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An efficient infinity norm minimization algorithm for under-determined inverse problems

DIGITAL SIGNAL PROCESSING 2025年 156卷

作者： Rateb, Ahmad M. Huaiyin Inst Technol Fac Elect & Informat Engn Meicheng Rd 1 Huaian 223002 Jiangsu Peoples R China

The problem of solving under-determined systems of linear equations with minimum peak magnitude (t degrees infinity infinity norm) has numerous applications in signal processing. These include Peak-to-Average Power Ratio (PAPR) reduction in MIMO-OFDM systems, vector quantization, approximate nearest neighbor search, optimal control in robotics, and power grid optimization. Several methods have been proposed to address this problem, but they often face limitations in computational speed or representation accuracy. Some methods also impose constraints on the frame matrix, such as restrictions on the type of its entries or its aspect ratio. In this paper, we present the Fast iterative Peak Shrinkage Algorithm (FIPSA), which iterates over feasible solutions to consistently reduce peak magnitude and provably converge to near-optimal solutions. Our experimental results, conducted across various frame matrix types and aspect ratios, demonstrate that FIPSA consistently achieves near-minimal t degrees infinity infinity norm values. In addition, it operates 1.3 to 7.3 times faster than previous methods, while maintaining an average representation error of 10-15. -15 . Notably, these advancements are achieved without imposing any constraints on the frame matrix.

关键词： Minimum peak representations Peak-to-average power ratio (PAPR) reduction Inverse problems Convex optimization iterative algorithms

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Adaptive Neural Control of Superheated Steam System in Ultra-Supercritical Units With Output Constraints Based on Disturbance Observer

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IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-REGULAR PAPERS 2025年

作者： Zhou, Zhongrui Zhang, Juan Wang, Yingchun Yang, Dongsheng Liu, Zeyi Northeastern Univ Coll Informat Sci & Engn Shenyang 110004 Liaoning Peoples R China

For the superheated steam temperature control system, an optimized disturbance observer and output-constrained control algorithm have been designed. Initially, the original system with output constraints is transformed into a system without any state constraints, suitable for backstepping design, through state transformation. Then, based on the concept of negative gradient optimization, a gain iterative disturbance observer is constructed, which dynamically improves the control accuracy of the system compared to a constant gain disturbance observer. Finally, an adaptive neural control scheme based on the gain iterative disturbance observer is proposed, proving that all output states are constrained within predefined bounds, and all closed-loop signals are semi-globally uniformly bounded. The effectiveness of the proposed scheme is demonstrated through a simulation example of the superheated steam temperature system.

关键词： Disturbance observers Temperature distribution Accuracy Vectors Power generation Optimization Mathematical models Predictive control iterative algorithms Backstepping Superheated steam temperature system output constraints disturbance observer

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A Riccati Matrix Equation Solver Design Based Neurodynamics Method and Its Application

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IEEE Transactions on Automation Science and Engineering 2025年 22卷 15163-15176页

作者： Pingdan Xiao Junjie Fang Zhengmiao Wei Yu Dong Sichun Du Shiping Wen Qinghui Hong College of Computer Science and Electronic Engineering Hunan University Changsha China Australian AI Institute Faculty of Engineering and Information Technology University of Technology Sydney Ultimo NSW Australia

Riccati matrix equation (RME), a critical nonlinear matrix equation in autonomous driving and deep learning. However, memory-compute separation in traditional solving systems leads to latency and inefficiency when solving nonlinear equations, particularly under real-time requirements. Existing hardware lacks dedicated accelerators for RME, no specialized solvers quick addressing its nonlinear complexity. To address this issue, we propose a novel RME solver based on a memristive array, which leverages the parallel and fast computing advantages of analog circuits to quickly solve any order RME. Inspired by Neurodynamics for non-linear matrix equations, we first introduce an innovative Neurodynamics-based RME solving algorithm specifically designed from an analog circuit perspective. Based on this algorithm, we constructed a pioneering closed-loop analog circuit solver, overcoming bottlenecks in using circuits for such nonlinear matrix equations. Our evaluation demonstrates that the proposed solver achieves over 90% accuracy for a 128th-order parameter Riccati matrix equation. Compared to traditional digital processors, the solver offers significant energy efficiency advantages and is three orders of magnitude faster than CPU. Additionally, the solver successfully accelerates our proposed dung beetle optimizer-linear quadratic control algorithm for vehicle suspension control, achieving high precision while significantly reducing time and energy consumption compared to CPU and GPU. Note to Practitioners—The motivation for this study arises from the need for Riccati matrix equation in real world applications. Currently the main factors leading to the high time complexity of Riccati matrix equation (e.g., in the optimal algorithm solving, trajectory tracking and autonomous driving) originate from the large number of iterative computations, and the nonlinear structure of its essence. As such, the work in this paper propose a Neurodynamics-based algorithm for solving nonlin

关键词： Mathematical models Analog circuits Neurodynamics Circuits Automation Accuracy iterative algorithms Energy consumption Costs Computer architecture

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Improved Bounds for Subband-Adaptive iterative Shrinkage/Thresholding algorithms

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IEEE TRANSACTIONS ON IMAGE PROCESSING 2013年第4期22卷 1373-1381页

作者： Zhang, Yingsong Kingsbury, Nick Univ Cambridge Dept Engn Cambridge CB1 2PZ England

This paper presents new methods for computing the step sizes of the subband-adaptive iterative shrinkage-thresholding algorithms proposed by Bayram & Selesnick and Vonesch & Unser. The method yields tighter wavelet-domain bounds of the system matrix, thus leading to improved convergence speeds. It is directly applicable to non-redundant wavelet bases, and we also adapt it for cases of redundant frames. It turns out that the simplest and most intuitive setting for the step sizes that ignores subband aliasing is often satisfactory in practice. We show that our methods can be used to advantage with reweighted least squares penalty functions as well as L1 penalties. We emphasize that the algorithms presented here are suitable for performing inverse filtering on very large datasets, including 3D data, since inversions are applied only to diagonal matrices and fast transforms are used to achieve all matrix-vector products.

关键词： Deconvolution iterative algorithms multiresolution sparsity wavelets

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Multidirection Gradient iterative Algorithm: A Unified Framework for Gradient iterative and Least Squares algorithms

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2022年第12期67卷 6770-6777页

作者： Chen, Jing Ma, Junxia Gan, Min Zhu, Quanmin Jiangnan Univ Sch Sci Wuxi 214122 Peoples R China Jiangnan Univ Sch Internet Things Engn Key Lab Adv Proc Control Light Ind Minist Educ Wuxi 214122 Peoples R China Qingdao Univ Coll Comp Sci & Technol Qingdao 266071 Peoples R China Univ West England Dept Engn Design & Math Bristol BS161QY England

In this article, a multidirection-based gradient iterative (GI) algorithm for Hammerstein systems with irregular sampling data is proposed. The algorithm updates the parameter estimates using several orthogonal directions at each iteration. The convergence rate is significantly improved with an increasing number of directions. The convergence property and two simulation examples are provided to demonstrate the effectiveness of the proposed algorithm. In addition, the multidirection-based GI algorithm establishes a relationship between the traditional GI and least squares (LS) algorithms. Thus, our algorithm that combines the LS and GI algorithms constructs an identification framework for a significantly wider class of systems.

关键词： Convergence Eigenvalues and eigenfunctions Computational modeling Mathematical models Load modeling Technological innovation iterative algorithms Computational load convergence rate gradient iterative (GI) algorithm Hammerstein system irregular sampling multidirection

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An iterative framework for sparse signal reconstruction algorithms

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SIGNAL PROCESSING 2015年 108卷 351-364页

作者： Ambat, Sooraj K. Hari, K. V. S. Indian Inst Sci Dept Elect Commun Engn Stat Signal Proc Lab Bangalore 560012 Karnataka India

It has been shown that iterative re-weighted strategies will often improve the performance of many sparse reconstruction algorithms. However, these strategies are algorithm dependent and cannot be easily extended for an arbitrary sparse reconstruction algorithm. In this paper, we propose a general iterative framework and a novel algorithm which iteratively enhance the performance of any given arbitrary sparse reconstruction algorithm. We theoretically analyze the proposed method using restricted isometry property and derive sufficient conditions for convergence and performance improvement. We also evaluate the performance of the proposed method using numerical experiments with both synthetic and real-world data. (C) 2014 Elsevier B.V. All rights reserved.

关键词： Compressed sensing Sparse recovery Sparse signal Signal reconstruction iterative algorithms

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Data-Driven Attack Detection and Identification for Cyber-Physical Systems Under Sparse Sensor Attacks: iterative Reweighted l2/l1 Recovery Approach

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IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-REGULAR PAPERS 2025年

作者： Wang, Jun-Lan Li, Xiao-Jian Northeastern Univ Coll Informat Sci & Engn Shenyang 110819 Peoples R China Northeastern Univ State Key Lab Synthet Automation Proc Ind Shenyang 110819 Peoples R China

This paper investigates the data-based attack detection and identification for cyber-physical systems (CPSs) under sparse sensor attacks. In order to improve the identification performance, a novel scheme based on an iterative reweighted l(2)/l(1) minimization algorithm is presented. Firstly, a threshold that characterizes the maximum number of identifiable attacks is determined. By introducing the reweighting technique, smaller weights are assigned to the relatively easy-to-identify attacks, namely, blocks with larger l(2)-norms, thus forcing the minimization to focus on the ones with smaller l(2)-norms. Then, the number of identifiable attacks is enhanced and a higher identification accuracy is guaranteed compared with the existing results. Finally, three examples are given to verify the effectiveness and advantages of the proposed scheme in both noisy and noiseless cases.

关键词： Vectors Noise Mathematical models Accuracy Minimization Cyber-physical systems Optimization Noise measurement iterative algorithms Security Attack detection and identification data-driven cyber-physical systems (CPSs) sparse attacks iterative reweighted l(2)/l(1)(IR-l(2)l(1)) minimization algorithm

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Robust Tensor Ring Decomposition for Urban Traffic Data Imputation

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IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS 2025年

作者： Yu, Linfang Guan, Chenyu Wang, Hao He, Yuxin Cao, Wenming Leung, Chi-Sing Shenzhen Univ Guangdong Multimedia Informat Serv Engn Technol Re Shenzhen 518060 Peoples R China State Key Lab Radio Frequency Heterogeneous Integr Shenzhen 518060 Peoples R China Guangdong Key Lab Intelligent Informat Proc Shenzhen 518060 Peoples R China Shenzhen Technol Univ Coll Urban Transportat & Logist Shenzhen 518118 Peoples R China City Univ Hong Kong Dept Elect Engn Hong Kong Peoples R China

In urban transportation systems, missing data and noise contamination are almost inevitable. To address the challenge of imputing traffic data corrupted by noise and outliers in real-world scenarios, this paper proposes a novel algorithm based on spatiotemporal tensor completion. The proposed method transforms observed data into three-dimensional spatiotemporal tensors and utilizes tensor ring decomposition for data completion. Furthermore, spatial and temporal information is incorporated into the model by utilizing the graph Laplacian matrix. To handle outliers, they are treated as unknown parameters, and the & ell;(0)-norm is introduced to ensure their sparsity, thereby achieving the Spatio-Temporal Tensor Completion model with & ell;(0)-norm term (STTC-& ell;(0)). The solution to the model is derived using the alternating optimization framework with the alternating direction method of multipliers. Then, we discuss the convergence of the solution method. To further enhance the efficiency of our proposed method, we combine the unrolling algorithm with our iterative optimization model, creating a lightweight and efficient neural network tailored for tensor completion, called STTC-& ell;(0)-NN. Extensive experiments conducted on real datasets demonstrate the superiority of our proposed method over several state-of-the-art methods across various experimental scenarios. It is worth noting that STTC-& ell;(0)-NN reduces computational time by one to two orders of magnitude compared to existing methods while maintaining or even improving imputation accuracy. The code is available at https://***/TCCofWANG/STTC-L0-and-STTC-L0-NN.

关键词： Tensors Imputation Noise Matrix decomposition Spatiotemporal phenomena Optimization Transportation iterative algorithms Accuracy Roads Urban traffic data tensor completion outliers sparsity optimization AO-ADMM

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Acceleration of iterative image restoration algorithms

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APPLIED OPTICS 1997年第8期36卷 1766-1775页

作者： Biggs, DSC Andrews, M []The authors are with the Department of Electrical Electronic Engineering University of Auckland Private Bag 92019 Auckland New Zealand.

A new technique for the acceleration of iterative image restoration algorithms is proposed. The method is based on the principles of vector extrapolation and does not require the minimization of a cost function. The algorithm is derived and its performance illustrated with Richardson-Lucy (R-L) and maximum entropy (ME) deconvolution algorithms and the Gerchberg-Saxton magnitude and phase retrieval algorithms. Considerable reduction in restoration times is achieved with little image distortion or computational overhead per iteration. The speedup achieved is shown to increase with the number of iterations performed and is easily adapted to suit different algorithms. An example R-L restoration achieves an average speedup of 40 times after 250 iterations and an ME method 20 times after only 50 iterations. An expression for estimating the acceleration factor is derived and confirmed experimentally. Comparisons with other acceleration techniques in the literature reveal significant improvements in speed and stability. (C) 1997 Optical Society of America.

关键词： image restoration acceleration deconvolution iterative algorithms vector extrapolation Richardson-Lucy maximum entropy Gerchberg-Saxton

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iterative image reconstruction algorithms based on cross-entropy minimization

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IEEE TRANSACTIONS ON IMAGE PROCESSING 1993年第1期2卷 96-103页

作者： Byrne, Charles L. Univ Massachusetts Dept Math Lowell MA 01854 USA

The cross-entropy (or Kullback-Leibler) distance between two nonnegative vectors a and b is KL(a,b) = Sigma a(n) log(a(n)/b(n)) + b(n) -a(n). Several well-known iterative algorithms for reconstructing tomographic images lead to solutions that minimize certain combinations of KL distances, and can be derived from alternating minimization of related KL distances between convex sets;these include the expectation maximization (EM) algorithm for likelihood maximization (ML), and the Bayesian maximum a posteriori (MAP) method with gamma-distributed priors, as well as the multiplicative algebraic reconstruction technique (MART). Each of these algorithms can be viewed as providing approximate nonnegative solutions to a (possibly inconsistent) linear system of equations, y = Px. In almost all cases, the ML problem has a unique solution (and so the EM iteration has a limit that is independent of the starting point) unless the system of equations y = Px has a nonnegative solution, regardless of the dimensions of y and x. We introduce the "simultaneous" MART (SMART) algorithm and prove convergence: for 0 < alpha, < 1, SMART converges to the x >= 0 for which alpha KL(Px, y) + (1 - alpha)KL(x, p) is minimized, where p denotes a prior estimate of the desired x;for alpha = 1, the SMART algorithm converges in the consistent case (as does MART) to the unique solution of y = Px minimizing KL(x,x(0)), where x(0) is the starting point for the iteration, and in the inconsistent case, to the unique nonnegative minimizer of KL(Px,y).

关键词： Image reconstruction iterative algorithms Minimization methods Maximum likelihood estimation Detectors Signal to noise ratio Tomography Bayesian methods Equations Cancer

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