-hard, and alternate minimization methods are often computationally expensive. In this article, we propose a method for Fourier domain robust denoising decomposition and adaptive patch MRI reconstruction (DDAPR). DDAPR is a two-step optimization method for MRI reconstruction in the presence of noise and low undersampled data. It includes the low-rank and sparse denoising reconstruction model (LSDRM) and the robust dictionary learning reconstruction model (RDLRM). In the first step, we propose LSDRM for different domains. For the optimization solution, the proximal gradient method is used to optimize LSDRM by singular value decomposition and soft threshold algorithms. In the second step, we propose RDLRM, which is an effective adaptive patch method by introducing a low-rank and sparse penalty adaptive patch dictionary and using a sparse rank-one matrix to approximate the undersampled data. Then, the block coordinate descent (BCD) method is used to optimize the variables. The BCD optimization process involves valid closed-form solutions. Extensive numerical experiments show that the proposed method has a better performance than previous methods in image reconstruction based on compressed sensing or deep learning.

Enhancing Data Freshness in Air-Ground Collaborative Heterogeneous Networks through Contract Theory and Generative Diffusion-Based Mobile Edge Computing.

Mobile edge computing is critical for improving the user experience of latency-sensitive and freshness-based applications. This paper provides insights into the potential of non-orthogonal multiple access (NOMA) convergence with heterogeneous air-ground collaborative networks to improve system throughput and spectral efficiency. Coordinated resource allocation between UAVs and MEC servers, especially in the NOMA framework, is addressed as a key challenge. Under the unrealistic assumption that edge nodes contribute resources indiscriminately, we introduce a two-stage incentive mechanism. The model is based on contract theory and aims at optimizing the utility of the service provider (SP) under the constraints of individual rationality (IR) and incentive compatibility (IC) of the mobile user. The block coordinate descent method is used to refine the contract design and complemented by a generative diffusion model to improve the efficiency of searching for contracts. During the deployment process, the study emphasizes the positioning of UAVs to maximize SP effectiveness. An improved differential evolutionary algorithm is introduced to optimize the positioning of UAVs. Extensive evaluation shows our approach has excellent effectiveness and robustness in deterministic and unpredictable scenarios.

Communication and computational resource optimization for Industry 5.0 smart devices empowered by MEC

Smart devices in Industry 5.0, such as sensors and robots, are often limited by low battery life and finite computational resources, hindering their ability to perform complex tasks. By offloading computation-intensive tasks to Mobile Edge Cloud Computing (MEC) servers at the network’s edge, businesses can achieve real-time data processing and analysis, reducing communication latency, quicker response times, and improved system reliability. This work presents an integrated framework for MEC and Industry 5.0, aimed at enhancing the performance, efficiency, and flexibility of industrial processes. In particular, we propose a joint optimization problem that maximizes computational energy efficiency by optimally allocating resources, such as processing power and computational resources, as well as device association, in the most efficient manner possible. The problem is formulated as nonconvex/nonlinear, which is intractable and poses high complexity. To solve this challenging problem, we first transform and decouple the original optimization problem into a series of subproblems using the block coordinate descent method. Then, we iteratively obtain an efficient solution using convex optimization methods. In addition, our work sheds light on the fundamental trade-off between local computation and partial offloading schemes. The results show that for small data size requirements, the performance is comparable among different schemes. However, as data size increases, our proposed hybrid scheme, which includes a partial offloading scheme, outperforms others, highlighting the effectiveness of the proposed joint optimization scheme.

Joint Trajectory Design and Resource Allocation for Secure Air–Ground Integrated IoT Networks

We investigate in this paper joint trajectory design and resource allocation for secure air-ground integrated Internet of Things (IoT) networks with unmanned aerial vehicle (UAV) jamming and device to device (D2D) enhancement. By jointly optimizing ground user scheduling, UAV flight trajectory and transmit power, we are able to maximize the minimum system secrecy rate of UAV and D2D communications. The formulated optimization problems of the two typical network scenarios, i.e., with and without UAV jamming, are challenging to be solved due to the corresponding non-smooth and non-concave objective functions. Therefore, we propose alternating iterative algorithms to solve the problems by employing the successive convex approximation and block coordinate descent methods. Extensive results indicate that the proposed joint optimization schemes can effectively improve the secrecy communication performance under different spatial distributions of ground users.

A UAV-Assisted Secure Communication System by Jointly Optimizing Transmit Power and Trajectory in the Internet of Things

Secure communication technology has attracted more and more attention to improve the security of the Internet of Things (IoT). In this article, we discuss the maximum secrecy capacity problem for a mobile unmanned aerial vehicle (UAV) assisted secure communication in IoT, where the UAV relays the covert information from the transmitter (Alice) to the legal receiver (Bob) without detection by an eavesdropper (Eve) though sharing the spectrum with the ground device-to-device (D2D) communications. Our design aims to maximize the sum secrecy capacity Bob received by optimizing the transmit power and the UAV’s trajectory jointly while guaranteeing that the normal communication behavior between ground D2D pairs is not affected. Therefore, we propose a jointly optimizing the transmit power and UAV trajectory algorithm (JOTUTA) based on the block coordinate descent (BCD) method. Specifically, we first transform the non-convex problem of transmit power based on a fixed UAV’s trajectory into a convex problem by D.C. (difference of two convex functions) programming. Secondly, we solve the problem of UAV’s trajectory optimization with given transmit power by the successive convex approximation (SCA) method. Experiments results show the effectiveness of JOTUTA and the advantages of improving the secrecy capacity are verified compared with existing work.

Energy Consumption Minimization in Unmanned Aerial Vehicle-Enabled Secure Wireless Sensor Networks

In wireless sensor networks (WSNs), unmanned aerial vehicles (UAVs) are considered an effective data collection tool. In this paper, we investigate the energy-efficient data collection problem in a UAV-enabled secure WSN without knowing the instantaneous channel state information of the eavesdropper (Eve). Specifically, the UAV collected the information from all the wireless sensors at the scheduled time and forward it to the fusion center while Eve tries to eavesdrop on this confidential information from the UAV. To surmount this intractable and convoluted mixed-integer non-convex problem, we propose an efficient iterative optimization algorithm using the block coordinate descent (BCD) method to minimize the maximum energy consumption of the ground sensor nodes (GSNs) under the constraints of secrecy outage probability (SOP), connection outage probability (COP), minimum secure data, information causality, and UAV trajectory. Numerical results demonstrate the superiority of the algorithm we proposed in energy consumption and secrecy rate compared with other schemes.

Robust Transmission Design for RIS-Assisted Secure Multiuser Communication Systems in the Presence of Hardware Impairments

This paper investigates reconfigurable intelligent surface (RIS)-assisted secure multiuser communication systems in the presence of hardware impairments (HIs) at the RIS and the transceivers. We jointly optimize the beamforming vectors at the base station (BS) and the phase shifts of the reflecting elements at the RIS so as to maximize the weighted minimum approximate ergodic secrecy rate (WMAESR), subject to the transmission power constraints at the BS and unit-modulus constraints at the RIS. To solve the formulated optimization problem, we first decouple it into two tractable subproblems and then use the block coordinate descent (BCD) method to alternately optimize the subproblems. Two different methods are proposed to solve the two obtained subproblems. The first method transforms each subproblem into a second order cone programming (SOCP) problem by invoking the penalty convexconcave procedure (CCP) method and the closed-form fractional programming (FP) criterion, and then directly solves them by using CVX. The second method leverages the minorization-maximization (MM) algorithm. Specifically, we first derive a concave approximation function, which is a lower bound of the original objective function, and then the two subproblems are transformed into two simple surrogate problems that admit closed-form solutions. Simulation results verify the performance gains of the proposed robust transmission methods over existing non-robust designs. In addition, the MM algorithm is shown to have much lower complexity than the SOCP-based algorithm.

Sum Rate Optimization for MIMO Multicasting Network with Active IRS

This paper considers a multiple-input multiple-output (MIMO) multicasting system aided by the intelligent reflecting surface (IRS). We aim to maximize the sum information rate via jointly designing the transmit precoding matrix and the reflecting coefficient (RC) matrix, subject to the transmit power constrains of the Tx and IRS. To tackle the nonconvex problem, we recast the original problem into an equivalent formulation by using some important facts about matrices and proposed a block coordinate descent (BCD) method to optimize the variables. Finally, simulation results validate the effectiveness of active IRS in enhancing the rate performance.

Image restoration via joint low-rank and external nonlocal self-similarity prior

Recent studies have revealed that joint priors, such as joint sparsity and external nonlocal self-similarity (ENSS) prior and joint low-rank and sparsity prior, are extremely effective in various image inverse problems. Few works, however, make use of both low-rank and ENSS priors. With this in mind, in this paper we propose a new joint prior, namely LRENSS prior, which utilizes low-rank and ENSS priors jointly in a unified framework, and successfully adapt the proposed LRENSS prior to image restoration problems. Specifically, low-rank and ENSS priors are bridged by treating ENSS prior as dictionaries for structural sparse representation. Further, an elegant block coordinate descent method is developed to solve the corresponding optimization problem. The proposed LRENSS prior is validated on image denoising and image deblurring tasks. Experimental results illustrate that the proposed LRENSS prior has better performance than other state-of-the-art algorithms in both qualitative and quantitative assessments.