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On Asymptotic Linear Convergence of Projected Gradient Descent for Constrained Least Squares

IEEE TRANSACTIONS ON signal processing 2022年 70卷 4061-4076页

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

Many recent problems in signal processing and machine learning such as compressed sensing, image restoration, matrix/tensor recovery, and non-negative matrix factorization can be cast as constrained optimization. Projected gradient descent is a simple yet efficient method for solving such constrained optimization problems. Local convergence analysis furthers our understanding of its asymptotic behavior near the solution, offering sharper bounds on the convergence rate compared to global convergence analysis. However, local guarantees often appear scattered in problem-specific areas of machine learning and signal processing. This manuscript presents a unified framework for the local convergence analysis of projected gradient descent in the context of constrained least squares. The proposed analysis offers insights into pivotal local convergence properties such as the conditions for linear convergence, the region of convergence, the exact asymptotic rate of convergence, and the bound on the number of iterations needed to reach a certain level of accuracy. To demonstrate the applicability of the proposed approach, we present a recipe for the convergence analysis of projected gradient descent and demonstrate it via a beginning-to-end application of the recipe on four fundamental problems, namely, linear equality-constrained least squares, sparse recovery, least squares with the unit norm constraint, and matrix completion.

关键词： Convergence Optimization Manifolds signal processing algorithms Machine learning Symmetric matrices Sparse matrices Asymptotic convergence rate constrained least squares local linear convergence projected gradient descent

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Improved Spike-Based Brain-Machine Interface Using Bayesian Adaptive Kernel Smoother and Deep Learning

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IEEE ACCESS 2022年 10卷 29341-29356页

作者： Ahmadi, Nur Adiono, Trio Purwarianti, Ayu Constandinou, Timothy G. Bouganis, Christos-Savvas Imperial Coll London Dept Elect & Elect Engn London SW7 2AZ England Imperial Coll London Ctr Bioinspired Technol Inst Biomed Engn London SW7 2AZ England Bandung Inst Technol Sch Elect Engn & Informat Bandung 40132 Indonesia Bandung Inst Technol Ctr Artificial Intelligence U CoE AI VLB Bandung 40132 Indonesia Imperial Coll London Care Res & Technol Ctr UK Dementia Res Inst London SW7 2AZ England

Multiunit activity (MUA) has been proposed to mitigate the robustness issue faced by single-unit activity (SUA)-based brain-machine interfaces (BMIs). Most MUA-based BMIs still employ a binning method for estimating firing rates and linear decoder for decoding behavioural parameters. The limitations of binning and linear decoder lead to suboptimal performance of MUA-based BMIs. To address this issue, we propose a method which consists of Bayesian adaptive kernel smoother (BAKS) as the firing rate estimation algorithm and deep learning, particularly quasi-recurrent neural network (QRNN), as the decoding algorithm. We evaluated the proposed method for reconstructing (offline) hand kinematics from intracortical neural data chronically recorded from the primary motor cortex of two non-human primates. Extensive empirical results across recording sessions and subjects showed that the proposed method consistently outperforms other combinations of firing rate estimation algorithm and decoding algorithm. Overall results suggest the effectiveness of the proposed method for improving the decoding performance of MUA-based BMIs.

关键词： Decoding Kernel Deep learning Estimation signal processing algorithms Bayes methods Kinematics Brain-machine interface Bayesian adaptive kernel smoother deep learning firing rate estimation multiunit activity neural decoding

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ChevOpt: Continuous-Time State Estimation by Chebyshev Polynomial Optimization

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IEEE TRANSACTIONS ON signal processing 2022年 70卷 3136-3147页

作者： Zhu, Maoran Wu, Yuanxin Shanghai Jiao Tong Univ Sch Elect Informat & Elect Engn Shanghai Key Lab Nav & Locat Based Serv Shanghai 200240 Peoples R China

In this paper, a new framework for continuous-time maximum a posteriori estimation based on the Chebyshev polynomial optimization (ChevOpt) is proposed, which transforms the nonlinear continuous-time state estimation into a problem of constant parameter optimization. Specifically, the time-varying system state is represented by a Chebyshev polynomial and the unknown Chebyshev coefficients are optimized by minimizing the weighted sum of the prior, dynamics and measurements. The proposed ChevOpt is an optimal continuous-time estimation in the least squares sense and needs a batch processing. A recursive sliding-window version is proposed as well to meet the requirement of real-time applications. Comparing with the well-known Gaussian filters, the ChevOpt better resolves the nonlinearities in both dynamics and measurements. Numerical results of demonstrative examples show that the proposed ChevOpt achieves remarkably improved accuracy over the extended/unscented Kalman filters and extended batch/fixed-lag smoother, close to the Cramer-Rao lower bound.

关键词： Chebyshev approximation State estimation Optimization Nonlinear dynamical systems Kalman filters Current measurement signal processing algorithms Chebyshev polynomial collocation method gaussian filter maximum a posteriori estimation nonlinear filter

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Compressive Sensing Technique for Mitigating Nonlinear Memory Effects in Radar Receivers

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IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS 2022年第2期58卷 1005-1020页

作者： Ward, Euan Gishkori, Shahzad Mulgrew, Bernard Univ Edinburgh Sch Engn & Elect Joint Res Inst Signal & Image Proc Inst Digital Commun Edinburgh EH9 3JL Midlothian Scotland King Abdullah Univ Sci & Technol Thuwal 23955 Saudi Arabia

Receiver nonlinearities pose a serious risk to the functionality of modern radars as they can compromise the sensor's immunity to interfering signals. With the radio frequency (RF) spectrum becoming increasingly crowded, it is now more important than ever that the sensor can maintain system performance when exposed to mutual interference. In this article, we present a nonlinear compressive sensing (NCS) solution, which, unlike the standard nonlinear equalization (NLEQ) techniques, is designed around the forward nonlinearity rather than the inverse. Importantly, in this article, the NCS theory is extended to include nonlinear memory. Furthermore, a radar-specific formalization is derived, which allows the nonlinear optimization to exploit the unique properties of pulsed-Doppler radar processing. As a result, the NCS solution can successfully restore system sensitivity back to the linear case when in-band interference drives the radar receiver into its nonlinear regime. Additionally, it is shown that the technique can consistently mitigate complex nonlinear memory effects generated in the RF receiver. This is a significant result as it proves that forward modeling techniques are a viable alternative to NLEQ. This is of particular importance to radar systems as they provide a far more explicit formalization to mitigate nonlinear memory effects.

关键词： Radar Receivers Interference Radio frequency signal processing algorithms Harmonic analysis Compressed sensing Forward modeling mutual interference nonlinear compressive sensing (NCS) nonlinear equalization (NLEQ) nonlinear optimization radar receiver nonlinearity

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Communication-Efficient Stochastic Zeroth-Order Optimization for Federated Learning

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IEEE TRANSACTIONS ON signal processing 2022年 70卷 5058-5073页

作者： Fang, Wenzhi Yu, Ziyi Jiang, Yuning Shi, Yuanming Jones, Colin N. Zhou, Yong ShanghaiTech Univ Sch Informat Sci & Technol Shanghai 201210 Peoples R China Ecole Polytech Fed Lausanne Automat Control Lab CH-1015 Lausanne Switzerland

Federated learning (FL), as an emerging edge artificial intelligence paradigm, enables many edge devices to collaboratively train a global model without sharing their private data. To enhance the training efficiency of FL, various algorithms have been proposed, ranging from first-order to second-order methods. However, these algorithms cannot be applied in scenarios where the gradient information is not available, e.g., federated black-box attack and federated hyperparameter tuning. To address this issue, in this paper we propose a derivative-free federated zeroth-order optimization (FedZO) algorithm featured by performing multiple local updates based on stochastic gradient estimators in each communication round and enabling partial device participation. Under non-convex settings, we derive the convergence performance of the FedZO algorithm on non-independent and identically distributed data and characterize the impact of the numbers of local iterates and participating edge devices on the convergence. To enable communication-efficient FedZO over wireless networks, we further propose an over-the-air computation (AirComp) assisted FedZO algorithm. With an appropriate transceiver design, we show that the convergence of AirComp-assisted FedZO can still be preserved under certain signal-to-noise ratio conditions. Simulation results demonstrate the effectiveness of the FedZO algorithm and validate the theoretical observations.

关键词： signal processing algorithms Convergence Optimization Atmospheric modeling Stochastic processes Performance evaluation Training Federated learning zeroth-order optimization convergence over-the-air computation

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Recovery algorithms for Pooled RT-qPCR Based Covid-19 Screening

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IEEE TRANSACTIONS ON signal processing 2022年 70卷 4353-4368页

作者： Bharadwaja, Sameera H. Murthy, Chandra R. Indian Inst Sci Dept ECE Bangalore 560012 Karnataka India

We consider the problem of sparse signal recovery in a non-adaptive pool-test setting using quantitative measurements from a non-linear model. The quantitative measurements are obtained using the reverse transcription (quantitative) polymerase chain reaction (RT-qPCR) test, which is the standard test used to detect Covid-19. Each quantitative measurement refers to the cycle threshold, a proxy for the viral load in the test sample. We propose two novel, robust recovery algorithms based on alternating direction method of multipliers and block coordinate descent to recover the individual sample cycle thresholds and hence determine the sick individuals, given the pooled sample cycle thresholds and the pooling matrix. We numerically evaluate the normalized mean squared error, false positive rate, false negative rate, and the maximum sparsity levels up to which error-free recovery is possible. We also demonstrate the advantage of using quantitative measurements (as opposed to binary outcomes) in non-adaptive pool testing methods in terms of the testing rate using publicly available data on Covid-19 testing. The simulation results show the effectiveness of the proposed algorithms.

关键词： Testing COVID-19 signal processing algorithms Diseases Protocols Standards Noise measurement RT-qPCR Covid-19 SARS-CoV-2 Group Testing Compressed Sensing Sparse signal Recovery

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Deep Expectation-Maximization for Joint MIMO Channel Estimation and signal Detection

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IEEE TRANSACTIONS ON signal processing 2022年 70卷 4483-4497页

作者： Zhang, Yiqing Sun, Jianyong Xue, Jiang Li, Geoffrey Ye Xu, Zongben Xi An Jiao Tong Univ Sch Math & Stat Xian 710049 Peoples R China Xi An Jiao Tong Univ Pengcheng Lab Pazhou Lab Huangpu Xian 710049 Peoples R China Imperial Coll London Dept Elect & Elect Engn London SW7 2BX England

To overcome the influence of channel estimation error on signal detection, this paper presents a model-driven deep learning method for joint channel estimation and signal detection in multiple-input multiple-output (MIMO) wireless communication systems. To improve the robustness of the method, we use the Student's t-distribution to model the environment noise, and model the joint problem probabilistically by taking the channel state information (CSI) as a latent variable, then derive a generalized expectation maximization (GEM) algorithm to fit the model. In GEM, the expectation step is used for robust CSI estimation while the maximization step detects the transmitted signal with the estimated CSI. To reduce the computational complexity of GEM, we unfold it into a deep neural network. The network contains only a few trainable parameters, which is easy to train and has low space complexity. Based on our experimental results, we find that the proposed GEM algorithm outperforms a variety of signal detection algorithms which take the CSI estimation and signal detection as independent modules. Further, we find empirically that the proposed GEM network outperforms state-of-the-art deep learning based joint channel estimation and signal detection methods and has a good generalization ability against the number of antennas, the modulation mode, the level of signal-to-noise ratio and channel correlation.

关键词： Channel estimation MIMO communication Detectors signal detection Deep learning signal processing algorithms Neural networks Channel estimation deep learning joint estimation learning to learn MIMO signal detection model-driven

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Distributed Learning With Sparsified Gradient Differences

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IEEE JOURNAL OF SELECTED TOPICS IN signal processing 2022年第3期16卷 585-600页

作者： Chen, Yicheng Blum, Rick S. Takac, Martin Sadler, Brian M. Lehigh Univ Bethlehem PA 18015 USA Mohamed Bin Zayed Univ Artificial Intelligence Abu Dhabi 51133 U Arab Emirates Army Res Lab Adelphi MD 20783 USA

A very large number of communications are typically required to solve distributed learning tasks, and this critically limits scalability and convergence speed in wireless communications applications. In this paper, we devise a Gradient Descent method with Sparsification and Error Correction (GD-SEC) to improve the communications efficiency in a general worker-server architecture. Motivated by a variety of wireless communications learning scenarios, GD-SEC reduces the number of bits per communication from worker to server with no degradation in the order of the convergence rate. This enables larger scale model learning without sacrificing convergence or accuracy. At each iteration of GD-SEC, instead of directly transmitting the entire gradient vector, each worker computes the difference between its current gradient and a linear combination of its previously transmitted gradients, and then transmits the sparsified gradient difference to the server. A key feature of GD-SEC is that any given component of the gradient difference vector will not be transmitted if its magnitude is not sufficiently large. An error correction technique is used at each worker to compensate for the error resulting from sparsification. We prove that GD-SEC is guaranteed to converge for strongly convex, convex, and nonconvex optimization problems with the same order of convergence rate as GD. Furthermore, if the objective function is strongly convex, GD-SEC has a fast linear convergence rate. Numerical results not only validate the convergence rate of GD-SEC but also explore the communication bit savings it provides. Given a target accuracy, GD-SEC can significantly reduce the communications load compared to the best existing algorithms without slowing down the optimization process.

关键词： Convergence Servers Optimization signal processing algorithms Wireless communication Distance learning Computer aided instruction Communication-efficient distributed learning error correction gradient compression sparsification wireless communications worker-server architecture

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Throughput Maximization for IRS-Aided MIMO FD-WPCN With Non-Linear EH Model

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IEEE JOURNAL OF SELECTED TOPICS IN signal processing 2022年第5期16卷 918-932页

作者： Hua, Meng Wu, Qingqing Univ Macau State Key Lab Internet Things Smart City Macau 999078 Peoples R China

This paper studies an intelligent reflecting surface (IRS)-aided multiple-input-multiple-output (MIMO) full-duplex (FD) wireless-powered communication network (WPCN), where a hybrid access point (HAP) operating in FD broadcasts energy signals to multiple devices for their energy harvesting (EH) in the downlink (DL) and meanwhile receives information signals from devices in the uplink (UL) with the help of an IRS. Taking into account the practical finite self-interference (SI) and the non-linear EH model, we formulate the weighted sum throughput maximization optimization problem by jointly optimizing DL/UL time allocation, precoding matrices at devices, transmit covariance matrices at the HAP, and phase shifts at the IRS. Since the resulting optimization problem is non-convex, there are no standard methods to solve it optimally in general. To tackle this challenge, we first propose an element-wise (EW) based algorithm, where each IRS phase shift is alternately optimized in an iterative manner. To reduce the computational complexity, a minimum mean-square error (MMSE) based algorithm is proposed, where we transform the original problem into an equivalent form based on the MMSE method, which facilities the design of an efficient iterative algorithm. In particular, the IRS phase shift optimization problem is recast as an second-order cone program (SOCP), where all the IRS phase shifts are simultaneously optimized. For comparison, we also study two suboptimal IRS beamforming configurations in simulations, namely partially dynamic IRS beamforming (PDBF) and static IRS beamforming (SBF), which strike a balance between the system performance and practical complexity. Simulation results demonstrate the effectiveness of proposed two algorithms. Besides, the results show the superiority of our proposed scheme over other benchmark schemes and also unveil the importance of the joint design of passive beamforming and resource allocation for achieving energy efficient MIMO FD-WPCN

关键词： MIMO communication Array signal processing Wireless communication Resource management signal processing algorithms Radio frequency Throughput Intelligent reflecting surface full-duplex WPCN MIMO passive beamforming resource allocation

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Wireless Sensor Network for Tactical Situation Assessment

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IEEE SENSORS JOURNAL 2022年第1期22卷 1051-1062页

作者： Pannetier, Benjamin Dezert, Jean Moras, Julien Levy, Raphael CS Grp F-92350 Le Plessis Robinson France Off Natl Etud & Rech Aerosp French Aerosp Lab F-91120 Palaiseau France

This paper describes a complete solution of a new dropped wireless sensor network (called "abandoned" since it is never picked up) dedicated to intelligence operation. The sensor network, named SEXTANT for Smart sEnsor X for Tactical situation AssessmeNT and presented in this paper is the achievement of several years of research and development in the fields of data fusion and smart sensors at the French Aerospace Lab. The main contribution of this paper is the presentation of experimental results obtained with our Joint Tracking and Classification (JTC) algorithm. The originality of this algorithm relies on the use contextual information in the target tracking processing and data fusion for target classification processing.

关键词： Sensors Target tracking Wireless sensor networks Sensor phenomena and characterization Classification algorithms signal processing algorithms Intelligent sensors Wireless sensor network mbed protocol data fusion multiple target tracking classification

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