Dual Gradient Research Articles

A deep unrolling network inspired by total variation for compressed sensing MRI

Compressed Sensing theory breaks through the limitation of the Nyquist sampling law and provides theoretical support for accelerating the imaging process of MRI while reconstructing high-quality images. It can use less sampling data through the reconstructed algorithm to restore the original signal. Reconstruction time and reconstruction algorithms play important roles in compressed sensing. However, it is difficult to apply the iterative reconstruction method in clinical applications because of the long reconstruction time. In addition, hand-crafted image prior which is widely used in traditional iterative method lacks of adaptivity for MRI reconstruction. In this paper, inspired by the total variation model, we propose a novel deep network for CSMRI, dubbed as TV-Inspired Network (TVINet), which incorporates the deep priors into the traditional iterative algorithm. We apply a general compressed sensing reconstruction framework inspired by TV regularization and solve it by combines the iterative method with deep learning. The design of TVINet comes from the inference process on the basis of Primal Dual Hybrid Gradient algorithm, which makes the network has preferable interpretability. The linear operator and regularization term are learned from the training dataset by using a convolution network. The proposed approach trains the network end-to-end and reconstructs the desired image directly from the under-sampling data. Experimental results show that the proposed method has better PSNR or SSIM than state-of-the-art methods, and maintains more complex and fine details in the reconstructed image.

Distributed Model Predictive Control and Optimization for Linear Systems With Global Constraints and Time-Varying Communication

In the article, we study the distributed model predictive control (DMPC) problem for a network of linear discrete-time systems, where the system dynamics are decoupled, the system constraints are coupled, and the communication networks are described by time-varying directed graphs. A novel distributed optimization algorithm called the push-sum dual gradient (PSDG) algorithm is proposed to solve the dual problem of the DMPC optimization problem in a fully distributed way. We prove that the sequences of the primal, and dual variables converge to their optimal values. Furthermore, to solve the implementation issues, stopping criteria are designed to allow early termination of the PSDG Algorithm, and the gossip-based push-sum algorithm is proposed to check the stopping criteria in a distributed manner. It is shown that the optimization problem is iteratively feasible, and the closed-loop system is exponentially stable. Finally, the effectiveness of the proposed DMPC approach is verified via an example.

On the convergence of exact distributed generalisation and acceleration algorithm for convex optimisation

In this paper, we study distributed multiagent optimisation over undirected graphs. The optimisation problem is to minimise a global objective function, which is composed of the sum of a set of local objective functions. Recent researches on this problem have made significant progress by using primal-dual methods. However, the inner link among different algorithms is unclear. This paper shows that some state-of-the-art algorithms differ in that they incorporate the slightly different last dual gradient terms based on the augmented Lagrangian analysis. Then, we propose a distributed Nesterov accelerated optimisation algorithm, where a doubly stochastic matrix is allowed to use, and nonidentical local step-sizes are employed. We analyse the convergence of the proposed algorithm by using the generalised small gain theorem under the assumption that each local objective function is strongly convex and has Lipschitz continuous gradient. We prove that the sequence generated by the proposed algorithm linearly converge to an optimal solution if the largest step-size is positive and less than an explicitly estimated upper bound, and the largest momentum parameter is nonnegative and less than an upper bound determined by the largest step-size. Simulation results further illustrate the efficacy of the proposed algorithm.

Restarted primal–dual Newton conjugate gradient method for enhanced spatial resolution of reconstructed cone-beam x-ray luminescence computed tomography images

Cone-beam x-ray luminescence computed tomography (CB-XLCT) has been proposed as a promising imaging tool, which enables three-dimensional imaging of the distribution of nanophosphors (NPs) in small animals. However, the reconstruction performance is usually unsatisfactory in terms of spatial resolution due to the ill-posedness of the CB-XLCT inverse problem. To alleviate this problem and to achieve high spatial resolution, a reconstruction method consisting of inner and outer iterations based on a restarted strategy is proposed. In this method, the primal–dual Newton conjugate gradient method (pdNCG) is adopted in the inner iterations to get fast reconstruction, which is used for resetting the permission region and increasing the convergence speed of the outer iteration. To assess the performance of the method, both numerical simulation and physical phantom experiments were conducted with a CB-XLCT system. The results demonstrate that compared with conventional reconstruction methods, the proposed re-pdNCG method can accurately and efficiently resolve the adjacent NPs with the least relative error.

Distributed Optimization Over Time-Varying Networks With Minimal Connectivity

Many existing distributed optimization algorithms are applicable to time-varying networks, whereas their convergence results are established under the standard $B$ -connectivity condition. In this letter, we establish the convergence of the Fenchel dual gradient methods, proposed in our prior work, under a less restrictive and indeed minimal connectivity condition on undirected networks, which, referred to as joint connectivity, requires the infinitely occurring agent interactions to form a connected graph. Compared to the existing distributed optimization algorithms that are guaranteed to converge under joint connectivity, the Fenchel dual gradient methods are able to handle nonlinear local cost functions and nonidentical local constraints. We also demonstrate the effectiveness of the Fenchel dual gradient methods over time-varying networks satisfying joint connectivity via simulations.

Dual smoothing ionospheric gradient monitoring algorithm for dual-frequency BDS GBAS

In this study, a Dual Smoothing Ionospheric Gradient Monitor Algorithm (DSIGMA) was developed for Code-Carrier Divergence (CCD) faults of dual-frequency Ground-Based Augmentation Systems (GBAS) based on the BeiDou Navigation Satellite System (BDS). Divergence-Free (DF) combinations of the signals were used to form test statistics for a dual-frequency DSIGMA. First, the single-frequency DSIGMA was reviewed, which supports the GBAS approach service type D (GAST-D) for protection against the effect of large ionospheric gradients. The single-frequency DSIGMA was used to create a novel input scheme for the dual-frequency DSIGMA by introducing DF combinations. The steady states of the test statistics were also analysed. The monitors were characterized using BDS measurement data, whereby standard deviations of 0.0432 and 0.0639 m for the proposed two test statistics were used to calculate the monitor threshold. An extensive simulation was designed to assess the monitor performance by comparing the Probability of Missed Detection (PMD) according to the differential error with the range domain PMD limits under different fault modes. The results showed that the proposed algorithm has a higher integrity performance than the single-frequency monitor. The minimum detectable divergence with the same missed probability is less than 50% that of GAST-D.

Online Stochastic Optimization of Networked Distributed Energy Resources

This paper investigates distributed control and incentive mechanisms to coordinate distributed energy resources (DERs) with both continuous and discrete decision variables as well as device dynamics in distribution grids. We formulate a multiperiod social welfare maximization problem, and based on its convex relaxation propose a distributed stochastic dual gradient algorithm for managing DERs. We further extend it to an online real-time setting with time-varying operating conditions, asynchronous updates by devices, and feedback being leveraged to account for nonlinear power flows as well as reduce communication overhead. The resulting algorithm provides a general online stochastic optimization algorithm for coordinating networked DERs with discrete power setpoints and dynamics to meet operational and economic objectives and constraints. We characterize the convergence of the algorithm analytically and evaluate its performance numerically.

Linear convergence of primal–dual gradient methods and their performance in distributed optimization

In this work, we revisit a classical incremental implementation of the primal-descent dual-ascent gradient method used for the solution of equality constrained optimization problems. We provide a short proof that establishes the linear (exponential) convergence of the algorithm for smooth strongly-convex cost functions and study its relation to the non-incremental implementation. We also study the effect of the augmented Lagrangian penalty term on the performance of distributed optimization algorithms for the minimization of aggregate cost functions over multi-agent networks.

Distributed Mirror-Prox Optimization for Multi-Access Edge Computing

In this paper, we address the problem of overall delay minimization in a cellular multi-access edge computing (MEC) network, where servers with limited computing and storage resources are co-located with a base station (BS) to execute the computation tasks offloaded by the users. We formulate this problem as a distributed mirror prox (DMP) optimization at individual users and the MEC servers’ local controller (LC) over a long-time horizon and develop an online algorithm to ensure queue stability of the overall network in the long run. Both, the cost and the constraint functions are time-varying with unknown statistics. We evaluate the performance of the proposed algorithm using two performance metrics: the dynamic regret to assess the closeness of the achievable cost against the dynamic optimal value; and the aggregate violation to measure the asymptotic satisfaction of the constraints. Given the optimum hindsight variation is sub-linear, we prove that both of the dynamic regret and the aggregate violation are sub-linear in the long run. The simulation results confirm the superiority of the proposed DMP algorithm over the stochastic dual gradient in terms of delay minimization, dynamic regret, aggregate violation and energy efficiency in battery-powered user devices.

Habitat amount mediates the effect of fragmentation on a pollinator's reproductive performance, but not on its foraging behaviour.

Agricultural intensification, with its associated habitat loss and fragmentation, is among the most important drivers of the ongoing pollination crisis. In this quasi-experimental study, conducted in intensively managed vineyards in southwestern Switzerland, we tested the separate and interdependent effects of habitat amount and fragmentation on the foraging activity and reproductive performance of bumblebee Bombus t. terrestris colonies. Based on a factorial design, we selected a series of spatially replicated study sites across a dual gradient of habitat amount (area of ground-vegetated vineyards) and fragmentation (density of ground-vegetated vineyard fields) in a landscape predominantly consisting of vineyards with bare grounds. The foraging activity of individual bumblebees was measured using the radio frequency identification (RFID) technology, and we assessed final colony size to measure reproductive performance. We found an interactive effect of habitat amount and fragmentation on colony size. More specifically, the degree of fragmentation had a negative effect on bumblebee colony size when the amount of habitat was low, while it had a weak positive effect on colony size in landscapes with high amounts of habitat. At the level of individual vineyard fields, ground vegetation cover exerted a positive effect on bumblebee colony size. Fragmentation, but not habitat amount, significantly influenced foraging activity, with more foraging trips in sites with lower degrees of fragmentation. Our results emphasise the importance of studying the separate and interdependent effects of habitat amount and fragmentation to understand their influence on pollinators, providing guidance for optimising the spatial configuration of agricultural landscapes from a biodiversity viewpoint.

Influence of Chemical Osmosis on Solute Transport and Fluid Velocity in Clay Soils

AbstractSolute transport through the clay liner is a significant process in many waste landfills or unmanaged landfills. At present, researchers mainly focus on the test study about semi-membrane property of clay material, however, the influence of chemical osmosis caused by membrane effect on solute transport and fluid velocity is insufficient. In this investigation, based on the classical advection-diffusion equation, a one-dimensional solute transport model for low-permeable clay material has been proposed, in which the coupled fluid velocity related with hydraulic gradient and concentration gradient is introduced, and the semi-membrane effect is embodied in the diffusion mechanism. The influence of chemical osmosis on fluid velocity and solute transport has been analyzed using COMSOL Multiphysics software. The simulated results show that chemical osmosis has a significant retarded action on fluid velocity and pollutant transport. The proposed model can effectively reveal the change in process of coupled fluid velocity under dual gradient and solute transport, which can provide a theoretical guidance for similar fluid movement in engineering.

Dual gradient microstructure to simultaneously improve strength and electrical conductivity of aluminum wire

High strength and high electrical conductivity are needed for the usage of aluminum wire in high-voltage lines. Strength and electrical conductivity are contradictory in metallic materials. Improving strength comes with the sacrifice of electrical conductivity. Here we produced a dual gradient microstructure to improve the strength of aluminum wire without compromising electrical conductivity. Aluminum wires with gradient microstructures and dual gradient microstructures were processed through clockwise torsion and subsequent anti-clockwise torsion. Compared with the gradient microstructural aluminum, aluminum with dual gradient microstructures possesses higher strength and higher electrical conductivity. Microstructural characterizations and numerical simulations further reveals that dual gradient grain size provides extra strain hardening and less electrical resistivity. This explains the high strength and high electrical conductivity in aluminum wire with dual gradient microstructure.

Design of a compact and broadband terahertz polarization splitter based on gradient dual-core photonic crystal fiber

We report a broadband polarization splitter based on polyethylene photonic crystal fiber with microstructured dual refractive index gradient cores. These dual cores consist of a properly optimized arrangement of air holes such that for individual fibers $x$x-polarized modes have large effective indices difference, while this index difference is almost zero for their $y$y-polarized modes, leading to efficient coupling between the $y$y-polarized modes. We have shown that by proper optimization of gradience created in the arrangement of air holes, efficient polarization splitting can be achieved for a broad range of terahertz frequencies. Device length and extinction ratio have been calculated numerically for the proposed configuration. Device length of $\sim{1.96}$∼1.96 to $\sim {60}\;{\rm cm}$∼60cm was found to be appropriate for frequencies in the 0.4-1.0 THz range to have high extinction ratios: $ - {38}$-38 to $ - {49}\;{\rm dB}$-49dB and $ - {15}$-15 to $ - {23}\;{\rm dB}$-23dB for the $x$x and $y$y polarizations, respectively. The bending loss for the proposed design is quite low: $\sim{0.05}\;{\rm dB/m}$∼0.05dB/m at 1 THz for the bend radius of 1 cm. These results suggest that a compact, low-loss, and broadband polarization splitter with very high extinction ratios can be achieved by wrapping the fiber around a small mandrel.

Distributed optimal load frequency control considering nonsmooth cost functions

This work addresses the distributed frequency control problem in power systems considering controllable load with a nonsmooth cost. The nonsmoothness exists widely in power systems, such as tiered price, greatly challenging the design of distributed optimal controllers. In this paper, we first formulate an optimization problem that minimizes the nonsmooth regulation cost, where both capacity limits of controllable load and tie-line flow are considered. Then, a distributed controller is derived based on the primal–dual gradient method, where the Clark generalized gradient is utilized to address the nonsmoothness. We also prove the optimality of the equilibrium of the closed-loop system as well as its stability. Simulations carried out on the IEEE 68-bus system verifies the effectiveness of the proposed method.

Terahertz dual phase gradient metasurfaces: high-efficiency binary-channel spoof surface plasmon excitation

Spoof surface plasmon meta-couplers are compact antennas that link propagating waves and surface waves. However, most of them are designed with a fixed phase gradient and channel for the incident waves with specific polarization, which limits their further applications in multichannel scenarios. In this Letter, a new, to the best of our knowledge, method that combines the Brillouin zone folding theory with the generalized Snell’s law is proposed. We demonstrate that when the phase gradient of the metasurface is large enough, Brillouin zone folding effect will occur, which will create dual phase gradient space in a single metasurface. With this method, we design two novel terahertz meta-couplers with functionalities of symmetrical and asymmetrical binary-channel spoof surface plasmon (SSP) excitation. Furthermore, finite element method simulations are performed to demonstrate their functionalities. Considering the orthogonality of the incident waves, there can be a total of four independent space channels to excite SSPs on one metasurface. This work may open up new routes in multichannel SSP meta-couplers and multibeam surface wave antennas.

A finite volume element scheme with a monotonicity correction for anisotropic diffusion problems on general quadrilateral meshes

We construct a finite volume element scheme with a monotonicity correction for anisotropic diffusion problems on general quadrilateral meshes, where the strict convexity restriction on the meshes is removed. The main contributions of this paper include three aspects. Firstly, the classical finite volume element (C-FVE) method is extended to severely distorted quadrilateral meshes even with concave cells by virtue of a new overlapping dual partition and a new gradient approximation. In fact, the choice of this dual partition and gradient approximation is also conducive to the construction of a monotone scheme. Secondly, a new monotonicity correction is suggested, based on which we obtain a monotone finite volume element (M-FVE) method. The resulting M-FVE method still keeps the local conservation and is easy for implementation. Finally, we analyze theoretically the truncation error and the monotonicity for this scheme. Besides, the existence of a solution to this nonlinear scheme is proved by applying the Brouwer's fixed point theorem. Numerical results demonstrate that the M-FVE method has the approximate second-order accuracy and preserves well the positivity of the solution for both isotropic and anisotropic diffusion problems on severely distorted quadrilateral meshes.

Distributed Dual Gradient Tracking for Resource Allocation in Unbalanced Networks

This paper proposes a distributed dual gradient tracking algorithm (DDGT) to solve resource allocation problems over an unbalanced network, where each node in the network holds a private cost function and computes the optimal resource by interacting only with its neighboring nodes. Our key idea is the novel use of the distributed push-pull gradient algorithm (PPG) to solve the dual problem of the resource allocation problem. To study the convergence of the DDGT, we first establish the sublinear convergence rate of PPG for non-convex objective functions, which advances the existing results on PPG as they require the strong-convexity of objective functions. Then we show that the DDGT converges linearly for strongly convex and Lipschitz smooth cost functions, and sublinearly without the Lipschitz smoothness. Finally, experimental results suggest that DDGT outperforms existing algorithms.

Ag, Ge dual-gradient substitution for low-energy loss and high-efficiency kesterite solar cells

A generic Ag, Ge dual gradient substitution is proposed to minimize the bulk and interface recombination losses in kesterite solar cells.

Virtual Reality Image Technology Assists Training Optimization of Motion Micro-Time Scale

Virtual reality image local features are highly repetitive and are not easily affected by target occlusion, so research on virtual reality image local feature extraction techniques has received increasing attention. For the purpose of global scale selection, this article considers the virtual reality image in the global scope from the theoretical perspectives of the continuity of virtual reality images, the repeatability of virtual reality image features, the scale of scene virtual reality images in the global scope, and the visual saliency. This paper gives a general framework of multi-scale geometric analysis and particle swarm optimization virtual reality image matching algorithm. For the problem of virtual reality image matching, the original particle swarm optimization algorithm is improved. A more reasonable inertia weight change formula, a method for selecting the optimal solution when two objectives are optimized at the same time, and a method for selecting a reasonable input are designed. In this paper, performance evaluation experiments are performed on several feature description algorithms. The experimental results show that the descriptors constructed by these feature description algorithms are significantly more robust than SIFT (Scale Invariant Feature Transform) descriptors. The improved multi-scale geometric analysis and particle swarm optimization are robust due to the introduction of multiple support domains. It has the best discriminative ability, but at the same time, the introduction of multiple support domains leads to the worst real-time algorithm; DGOH (Dual Gradient Orientation Histogram) algorithm is more robust than FRDOH (Fast Repre-sentation Based on a Double Orientation Histogram) and SIFT algorithm, and DGOH algorithm has the best real-time performance.

An Online Learning Algorithm for Distributed Task Offloading in Multi-Access Edge Computing

This paper addresses the problem of distributed task offloading centred at individual user terminals in a cellular multi-access edge computing (MEC) system. We introduce an online learning-assisted algorithm based on distributed bandit optimization (DBO) to cope with time-varying cost and time-varying constraint functions with unknown statistics on-the-go. The proposed algorithm jointly exploits the projected dual gradient iterations and a greedy method as well as a single broadcast communicating the MEC states to the users at the end of each decision cycle to minimize task computing-communication delay in the long run at user terminals. To track the performance of the proposed online learning algorithm over time, we define a dynamic regret to assess the closeness of the underlying delay cost of the DBO to a clairvoyant dynamic optimum, and an aggregate violation metric to evaluate the asymptotic satisfaction of the constraints. We derive lower and upper bounds for dynamic regret as well as an upper-bound for the aggregate violation and show that the upper-bounds are sub-linear under sub-linear accumulated hindsight variations. The simulation results and comparisons confirm the effectiveness of the proposed algorithm in the long run.