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作者： Shaw, Calvin B. Yalavarthy, Phaneendra K. Supercomputer Education and Research Centre Indian Institute of Science Bangalore 560 012 India

The sparse estimation methods that utilize the lp-norm, with p being between 0 and 1, have shown better utility in providing optimal solutions to the inverse problem in diffuse optical tomography. These lp-norm-based regularizations make the optimization function nonconvex, and algorithms that implement lp-norm minimization utilize approximations to the original lp-norm function. In this work, three such typical methods for implementing the lp-norm were considered, namely, iteratively reweighted l1-minimization (IRL1), iteratively reweighted least squares (IRLS), and the iteratively thresholding method (ITM). These methods were deployed for performing diffuse optical tomographic image reconstruction, and a systematic comparison with the help of three numerical and gelatin phantom cases was executed. The results indicate that these three methods in the implementation of lp-minimization yields similar results, with IRL1 fairing marginally in cases considered here in terms of shape recovery and quantitative accuracy of the reconstructed diffuse optical tomographic images. © 2014 Optical Society of America.

关键词： approximation algorithms

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VLSI Architectures of Approximate Arithmetic Units Applied to Parallel Sensors Calibration

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IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-REGULAR PAPERS 2024年第3期71卷 1000-1013页

作者： da Rosa, Morgana Macedo Azevedo da Costa, Patricia Ucker Leleu da Costa, Eduardo Antonio Cesar Soares, Rafael I. Bampi, Sergio Univ Fed Pelotas UFPel Programade Posgrad Comp PPGC BR-96010770 Pelotas Brazil Univ Fed Rio Grande do Sul UFRGS PGMICRO BR-90010150 Porto Alegre Brazil Univ Catolica Pelotas UCPel Engn Elet & Comp MEEC BR-96015560 Pelotas Brazil

Approximate computing maximizes area and energysavings for a trade-off between quality and efficiency. Approx-imate arithmetic operators have emerged as an efficientalternative to design low-power VLSI circuits. This paper inves-tigates the design of approximate arithmetic operator unitsused in the calibration procedure for radio astronomy lightsensors - the so-called StEFCal (statistically efficient and fastcalibration) method. The StEFCal algorithm comprises arith-metic operations like a divider, square-accumulate (SAC), andmultiply-accumulate (MAC) units. The StEFCal circuit of thiswork explores the following arithmetic operators: i) two approx-imate squarer units from the literature, i.e., radix-4 (AxRSU) andSquASH, ii) two approximate iterative-based Newton-Raphson(NR) and Goldschmidt (GLD) dividers, iii) one approximateparallel prefix adder (AxPPA), and iv) a new approximateradix-4 multiplier (AxRMU), proposed in this work, exploredin the StEFCal multiply-accumulate circuit design. The AxRSUutilizes the parametersK1 andK2 to represent the number ofexact encoders for squarer- and conventional-partial products,respectively, subsequently replaced with approximate *** same principle applies to AxRMU, where the parameterKindicates the number of exact encoders for conventional-partialproducts, subsequently exchanged with approximate *** demonstrate the efficiency of StEFCal using the approximatearithmetic operators from the Pareto-optimal front that expressesthe area- and power-quality trade-off. The results show that usingthe AxRSU withK1=4 andK2=6, AxRMU, and AxPPA withK=16 and NR with one iteration has an MSE equal to 89.98dBand offers up to 158xenergy-savings compared to the exactStEFCal, and up to 25xmore energy-savings and 3.33xarea-savings compared with our previous work, 440xenergy-savingscompared to the accurate state-of-the-art, and 258xcomparedwith the approximate state-of-the-art.

关键词： Adders Calibration approximation algorithms Arithmetic Radio astronomy Very large scale integration Signal processing algorithms VLSI StEFCal AxRSU AxRMU AxPPA SquASH Newton-Raphson Goldschmidt

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An Arbitrary-Phase-Varying Digital Chirp Signal Generator Based on Improved CORDIC Algorithm and Trajectory Approximator

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IEEE ACCESS 2024年 12卷 135362-135371页

作者： Zhang, Haoran Chen, Minqi Wan, Shuqin Jiao, Zihao Hu, Shenglin Song, Peng China Elect Technol Grp Corp Res Inst 58 Wuxi 214026 Peoples R China Xi An Jiao Tong Univ Dept Microelect Xian 713599 Peoples R China Harbin Inst Technol Res Inst Intelligent Control & Syst Harbin 150001 Peoples R China

The digital chirp signal (DCS) is commonly used in modern radar system and ultrashort pulse application. The traditional method is using DDS device, but this method is limited by many restrictions, including device limit, cost limit and application range. In consideration of those restrictions, we propose a new method implemented on field programmable gate array (FPGA). It has a composite architecture featuring an improved CORDIC algorithm core to generate arbitrary-phase-varying DCS and a trajectory approximator to eliminate uncertain error. The improved CORDIC algorithm core is embedded in a finite state machine (FSM) which make the design more efficient. Meanwhile, the trajectory approximator is used to counteract the uncertainty influence from the output error and disturbance. An experiment is built for the efficiency and validation of the proposed method. We generated a DCS with frequency bandwidth of 1.25MHz, starting from 0Hz to 1.25MHz and its pulse duration is 81.92us. Another experiment is done to validate the feasibility generating nonlinear phase chirp digital signal. According to the results of the practical implementation in FPGA, the main advantage of the proposed technique is that it can reduce the usage of Memory, Slice Register and Logic gates of FPGA.

关键词： approximation algorithms Field programmable gate arrays Trajectory Logic Chirp Table lookup Radar antennas Scaling-free coordinate rotation digital computer (CORDIC) algorithm finite state machine (FSM) discrete-time PID controller neural network FPGA

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Maximizing the number of rides served for time-limited Dial-a-Ride

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OPTIMIZATION METHODS & SOFTWARE 2024年第6期39卷 1407-1427页

作者： Anthony, Barbara M. Chung, Christine Das, Ananya Yuen, David Southwestern Univ Dept Math & Comp Sci Georgetown TX USA Connecticut Coll Comp Sci Dept New London CT USA Middlebury Coll Comp Sci Dept Middlebury VT USA 1001 E Univ Ave Georgetown TX 78626 USA

We consider a variant of the offline Dial-a-Ride problem on weighted graphs with a single server where each request has a source and destination. The server's goal is to serve requests so as to maximize the total number of requests served within a given time limit. We first prove that no polynomial-time algorithm will always serve the optimal number of requests, even when the algorithm's time limit is augmented by any factor c >= 1, unless P = NP. We also show that the approximation ratio is unbounded for a reasonable class of algorithms for this problem. We then present k-Sequence, an algorithm that repeatedly serves the fastest set of k remaining requests. We show that k-Sequence has approximation ratio at most 2 + [lambda]/k and at least 1 + lambda/k, where lambda denotes the aspect ratio of the graph, and that the ratio 1 + lambda/k is tight when 1 + lambda/k >= k. We also show that even as k grows beyond the size of lambda, the ratio never improves below 9/7.

关键词： approximation algorithms dial-a-ride problems paratransit problems prize collection

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Residual Analysis-Based Model Improvement for State Space Models With Nonlinear Responses

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IEEE TRANSACTIONS ON EMERGING TOPICS IN COMPUTATIONAL INTELLIGENCE 2024年第2期8卷 1728-1743页

作者： Shen, Xun Zhuang, Jiancang Osaka Univ Grad Sch Engn Osaka 5650871 Japan Inst Stat Math Tokyo 1908562 Japan

This paper concerns the learning problem of state space models with unknown nonlinear responses. A state space model with unknown nonlinear responses has a linear state equation, while the observation equation consists of linear and nonlinear parts. The model structure of the nonlinear part is unknown. This paper uses the neural network model to approximate the unknown nonlinear part of the observation equation. A residual analysis-based algorithm is proposed to iteratively improve the performance of hidden state inference and parameter estimation for state space models with unknown nonlinear responses. The essence of the proposed algorithm is to use the residual of the linear model to learn the unknown nonlinear part. We show that the proposed algorithm can improve the model iteratively by applying the minorization-maximization principle. A numerical example and a battery capacity estimation case study have been conducted to validate the proposed method. The results show that the proposed method can perform better on parameter estimation and hidden state inference than previously developed tools.

关键词： Mathematical models Maximum likelihood estimation Computational modeling Estimation Analytical models approximation algorithms Numerical models Extreme learning machine learning predictive models statistics time series analysis

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A Polynomial-Time approximation Scheme for Sequential Batch Testing of Series Systems

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OPERATIONS RESEARCH 2022年第2期70卷 1153-1165页

作者： Segev, Danny Shaposhnik, Yaron Tel Aviv Univ Sch Math Sci Dept Stat & Operat Res IL-69978 Tel Aviv Israel Univ Rochester Simon Business Sch Rochester NY 14627 USA

We study a recently introduced generalization of the classic sequential testing problem for series systems, consisting of multiple stochastic components. The conventional assumption in such settings is that the overall system state can be expressed as an AND function, defined with respect to the states of individual components. However, unlike the classic setting, rather than testing components separately, one after the other, we allow aggregating multiple tests to be conducted simultaneously, while incurring an additional set-up cost. This feature is present in numerous practical applications, where decision makers are incentivized to exploit economy of scale by testing subsets of components in batches. The main contribution of this paper is to devise a polynomial-time approximation scheme (PTAS) for the sequential batch-testing problem, thereby significantly improving on the constant-factor performance guarantee of 6.829 + epsilon due to Daldal et al. [Daldal R, Ozluk O, Selcuk B, Shahmoradi Z, Unluyurt T (2017) Sequential testing in batches. Ann. Oper. Res. 253(1):97-116.]. Our approach is based on developing and leveraging a number of techniques in approximate dynamic programming, based on ideas related to efficient enumeration methods, state-space collapse, and charging schemes. These theoretical findings are complemented by extensive computational experiments, where we demonstrate the practical advantages of our methods.

关键词： sequential testing approximation algorithms PTAS dynamic programming

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Exploiting Structured Sparsity With Low Complexity Sparse Bayesian Learning for RIS-Assisted MIMO mmWave Channel Estimation

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IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY 2024年第5期73卷 6752-6764页

作者： Li, Weijie Lin, Zihuai Guo, Qinghua Vucetic, Branka Univ Sydney Sch Elect & Informat Engn Sydney NSW 2006 Australia Univ Wollongong Sch Elect Comp & Telecommun Engn Wollongong NSW 2522 Australia

As an emerging communication auxiliary technology, reconfigurable intelligent surface (RIS) is expected to play a significant role in the upcoming 6G networks. Due to its total reflection characteristics, it is challenging to implement conventional channel estimation algorithms. This work focuses on RIS-assisted MIMO communications. Although many algorithms have been proposed to address this issue, there are still ample opportunities for improvement in terms of estimation accuracy, complexity, and applicability. To fully exploit the structured sparsity of the multiple-input-multiple-output (MIMO) channels, we propose a new channel estimation algorithm called unitary approximate message passing sparse Bayesian learning with partial common support identification (UAMPSBL-PCI). Thanks to the mechanism of PCI and the use of UAMP, the proposed algorithm has a lower complexity while delivering enhanced performance relative to existing channel estimation algorithms. Extensive simulations demonstrate its excellent performance in various environments.

关键词： Channel estimation Millimeter wave communication MIMO communication Estimation Complexity theory approximation algorithms Reflection Reconfigurable intelligent surface channel estimation unitary approximate message passing sparse Bayesian learning

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Collect Spatiotemporally Correlated Data in IoT Networks With an Energy-Constrained UAV

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IEEE INTERNET OF THINGS JOURNAL 2024年第11期11卷 20486-20498页

作者： Xu, Wenzheng Shao, Heng Shen, Qunli Peng, Jian Huang, Wen Liang, Weifa Liu, Tang Yao, Xin-Wei Lin, Tao Das, Sajal K. Sichuan Univ Coll Comp Sci Chengdu 610065 Peoples R China City Univ Hong Kong Dept Comp Sci Hong Kong Peoples R China Sichuan Normal Univ Coll Comp Sci Chengdu 610101 Peoples R China Zhejiang Univ Technol Sch Comp Sci & Technol Hangzhou 310023 Peoples R China Zhejiang Univ Technol Inst Frontier & Interdisciplinary Sci Hangzhou 310023 Peoples R China Missouri Univ Sci & Technol Dept Comp Sci Rolla MO 65409 USA

Unmanned aerial vehicles (UAVs) are promising tools for efficient data collections of sensors in Internet of Things networks. Existing studies exploited both spatial and temporal data correlations to reduce the amount of collected redundant data, in which sensors are first partitioned into different clusters, a master sensor in each cluster then collects raw data from other sensors and compresses the received data. An energy-constrained UAV finally collects the maximum amount of compressed data from different master sensors. We however notice that the compressed data from only a portion of clusters are collected by the UAV in the existing studies, while the data from other clusters are not collected at all. In this article, we study a problem of finding a data collection trajectory for an energy-constrained UAV, so that the accumulative utility of collected data is maximized, where the accumulative utility measures the quality of spatiotemporally correlated data collected from different clusters. We propose a novel [1/(6+epsilon)] -approximation algorithm for the problem, where epsilon is a given constant with epsilon > 0. Experimental results with real data sets show that the accumulative utility by the proposed algorithm is at least 23% larger than those by the existing studies, and the number of clusters collected by the proposed algorithm is from 45% to 105% larger than those by the existing studies.

关键词： Sensors Autonomous aerial vehicles Data collection Correlation Internet of Things Spatial databases Clustering algorithms approximation algorithms mobile data collections spatial data correlations unmanned aerial vehicles (UAVs)

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Hamiltonian-Driven Adaptive Dynamic Programming With approximation Errors

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IEEE TRANSACTIONS ON CYBERNETICS 2022年第12期52卷 13762-13773页

作者： Yang, Yongliang Modares, Hamidreza Vamvoudakis, Kyriakos G. He, Wei Xu, Cheng-Zhong Wunsch, Donald C. Univ Sci & Technol Beijing Sch Automat & Elect Engn Beijing 100083 Peoples R China Univ Sci & Technol Beijing Inst Artificial Intelligence Beijing 100083 Peoples R China Michigan State Univ Mech Engn Dept E Lansing MI 48824 USA Georgia Tech Daniel Guggenheim Sch Aerosp Engn Atlanta GA 30332 USA Univ Macau Fac Sci & Technol State Key Lab Internet Things Smart City Macau Peoples R China Missouri Univ Sci & Technol Dept Elect & Comp Engn Rolla MO 65401 USA

In this article, we consider an iterative adaptive dynamic programming (ADP) algorithm within the Hamiltonian-driven framework to solve the Hamilton-Jacobi-Bellman (HJB) equation for the infinite-horizon optimal control problem in continuous time for nonlinear systems. First, a novel function, ``min-Hamiltonian,'' is defined to capture the fundamental properties of the classical Hamiltonian. It is shown that both the HJB equation and the policy iteration (PI) algorithm can be formulated in terms of the min-Hamiltonian within the Hamiltonian-driven framework. Moreover, we develop an iterative ADP algorithm that takes into consideration the approximation errors during the policy evaluation step. We then derive a sufficient condition on the iterative value gradient to guarantee closed-loop stability of the equilibrium point as well as convergence to the optimal value. A model-free extension based on an off-policy reinforcement learning (RL) technique is also provided. Finally, numerical results illustrate the efficacy of the proposed framework.

关键词： Costs Mathematical model Stability analysis approximation error approximation algorithms Dynamic programming Iterative algorithms Hamilton-Jacobi-Bellman (HJB) equation Hamiltonian-driven framework inexact adaptive dynamic programming (ADP) optimal control

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Improved Iterative Inverse Matrix approximation Algorithm for Zero Forcing Precoding in Large Antenna Arrays

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IEEE ACCESS 2022年 10卷 100964-100975页

作者： Ertug Zorkun, Aral Salas-Natera, Miguel Alejandro Rodriguez-Osorio, Ramon Martinez Univ Politecn Madrid ETSI Telecomunicac Madrid 28040 Spain Univ Politecn Madrid Informat Proc & Telecommun Ctr IPTC Madrid 28040 Spain

Precoding algorithms are used in massive multiple-input multiple-output (mMIMO) communication systems to ensure effective signal transmission. The zero-forcing (ZF) is one of the most common linear precoding algorithms used in MIMO and mMIMO systems. ZF precoding is complex to implement because it requires direct matrix inversion of the gram matrix. Iterative algorithms have been proposed for approximating matrix inversions. However, iterative algorithms require initial conditions and pre-computations to converge to the optimal transmitted signal vector. This paper proposes a new improved iterative algorithm that guarantees convergence under any circumstances without dependency on any optimized initial parameter or condition. The proposed algorithm is based on a three-step iterative and iterative generalized inverse matrix approximation algorithm. The proposed algorithm was verified using a new correlated channel model that included mutual coupling effects and gain and phase variances caused by radio frequency elements at a base station (BS). The computational complexity of the proposed algorithm was then computed. This study analyzes and compares the bit error rate (BER) performance of the proposed algorithm with that of prominent existing algorithms. Moreover, the sum-rate performance of the proposed algorithm was analyzed. Simulations were performed under both correlated and uncorrelated channel conditions, for comparison and analysis. The simulation results demonstrate that the proposed algorithm outperforms the compared algorithms in terms of the convergence and convergence rates.

关键词： approximation algorithms Precoding Convergence Iterative algorithms Classification algorithms Antenna arrays Channel models Adaptive antenna system approximate matrix inversion iterative algorithms massive MIMO ZF~precoding

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