Fast Convergent Algorithm Research Articles

Subgradient-projection-based stable phase-retrieval algorithm for X-ray ptychography.

X-ray ptychography is a lensless imaging technique that visualizes the nano-structure of a thick specimen which cannot be observed with an electron microscope. It reconstructs a complex-valued refractive index of the specimen from observed diffraction patterns. This reconstruction problem is called phase retrieval (PR). For further improvement in the imaging capability, including expansion of the depth of field, various PR algorithms have been proposed. Since a high-quality PR method is built upon a base PR algorithm such as ePIE, developing a well performing base PR algorithm is important. This paper proposes an improved iterative algorithm named CRISP. It exploits subgradient projection which allows adaptive step size and can be expected to avoid yielding a poor image. The proposed algorithm was compared with ePIE, which is a simple and fast-convergence algorithm, and its modified algorithm, rPIE. The experiments confirmed that the proposed method improved the reconstruction performance for both simulation and real data.

Fast High-Precision Bisection Feedback Search Algorithm and Its Application in Flattening the NURBS Curve

It is important to accurately calculate flattening points when reconstructing ship hull models, which require fast and high-precision computation. However, some search algorithms, such as the bisection method, iterate near the optimal value too many times before converging in high-precision computation. The paper proposes a fast high-precision bisection feedback search (FHP-BFS) algorithm to solve the problem. In the FHP-BFS algorithm, the Newton–Raphson (NR) method is adopted to accelerate the convergence speed by considering the iteration characteristics of subintervals. Furthermore, a new feedback mechanism is proposed to control the feedback directions. In addition, an acceleration algorithm, called the interval reformation method, is used to guide the FHP-BFS algorithm for fast convergence. Finally, the flattening algorithm is improved by the FHP-BFS algorithm. In the comparative experiments, the practical efficacy of the FHP-BFS algorithm is first demonstrated, and then the optimal range of the threshold precision is determined. Next the FHP-BFS algorithm is compared to the best existing algorithms. Finally, the performance of the improved flattening algorithm is verified. The experiments demonstrate that the FHP-BFS algorithm has optimal performance among the compared algorithms, and it has an improved computation efficiency while maintaining robustness. The improved flattening algorithm reduces the computation time, ensures smoothness and meets practical engineering requirements.

A Fast Convergent Ordered-Subsets Algorithm With Subiteration-Dependent Preconditioners for PET Image Reconstruction.

We investigated the imaging performance of a fast convergent ordered-subsets algorithm with subiteration-dependent preconditioners (SDPs) for positron emission tomography (PET) image reconstruction. In particular, we considered the use of SDP with the block sequential regularized expectation maximization (BSREM) approach with the relative difference prior (RDP) regularizer due to its prior clinical adaptation by vendors. Because the RDP regularization promotes smoothness in the reconstructed image, the directions of the gradients in smooth areas more accurately point toward the objective function's minimizer than those in variable areas. Motivated by this observation, two SDPs have been designed to increase iteration step-sizes in the smooth areas and reduce iteration step-sizes in the variable areas relative to a conventional expectation maximization preconditioner. The momentum technique used for convergence acceleration can be viewed as a special case of SDP. We have proved the global convergence of SDP-BSREM algorithms by assuming certain characteristics of the preconditioner. By means of numerical experiments using both simulated and clinical PET data, we have shown that the SDP-BSREM algorithms substantially improve the convergence rate, as compared to conventional BSREM and a vendor's implementation as Q.Clear. Specifically, SDP-BSREM algorithms converge 35%-50% faster in reaching the same objective function value than conventional BSREM and commercial Q.Clear algorithms. Moreover, we showed in phantoms with hot, cold and background regions that the SDP-BSREM algorithms approached the values of a highly converged reference image faster than conventional BSREM and commercial Q.Clear algorithms.

Fast-Converging Constant Modulus Algorithm with Variable Step Size for Multibeam Massive MIMO

Fast-Converging Constant Modulus Algorithm with Variable Step Size for Multibeam Massive MIMO

Adolescent Identity Search Algorithm Based on Fast Search and Balance Optimization for Numerical and Engineering Design Problems.

This paper proposed a fast convergence and balanced adolescent identity search algorithm (FCBAISA) for numerical and engineering design problems. The main contributions are as follows. Firstly, a hierarchical optimization strategy is proposed to balance the exploration and exploitation better. Secondly, a fast search strategy is proposed to avoid the local optimization and improve the accuracy of the algorithm; that is, the current optimal solution combines with the random disturbance of Brownian motion to guide other adolescents. Thirdly, the Chebyshev functional-link network (CFLN) is improved by recursive least squares estimation (RSLE), so as to find the optimal solution more effectively. Fourthly, the terminal bounce strategy is designed to avoid the algorithm falling into local optimization in the later stage of iteration. Fifthly, FCBAISA and comparison algorithms are tested by CEC2017 and CEC2022 benchmark functions, and the practical engineering problems are solved by algorithms above. The results show that FCBAISA is superior to other algorithms in all aspects and has high precision, fast convergence speed, and excellent performance.

FAST CONVERGENCE METHOD FOR GLOBAL OPTIMAL 4DOF REGISTRATION

Abstract. Four degrees of freedom (4DoF) registration is a class of point cloud registration problems for finding a rigid transformation to align two point clouds under the constraint that the rigid transformation is composed of a three-dimensional (3D) translation and 1D rotation. This constraint is suitable to align scan pairs acquired using modern terrestrial Light Detection and Ranging (LiDAR) scanners, the scans of which can share the direction of gravity as the Z-axis due to such scanners using tripods or internal inclinometers. We propose a fast convergence method for global optimal 4DoF registration. The proposed method consists of (i) our newly developed 4DoF registration model formulated as an optimization problem involving the cylindrical norm to measure the distance between two points, and (ii) a fast convergence algorithm to find a global optimal solution of the model. We experimentally demonstrated that the proposed method reduced the number of iterations to convergence and computation time compared with a current 4DoF registration method, especially when the given scan pairs are similar but cannot be aligned, which often appears in registration of multiple point clouds.

Optimal Sizing of Different Energy Sources in an Isolated Hybrid Microgrid Using Turbulent Flow Water-Based Optimization Algorithm

This paper proposes a relatively new optimization algorithm namely the Turbulent Flow Water-Based Optimization (TFWO) to find the optimal size of a hybrid isolated microgrid generation. Moreover, validation of the proposed algorithm is proved through a comprehensive comparison with three robust performance and fast convergence algorithms which are the Harris Hawks Optimization (HHO), Whale Optimization Algorithm (WOA) and Jellyfish Search Optimizer (JSO). Two topologies with different renewable sources were considered in studying which are based on the meteorological data of the Zafarana area, a site located on the eastern coast of Egypt. The study minimizes the annual system cost (ASC) and CO₂ emissions of the proposed hybrid system while considering the following constraints: Loss of Power Supply Probability (LPSP), Fraction Renewable (FR) and System Excess Energy Ratio (EER). Violation of constraints is penalized by including a penalty factor into the objective function that varies according to the amount of the violation. Moreover, a sensitivity study is presented at the end of the paper through Load variation, irradiance variation, wind speed variation, and diesel generator efficiency decreasing. Results show not only the robustness and the fast convergence of the TFWO algorithm but also its ability to minimize the annual system cost and emission costs to values better than the aforementioned optimization techniques.

LOKO: Localization-aware Roll-out Planning for Future Mobile Networks

The roll-out phase of the next generation of mobile networks (5G) has started and operators are required to devise deployment solutions while pursuing localization accuracy maximization. Enabling location-based services is expected to be a unique selling point for service providers now able to deliver critical mobile services, e.g., autonomous driving, public safety, remote operations. In this paper, we propose a novel roll-out base station placement solution that, given a Throughput-Positioning Ratio (TPR) target, selects the location of new-generation base stations (among available candidate sites) such that the throughput and localization accuracy are jointly maximized. Moving away from the canonical position error bound (PEB) analysis, we develop a realistic framework in which each positioning measurement is affected by errors depending upon the actual wireless channel between the measuring base station and the target device. Our solution, referred to as LOKO, is a fast-converging algorithm that can be readily applied to current 5G (or future) roll-out processes. LOKO is validated by means of an exhaustive simulation campaign considering real existing deployments of a major European network operator as well as synthetic scenarios.

Efficient Design of Scaled Rectangular (Saramäki) Window

A rectangular-window sidelobe magnitude reduction method by widening the main lobe width was proposed by Saramäki. A technique for trading off main lobe width against sidelobe magnitude for any arbitrary window was reported by Lim et al.; a fast convergence algorithm for its implementation was proposed by the same authors in another article, where the derivatives of the window function are expressed in Chebyshev polynomials which have high arithmetic complexity. All the coefficients of a rectangular-window are equal; this special property is exploited, in this paper, for deriving the window function’s derivatives without the use of Chebyshev polynomials resulting in a great reduction in the arithmetic complexity.

Low-Complexity Algorithm for Outage Optimal Resource Allocation in Energy Harvesting-Based UAV Identification Networks

We study an unmanned aerial vehicle (UAV) identification network equipped with an energy harvesting (EH) technique. In the network, the UAVs harvest energy through radio frequency (RF) signals transmitted from ground control stations (GCSs) and then transmit their identification information to the ground receiver station (GRS). Specifically, we first derive a closed-form expression of the outage probability to evaluate the network performance. Then we obtain the closed-form expression of the optimal time allocation when the bandwidth is equally allocated to the UAVs. We also propose a fast-converging algorithm for time and the bandwidth allocation, which is necessary for the UAV environment with high mobility, to optimize the outage performance of EH-based UAV identification network. Simulation results show that the proposed algorithm outperforms the conventional bisection algorithm and achieves near-optimal performance.

General simultaneous motion estimation and image reconstruction (G-SMEIR)

To achieve better performance for 4D multi-frame reconstruction with the parametric motion model (MF-PMM), a general simultaneous motion estimation and image reconstruction (G-SMEIR) method is proposed. In G-SMEIR, projection domain motion estimation and image domain motion estimation are performed alternatively to achieve better 4D reconstruction. This method can mitigate the local optimum trapping problem in either domain. To improve computational efficiency, the image domain motion estimation is accelerated by adapting fast convergent algorithms and graphics processing unit (GPU) computing. The proposed G-SMEIR method is tested using a cone-beam computed tomography (CBCT) simulation study of 4D XCAT phantom at different dose levels and compared with 3D total variation-based reconstruction (3D TV), 4D reconstruction with image domain motion estimation (IM4D), and SMEIR. G-SMEIR shows strong denoising capability and achieves similar performance at regular dose and half dose. The root mean squared error (RMSE) of G-SMEIR is the best among the four methods and improved about 12% over SMEIR for all respiratory phase images at full dose. G-SMEIR also achieved the best structural similarity index (SSIM) values among all methods. More importantly, G-SMEIR leads to more than 40% improvement of the mean deviation from the phantom tumor motion over SMEIR. A preliminary patient CBCT image reconstruction also shows better image quality of G-SMEIR than that of the frame-by-frame reconstruction (3D TV) and MF-PMM either using image domain motion estimation (IM4D) or using projection domain motion estimation (SMEIR) alone. G-SMEIR with a flexible combination of image domain and projection domain motion estimation provides an effective tool for 4D tomographic reconstruction.

Signed Convex Combination of Fast Convergence Algorithm to Generalized Sidelobe Canceller Beamformer for Multi-Channel Speech Enhancement

In speech communication applications such as teleconferences, mobile phones, etc., the real-time noises degrade the desired speech quality and intelligibility. For these applications, in the case of multichannel speech enhancement, the adaptive beamforming algorithms play a major role compared to fixed beamforming algorithms. Among the adaptive beamformers, Generalized Sidelobe Canceller (GSC) beamforming with Least Mean Square (LMS) Algorithm has the least complexity but provides poor noise reduction whereas GSC beamforming with Combined LMS (CLMS) algorithm has better noise reduction performance but with high computational complexity. In order to achieve a tradeoff between noise reduction and computational complexity in real-time noisy conditions, a Signed Convex Combination of Fast Convergence (SCCFC) algorithm based GSC beamforming for multi-channel speech enhancement is proposed. This proposed SCCFC algorithm is implemented using a signed convex combination of two Fast Convergence Normalized Least Mean Square (FCNLMS) adaptive filters with different step-sizes. This improves the overall performance of the GSC beamformer in real-time noisy conditions as well as reduces the computation complexity when compared to the existing GSC algorithms. The performance of the proposed multi-channel speech enhancement system is evaluated using the standard speech processing performance metrics. The simulation results demonstrate the superiority of the proposed GSC-SCCFC beamformer over the traditional methods.

Distributed Secondary Control of Islanded Microgrids for Fast Convergence Considering Arbitrary Sampling

This paper proposes a novel distributed secondary control of MGs for fast convergence considering asynchronous sampling. With the employment of the algorithm, optimal power sharing and voltage restoration are implemented simultaneously. First, the hierarchical control objectives concerned with economic operation and voltage quality are introduced. Then, the execution process of the fast convergence algorithm is described for weighted average state estimation, with the illustration of corresponding features and the application in cooperative control. Further, the relevant stability issue is discussed based on large-signal dynamic modeling and a sufficient stability condition is derived based on the Lyapunov–Krasovskii theory. Our approach offers superior reliability, flexibility and robustness because of the loose implementation in terms of its performance concern, which is essential when the distributed consensus protocol is likely to yield toward deviation or even instability under arbitrary sampling and delays. The effectiveness of the proposed methodology is verified via simulations.

Distributed Algorithms for Average Consensus of Input Data With Fast Convergence

This paper proposes fast convergent distributed algorithms for weighted average consensus of input data. For acyclic graphs, we give an algorithm that converges to the exact weighted average consensus in a finite number of iterations, equal to the graph diameter. For loopy (cyclic) graphs, we offer two remedies. In the first one, we give another distributed algorithm to enable our average consensus algorithm applicable to a loopy graph by converting it into a spanning tree. In the second one, we consider a slightly modified average consensus problem whose optimal solution approximates the consensus solution with arbitrary precision, and give a modified average consensus algorithm with guaranteed exponential convergence to the optimal solution. The proposed average consensus algorithms enjoy low complexities, robustness to transmission adversaries, and asynchronous implementation. Our algorithms are conceptually different from the popular graph Laplacian approach, and converge much faster than the latter approach.

Efficient Algorithms for Rotation Averaging Problems

The rotation averaging problem is a fundamental task in computer vision applications. It is generally very difficult to solve due to the nonconvex rotation constraints. While a sufficient optimality condition is available in the literature, there is a lack of a fast convergent algorithm to achieve stationary points. In this paper, by exploring the problem structure, we first propose a block coordinate descent (BCD)-based rotation averaging algorithm with guaranteed convergence to stationary points. Afterwards, we further propose an alternative rotation averaging algorithm by applying successive upper-bound minimization (SUM) method. The SUM-based rotation averaging algorithm can be implemented in parallel and thus is more suitable for addressing large-scale rotation averaging problems. Numerical examples verify that the proposed rotation averaging algorithms have superior convergence performance as compared to the state-of-the-art algorithm. Moreover, by checking the sufficient optimality condition, we find from extensive numerical experiments that the proposed two algorithms can achieve globally optimal solutions.

An energy efficient IoD static and dynamic collision avoidance approach based on gradient optimization

Internet of Drones (IoD) formation offers a wide variety of applications in military and civilian environments. In highly congested terrain, dynamic and static obstacles have a critical impact on IoD performance. One of the critical challenges in IoD missions is avoiding obstacles for successfully and safely completing their tasks. The limited flight time of a drone is another challenge. Thus, IoD has to be provided by an intelligent and accurate energy-efficient collision avoidance algorithm in which IoD paths are modified online to guarantee drones safety. This paper presents an energy-efficient strategy to avoid static and dynamic collisions with minimum energy required for drones to reach their destinations safely. We develop a novel algorithm to avoid multiple static and dynamic obstacles of different sizes within a limited detection range with energy consumption minimization. To do so, the gradient-based approach is utilized in the proposed algorithm for fast and quick convergence. Furthermore, the proposed algorithm allows drones to be in hovering or backtracking states; or they can fly vertically in other cases. More importantly, the results validate the efficiency and accuracy of the proposed algorithm in a dense environment that involves high collision risk with obstacle relative speed up to 10 meters/sec.

A fast-convergence algorithm for reliability analysis based on the AK-MCS

In the field of reliability engineering, assessing the probability of failure of an event is usually a computationally demanding task. One way of tackling this issue is by metamodelling, in which the original computational-expensive model is approximated by a simpler metamodel. A method called AK-MCS for Active learning reliability method combining Kriging and Monte Carlo Simulation, was developed for the metamodel construction, and proved effective in reliability analysis. However, the performance of the AK-MCS algorithm is sensitive to the candidate size and the Kriging trend. Moreover, it cannot take advantage of parallel computing, a highly efficient way to speed up the simulation process. Focusing on the identified issues, this study proposes three methods to improve algorithm performance: the candidate size control method, multiple trends method, and weighted clustering method. These three methods are integrated into the AK-MCS structure, with their individual and combined performances being tested using four examples. Results suggest that all three methods contribute to the improvement of algorithm efficiency. When the three methods working together, the computational time is reduced significantly, and in the meantime, higher accuracy can be achieved.

Distributed Algorithms for Spectral and Energy-Efficiency Maximization of K-User Interference Channels

In this paper, we propose a cooperative distributed framework to optimize a variety of rate and energy-efficiency (EE) utility functions, such as the minimum-weighted rate or the global EE, for the K-user interference channel. We focus on the single-input multiple-output (SIMO) case, where each user, based solely on local channel state information (CSI) and limited exchange information from other users, optimizes its transmit power and receive beamformer, although the framework can also be extended to the multiple-output multiple-input (MIMO) case. The distributed framework combines an alternating optimization approach with majorization-minimization (MM) techniques, thus ensuring convergence to a stationary point of the centralized cost function. Closed-form power update rules are obtained for some utility functions, thus obtaining very fast convergence algorithms. The receivers treat interference as noise (TIN) and apply the beamformers that maximize the signal-to-interference-plus-noise (SINR). The proposed cooperative distributed algorithms are robust against channel variations and network topology changes and, as our simulation results suggest, they perform close to the centralized solution that requires global CSI. As a benchmark, we also study a non-cooperative distributed framework based on the so-called “signal-to-leakage-plus-noise ratio” (SNLR) that further reduces the overhead of the cooperative version.

Fuzzy Finite-Time Command Filtering Output Feedback Control of Nonlinear Systems

This article presents a fuzzy finite-time command filtering output feedback control method for a class of nonlinear systems. A fast convergent output feedback control algorithm based on backstepping finite-time command filtering is developed. Fuzzy logic system is used to estimate uncertain functions in nonlinear systems. A fuzzy state observer is designed to measure the unknown state. The developed finite-time command filtering feedback control method overcomes well the computational complexity problem due to the calculation of the derivatives of virtual control signals. A compensation mechanism is also introduced to compensate for the error caused by the filter. The proposed method ensures not only that all signals in the closed-loop system are finite-time bound, but also that the tracking error converges to a small neighborhood around the origin. The effectiveness of the proposed method is demonstrated in the simulation results.

A hybrid recurrent neural network‐logistic chaos‐based whale optimization framework for heart disease prediction with electronic health records

AbstractHeart disease, known interchangeably as “Cardio Vascular Disease,” blocks the blood vessels in the heart and causes heart attack, chest pain, and stroke. Heart disease is one of the leading causes of morbidity and mortality worldwide and it is one of the major causes of morbidity and mortality globally and a trending topic in clinical data analysis. Assessing risk factors related to heart disease is considered as an important step in diagnosing the disease at an early stage. Clinical data present in the form of electronic health records (EHR) can be extracted with the aid of machine learning (ML) algorithms to provide valuable decisions and predictions. ML approaches also play a vital role in early diagnosis and therapeutic monitoring of heart disease. Several research works have been carried out recently to predict heart disease. To this end, we propose a novel hybrid recurrent neural network (RNN)‐logistic chaos‐based whale optimization (LCBWO) structured hybrid framework for predicting heart disease within 5 years using EHR data. Meanwhile, in the hybrid model established multilayer bidirectional LSTM is used for feature selection, LCBWO algorithm for structural improvement and fast convergence, and LSTM for disease prediction. This research used 10 cross‐validations to obtain generalized accuracy and error values. The findings and observations provided here are focused on the knowledge obtained from the EHR report. The results show that the proposed novel hybrid RNN‐LCBWO framework achieves a higher accuracy of 98%, a specificity of 99%, precision of 96%, Mathews correlation coefficient of 91%, F‐measure of 0.9892, an area under the curve value of 98%, and a prediction time of 9.23 seconds. The accurate predictions obtained from the comparative analysis shows the significant performance of our proposed framework.