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On OAMP: Impact of the Orthogonal Principle

IEEE TRANSACTIONS ON COMMUNICATIONS 2023年第5期71卷 2992-3007页

作者： Liu, Lei Cheng, Yiyao Liang, Shansuo Manton, Jonathan H. Ping, Li Zhejiang Univ ZJU Coll Informat Sci & Elect Engn Hangzhou 310007 Peoples R China City Univ Hong Kong CityU Dept Elect Engn Hong Kong Peoples R China Huawei Technol Co Ltd Cent Res Inst Theory Lab Labs 2012 Hong Kong Peoples R China Univ Melbourne Dept Elect & Elect Engn Parkville Vic 3010 Australia

Approximate Message Passing (AMP) is an efficient iterative parameter-estimation technique for certain high-dimensional linear systems with non-Gaussian distributions, such as sparse systems. In AMP, a so-called Onsager term is added to keep estimation errors approximately Gaussian. Orthogonal AMP (OAMP) does not require this Onsager term, relying instead on an orthogonalization procedure to keep the current errors uncorrelated with (i.e., orthogonal to) past errors. In this paper, we show the generality and significance of the orthogonality in ensuring that errors are "asymptotically independently and identically distributed Gaussian" (AIIDG). This AIIDG property, which is essential for the attractive performance of OAMP, holds for separable functions. We present a simple and versatile procedure to establish the orthogonality through Gram-Schmidt (GS) orthogonalization, which is applicable to any prototype. We show that different AMP-type algorithms, such as expectation propagation (EP), turbo, AMP and OAMP, can be unified under the orthogonal principle. The simplicity and generality of OAMP provide efficient solutions for estimation problems beyond the classical linear models. As an example, we study the optimization of OAMP via the GS model and GS orthogonalization. More related applications will be discussed in a companion paper where new algorithms are developed for problems with multiple constraints and multiple measurement variables.

关键词： Message passing Iterative methods Program processors Sensors Linear systems Electronic mail signal processing algorithms Expectation propagation (EP) turbo belief propagation (BP) approximate message passing (AMP) vector AMP (VAMP) unified framework state evolution Haar matrices

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Federated Learning Using Three-Operator ADMM

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IEEE JOURNAL OF SELECTED TOPICS IN signal processing 2023年第1期17卷 205-221页

作者： Kant, Shashi da Silva, Jose Mairton B., Jr. Fodor, Gabor Goransson, Bo Bengtsson, Mats Fischione, Carlo Ericsson AB S-16480 Stockholm Sweden KTH Royal Inst Technol S-16480 Stockholm Sweden KTH Royal Inst Technol S-11428 Stockholm Sweden Princeton Univ Princeton NJ 08544 USA

Federated learning (FL) has emerged as an instance of distributed machine learning paradigm that avoids the transmission of data generated on the users' side. Although data are not transmitted, edge devices have to deal with limited communication bandwidths, data heterogeneity, and straggler effects due to the limited computational resources of users' devices. A prominent approach to overcome such difficulties is FedADMM, which is based on the classical two-operator consensus alternating direction method of multipliers (ADMM). The common assumption of FL algorithms, including FedADMM, is that they learn a global model using data only on the users' side and not on the edge server. However, in edge learning, the server is expected to be near the base station and has often direct access to rich datasets. In this paper, we argue that it is much more beneficial to leverage the rich data on the edge server then utilizing only user datasets. Specifically, we show that the mere application of FL with an additional virtual user node representing the data on the edge server is inefficient. We propose FedTOP-ADMM, which generalizes FedADMM and is based on a three-operator ADMM-type technique that exploits a smooth cost function on the edge server to learn a global model in parallel to the edge devices. Our numerical experiments indicate that FedTOP-ADMM has substantial gain up to 33% in communication efficiency to reach a desired test accuracy with respect to FedADMM, including a virtual user on the edge server.

关键词： Servers Optimization signal processing algorithms Data models Convergence Base stations Numerical models Federated learning three-operator ADMM distributed machine learning communication efficiency

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Brain-Inspired Remote Sensing Interpretation: A Comprehensive Survey

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IEEE JOURNAL OF SELECTED TOPICS IN APPLIED EARTH OBSERVATIONS AND REMOTE SENSING 2023年 16卷 2992-3033页

作者： Jiao, Licheng Huang, Zhongjian Liu, Xu Yang, Yuting Ma, Mengru Zhao, Jiaxuan You, Chao Hou, Biao Yang, Shuyuan Liu, Fang Ma, Wenping Li, Lingling Chen, Puhua Feng, Zhixi Tang, Xu Guo, Yuwei Zhang, Xiangrong Quan, Dou Wang, Shuang Li, Weibin Bai, Jing Li, Yangyang Shang, Ronghua Feng, Jie Xidian Univ Xian 710071 Peoples R China

Brain-inspired algorithms have become a new trend in next-generation artificial intelligence. Through research on brain science, the intelligence of remote sensing algorithms can be effectively improved. This article summarizes and analyzes the essential properties of brain cognize learning and the recent advance of remote sensing interpretation. First, this article introduces the structural composition and the properties of the brain. Then, five represent brain-inspired algorithms are studied, including multiscale geometry analysis, compressed sensing, attention mechanism, reinforcement learning, and transfer learning. Next, this article summarizes the data types of remote sensing, the development of typical applications of remote sensing interpretation, and the implementations of remote sensing, including datasets, software, and hardware. Finally, the top ten open problems and the future direction of brain-inspired remote sensing interpretation are discussed. This work aims to comprehensively review the brain mechanisms and the development of remote sensing and to motivate future research on brain-inspired remote sensing interpretation.

关键词： Remote sensing Biology Artificial intelligence signal processing algorithms Sensors Cognition Heuristic algorithms Brain modeling deep learning image processing remote sensing

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Online Orthogonal Dictionary Learning Based on Frank-Wolfe Method

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IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2023年第9期34卷 5774-5788页

作者： Xue, Ye Lau, Vincent K. N. Hong Kong Univ Sci & Technol Dept Elect & Comp Engn Hong Kong Peoples R China

Dictionary learning is a widely used unsupervised learning method in signal processing and machine learning. Most existing works on dictionary learning adopt an off-line approach, and there are two main off-line ways of conducting it. One is to alternately optimize both the dictionary and the sparse code, while the other is to optimize the dictionary by restricting it over the orthogonal group. The latter, called orthogonal dictionary learning (ODL), has a lower implementation complexity and, hence, is more favorable for low-cost devices. However, existing schemes for ODL only work with batch data and cannot be implemented online, making them inapplicable for real-time applications. This article, thus, proposes a novel online orthogonal dictionary scheme to dynamically learn the dictionary from streaming data, without storing the historical data. The proposed scheme includes a novel problem formulation and an efficient online algorithm design with convergence analysis. In the problem formulation, we relax the orthogonal constraint to enable an efficient online algorithm. We then propose the design of a new Frank-Wolfe-based online algorithm with a convergence rate of O(ln t/t1/4). The convergence rate in terms of key system parameters is also derived. Experiments with synthetic data and real-world Internet of things (IoT) sensor readings demonstrate the effectiveness and efficiency of the proposed online ODL scheme.

关键词： Dictionaries Convergence Machine learning Optimization Random variables Codes signal processing algorithms Convergence analysis dictionary learning Frank-Wolfe online learning sensor

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Robust Interferometric ISAR Imaging With UAMP-Based Joint Sparse signal Recovery

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IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS 2023年第4期59卷 3890-3906页

作者： Kang, Hailong Li, Jun Guo, Qinghua Martorella, Marco Giusti, Elisa Cai, Jinjian Xidian Univ Hangzhou Inst Technol Hangzhou 311200 Peoples R China Xidian Univ Natl Lab Radar Signal Proc Xian 710071 Peoples R China Univ Wollongong Sch Elect Comp & Telecommun Engn Wollongong NSW 2522 Australia Natl Lab Radar & Surveillance Syst RaSS CNIT Pisa Italy Beijing Inst Technol Key Lab Elect & Informat Technol Satellite Nav Minist Educ Beijing 100081 Peoples R China Natl Lab Radar & Surveillance Syst CNIT I-56124 Pisa Italy

Sparse Bayesian learning (SBL) has found successful applications in interferometric inverse synthetic aperture radar (InISAR) imaging, especially in the presence of limited number of pulses or when using sparse apertures. SBL-based InISAR algorithms have been proven to be significantly superior to Fourier transform-based ones. However, the existing SBL-based algorithms are slow due to their high computational complexity. Moreover, there is also much room to improve in terms of imaging performance. In this article, leveraging the approximate message passing with unitary transformation (UAMP), we propose an InISAR imaging algorithm named UAMP joint sparse recovery (JSR), which is much faster and delivers notably higher imaging accuracy than the existing SBL-based algorithms. Specifically, we develop a type-2 joint sparse model for InISAR imaging and formulate it as a two-layer multiple measurement vectors joint sparse problem. Based on a factor graph representation, the message passing techniques are used to efficiently solve this problem, which leads to the UAMP-JSR algorithm. Results based on extensive simulations and experiments based on the real data collected by the Pisa Radar demonstrate the effectiveness and superiority of the proposed algorithm compared to existing algorithms.

关键词： Imaging Radar imaging Approximation algorithms Three-dimensional displays signal processing algorithms Antenna measurements Spaceborne radar Interferometric inverse synthetic aperture radar (InISAR) joint sparse recovery sparse Bayesian learning (SBL) unitary transformation (UAMP)

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An Iterative Warping and Clustering Algorithm to Estimate Multiple Wave-Shape Functions From a Nonstationary Oscillatory signal

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IEEE TRANSACTIONS ON signal processing 2023年 71卷 701-712页

作者： Colominas, Marcelo A. Wu, Hau-Tieng Inst Res & Dev Bioengn & Bioinformat IBB CONICET Oro Verde Argentina UNER Fac Engn RA-3285 Oro Verde Entre Rios Argentina Duke Univ Dept Math Dept Stat Sci Durham NC USA

Nonsinusoidal oscillatory signals are everywhere. In practice, the nonsinusoidal oscillatory pattern, modeled as a 1 periodic wave-shape function (WSF), might vary from cycle to cycle. When there are finite different WSFs, s(1), . . . , s(K), so that the WSF jumps from one to another suddenly, the different WSFs and jumps encode useful information. We present an iterative warping and clustering algorithm to estimate s(1), . . . , s(K) from a nonstationary oscillatory signal with time-varying amplitude and frequency, and hence the change points of the WSFs. The algorithm is a novel combination of time-frequency analysis, singular value decomposition entropy and vector spectral clustering. We demonstrate the efficiency of the proposed algorithm with simulated and real signals, including the voice signal, arterial blood pressure, electrocardiogram and accelerometer signal. Moreover, we provide a mathematical justification of the algorithm under the assumption that the amplitude and frequency of the signal are slowly time-varying and there are finite change points that model sudden changes from one wave-shape function to another one.

关键词： Time-frequency analysis signal processing algorithms Mathematical models Electrocardiography Analytical models Harmonic analysis Clustering algorithms Wave-shape functions signal modeling instan-taneous frequency biomedical signals

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High-Performance Permanent Magnet Synchronous Motor Control With Electrical Angle Delayed Component Compensation

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IEEE ACCESS 2023年 11卷 129467-129478页

作者： Kim, Seonhyeong Park, Keunho Kang, Dongkil Lee, Geun Ho Kookmin Univ Dept Automot Engn Seoul 02707 South Korea Korea Elect Technol Inst Jeonju Si 54853 Jeollabuk Do South Korea

Electrical angle delay resulting from inverter part and design errors causes rotor position errors. It significantly lowers motor control performance as the rotor position error rate increases owing to increased speed. Rotor position detections considering the delay component can be classified into initial rotor-position and time-delay position detections. The initial rotor position detection method causes initial rotor position errors based on speed because it does not consider the electrical angle delay component. The conventional time-delay position detection method involves current-voltage time-delay position detection. The dynamo system manually measures and compensates for current and voltage delay coefficients based on speed to detect the time-delay position. However, achieving precise torque control performance is challenging because detecting the delay coefficient at high speeds is dangerous, and separating the electrical angle delay component is impossible. This study proposes a delay component detection and compensation algorithm by analyzing the electrical angle delay component due to inverter parts and design errors. The new initial rotor and time-delay positions are estimated to improve the torque control performance by compensating for the detected delay component. The proposed algorithm is based on the PMSM voltage equation and validated through simulation using MATLAB Simulink. The initial rotor position, time-delay position, and torque control performance are verified by experimentally detecting and compensating for the electrical angle delay component using the proposed algorithm. The results demonstrate that the proposed algorithm is robust to inverter part and design errors. Moreover, the proposed algorithm is advantageous in considerably improving the torque control performance.

关键词： Rotors Sensors Torque control Hardware Voltage measurement signal processing algorithms Delay effects Permanent magnet motors Voltage control Current time delay delayed components electrical angle electrical angle offset initial rotor position permanent magnet synchronous motor time-delay position torque control voltage time delay

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Distributed Scaled Proximal ADMM algorithms for Cooperative Localization in WSNs

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IEEE TRANSACTIONS ON signal processing 2023年 71卷 3312-3327页

作者： Zhang, Mei Wang, Zhiguo Yin, Feng Shen, Xiaojing Sichuan Univ Dept Math Chengdu 610064 Sichuan Peoples R China Chinese Univ Hong Kong Shenzhen Sch Sci & Engn Shenzhen 518172 Peoples R China Shenzhen Res Inst Big Data Shenzhen 518172 Peoples R China

Distributed cooperative localization in wireless networks is a challenging problem since it typically requires solving a large-scale nonconvex and nonsmooth optimization problem. In this article, we reformulate the classic cooperative localization problem as a smooth and constrained nonconvex minimization problem while its loss function is separable over nodes. By utilizing the structure of the reformulation, we propose two novel scaled proximal alternating direction method of multipliers (SP-ADMM) algorithms, which can be implemented in a distributed manner. Compared with the classic semi-definite programming relaxation techniques, the proposed algorithms can provide more accurate position estimates with significantly lower computation complexity. The associated theoretical analysis shows that our algorithms globally converge to a KKT point of the reformulated problem and a critical point of the original problem, with a favorable sublinear O(1/T) convergence rate, where T is the iteration counter. Numerical experiments have consistently shown that the proposed SP-ADMM algorithms are superior to state-of-the-art methods in terms of localization accuracy and computational complexity across all tested scenarios, varying network size, number of anchors, average number of neighbors, and noise variance levels.

关键词： signal processing algorithms Location awareness Convergence Optimization Wireless sensor networks Minimization Computational complexity Proximal ADMM distributed algorithm global convergence rate cooperative localization wireless sensor network

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Single-Timescale Multi-Sequence Stochastic Approximation Without Fixed Point Smoothness: Theories and Applications

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IEEE TRANSACTIONS ON signal processing 2025年 73卷 1939-1953页

作者： Huang, Yue Wu, Zhaoxian Ma, Shiqian Ling, Qing Sun Yat Sen Univ Sch Comp Sci & Engn Guangzhou 510006 Peoples R China Sun Yat Sen Univ Guangdong Prov Key Lab Computat Sci Guangzhou 510006 Peoples R China Rice Univ Dept Computat Appl Math & Operat Res Houston TX 77251 USA Pazhou Lab Guangzhou 510275 Peoples R China

Stochastic approximation (SA) that involves multiple coupled sequences, also known as multiple-sequence SA (MSSA), finds diverse applications in the fields of signal processing and machine learning. However, existing theoretical understandings of MSSA are limited: the multi-timescale analysis implies a slow convergence rate, whereas the single-timescale analysis relies on a stringent fixed point smoothness assumption. In this paper, we establish tighter single-timescale analysis for MSSA, without assuming smoothness of the fixed points. Our theoretical findings reveal that, when all involved operators are strongly monotone, MSSA converges at a rate of $\tilde{\mathcal{O}}(K<^>{-1})$, where $K$ denotes the total number of iterations. When all involved operators are strongly monotone except for the main one, MSSA converges at a rate of $O(K<^>{-\fracalgorithms{2}})$. These rates align with the ones established for single-sequence SA. Applying our novel theoretical findings to bilevel optimization and communication-efficient distributed learning offers relaxed assumptions and/or simpler algorithms with perfor- mance guarantees, as validated by numerical experiments.

关键词： Convergence Optimization Distance learning Computer aided instruction Noise Training signal processing algorithms Data mining Standards Speech processing Stochastic approximation convergence analysis bilevel optimization distributed learning

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On Local Linear Convergence of Projected Gradient Descent for Unit-Modulus Least Squares

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IEEE TRANSACTIONS ON signal processing 2023年 71卷 3883-3897页

作者： Vu, Trung Raich, Raviv Fu, Xiao Oregon State Univ Sch Elect Engn & Comp Sci Corvallis OR 97331 USA

The unit-modulus least squares (UMLS) problem has a wide spectrum of applications in signal processing, e.g., phase-only beamforming, phase retrieval, radar code design, and sensor network localization. Scalable first-order methods such as projected gradient descent (PGD) have recently been studied as a simple yet efficient approach to solving the UMLS problem. Existing results on the convergence of PGD for UMLS often focus on global convergence to stationary points. As a non-convex problem, only a sublinear convergence rate has been established. However, these results do not explain the fast convergence of PGD frequently observed in practice. This manuscript presents a novel analysis of convergence of PGD for UMLS, justifying the linear convergence behavior of the algorithm near the solution. By exploiting the local structure of the objective function and the constraint set, we establish an exact expression for the convergence rate and characterize the conditions for linear convergence. Simulations show that our theoretical analysis corroborates numerical examples. Furthermore, variants of PGD with adaptive step sizes are proposed based on the new insight revealed in our convergence analysis. The variants show substantial acceleration in practice.

关键词： Convergence Unified modeling language Array signal processing Codes signal processing algorithms signal to noise ratio Standards Unit-modulus least squares projected gradient descent linear convergence analysis

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