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Minimizing Low-Rank Models of High-Order Tensors: Hardness, Span, Tight Relaxation, and Applications

IEEE TRANSACTIONS ON signal processing 2024年 72卷 129-142页

作者： Sidiropoulos, Nicholas D. Karakasis, Paris A. Konar, Aritra Univ Virginia Dept Elect & Comp Engn Charlottesville VA 22904 USA Katholieke Univ Leuven Dept Elect Engn B-3001 Leuven Belgium

We consider the problem of finding the smallest or largest entry of a tensor of order $N$ that is specified via its rank decomposition. Stated in a different way, we are given $N$ sets of $R$-dimensional vectors and we wish to select one vector from each set such that the sum of the Hadamard product of the selected vectors is minimized or maximized. We show that this fundamental tensor problem is NP-hard for any tensor rank higher than one, and polynomial-time solvable in the rank-one case. We also propose a continuous relaxation and prove that it is tight for any rank. For low-enough ranks, the proposed continuous reformulation is amenable to low-complexity gradient-based optimization, and we propose a suite of gradient-based optimization algorithms drawing from projected gradient descent, Frank-Wolfe, or explicit parametrization of the relaxed constraints. We also show that our core results remain valid no matter what kind of polyadic tensor model is used to represent the tensor of interest, including Tucker, HOSVD/MLSVD, tensor train, or tensor ring. Next, we consider the class of problems that can be posed as special instances of the problem of interest. We show that this class includes the partition problem (and thus all NP-complete problems via polynomial-time transformation), integer least squares, integer linear programming, integer quadratic programming, sign retrieval (a special kind of mixed integer programming / restricted version of phase retrieval), and maximum likelihood decoding of parity check codes. We demonstrate promising experimental results on a number of hard problems, including state-of-art performance in decoding low density parity check codes and general parity check codes.

关键词： Tensors Computational modeling Complexity theory Maximum likelihood decoding Matrix decomposition signal processing algorithms Optimization rank decomposition inner product algorithms complexity theory NP-hard problems error control coding maximum likelihood decoding parity check codes belief propagation under/over-determined linear equations Galois fields sign retrieval

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An Intelligent Anti-Interference Scheme for FDA-MIMO Radar Under Nonideal Condition

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IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS 2024年第3期60卷 3269-3281页

作者： Ding, Zihang Xie, Junwei Lan, Lan Qi, Cheng Gao, Xuchen Air Force Engn Univ Xian 710051 Peoples R China Xidian Univ Natl Lab Radar Signal Proc Xian Peoples R China

The realization of anti-interference technologies via beamforming for applications in frequency diverse arrays and multiple-input and multiple-output (FDA-MIMO) radar is a field that is undergoing intensive research due to its two-dimensional range-angle-dependent beampattern characteristics. To solve the missing covariance matrix problem and improve the anti-interference capability of FDA-MIMO radar, we present a two-stage based intelligent anti-interference scheme for FDA-MIMO radar under the nonideal condition. The scheme consists of two parts: signal covariance matrix missing data recovery and intelligent beamforming vector estimation. A dual-channel generation adversarial network (DC-GAN) structure is proposed to effectively recover both real and imaginary parts of data from a covariance matrix. Based on the recovered covariance matrix, the beamforming vectors are accurately estimated by constructing a one-dimensional convolution neural network (1D-CNN). Meanwhile, a multiple-target process scheme combined with the 1D-CNN is introduced to deal with multitarget situation. In the numerical simulation part, the simulation results reveal that the DC-GAN network can effectively recover the missing data from the covariance matrix, and the lower the missing data rate, the better the data recovery performance. In addition, in the simulation of beamforming vector estimation, the effects of two different input modes on network training performance are evaluated, and the performance differences between a fully connected neural network and 1D-CNN are analyzed and compared. The numerical simulation results verify the effectiveness of the proposed FDA-MIMO radar anti-interference scheme under different number of interference signal scenarios and improve the interference suppression capability of FDA-MIMO radar.

关键词： Array signal processing Radar Covariance matrices Interference Manganese Aerospace and electronic systems signal processing algorithms

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XSNet: A Lightweight X-Ray Security Image Segmentation Model Combining State-Space Models and Convolutional Neural Networks

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IEEE signal processing LETTERS 2025年 32卷 1351-1355页

作者： Jia, Weichao Liu, Wei Zhang, Changsheng Fu, Jian Liu, Qiong Beijing Informat Sci & Technol Univ Beijing 100192 Peoples R China Beihang Univ Ningbo Innovat Res Inst Ningbo 315800 Peoples R China Beijing Univ Aeronaut & Astronaut Beijing 100191 Peoples R China

In this letter, we propose a novel lightweight X-ray image contraband segmentation network, XSNet, which integrates State Space Models (SSM) with Convolutional Neural Networks (CNNs) to achieve a significant trade-off between segmentation accuracy and lightweight design for computer-aided X-ray security check. The model is built based on the encoder-decoder framework. Specifically, we design an Multi-scale Convolution Fusion (MCF) block for multi-scale information extraction and a Dual-branch State Space Model (DSSM) block to relieve the bias caused by the imbalance of single branch structure in feature extraction and maintain the capabilities of SSM in modeling long range pixel dependencies. In addition, we present two versions of the model in two different sizes called XSNet-s and XSNet-l respectively. The quantitative and qualitative evaluations on the public PIDray and PIXray datasets both show the superiority of two models in terms of mean Intersection over Union (mIoU) and FLOPs.

关键词： Computational modeling Image segmentation Feature extraction X-ray imaging Security Training Decoding Accuracy Data mining signal processing algorithms Contraband segmentation state space models X-ray images deep learning

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Internal Model-Based Online Optimization

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2024年第1期69卷 689-696页

作者： Bastianello, Nicola Carli, Ruggero Zampieri, Sandro KTH Royal Inst Technol Sch Elect Engn & Comp Sci S-11428 Stockholm Sweden Univ Padua Dept Informat Engn DEI I-35131 Padua Italy

In this article, we propose a model-based approach to the design of online optimization algorithms, with the goal of improving the tracking of the solution trajectory (trajectories) w.r.t. state-of-the-art methods. We focus first on quadratic problems with a time-varying linear term, and use digital control tools (a robust internal model principle) to propose a novel online algorithm that can achieve zero tracking error by modeling the cost with a dynamical system. We prove the convergence of the algorithm for both strongly convex and convex problems. We further discuss the sensitivity of the proposed method to model uncertainties and quantify its performance. We discuss how the proposed algorithm can be applied to general (nonquadratic) problems using an approximate model of the cost, and analyze the convergence leveraging the small gain theorem. We present numerical results that showcase the superior performance of the proposed algorithms over previous methods for both quadratic and nonquadratic problems.

关键词： signal processing algorithms Optimization Heuristic algorithms Costs Trajectory Convergence Approximation algorithms Digital control online gradient descent online optimization robust control structured algorithms

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Self-Weighted Multi-View Fuzzy Clustering With Multiple Graph Learning

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IEEE signal processing LETTERS 2025年 32卷 1585-1589页

作者： Liu, Chaodie Chang, Cheng Nie, Feiping Henan Normal Univ Sch Comp & Informat Engn Xinxiang 453007 Peoples R China Henan Normal Univ Key Lab Artificial Intelligence & Personalized Lea Xinxiang 453007 Peoples R China Northwestern Polytech Univ Sch Artificial Intelligence Opt & Elect IOPEN Xian 710072 Peoples R China Minist Ind & Informat Technol Key Lab Intelligent Interact & Applicat Xian 710072 Peoples R China

Graph-based multi-view clustering has garnered considerable attention owing to its effectiveness. Nevertheless, despite the promising performance achieved by previous studies, several limitations remain to be addressed. Most graph-based models employ a two-stage strategy involving relaxation and discretization to derive clustering results, which may lead to deviation from the original problem. Moreover, graph-based methods do not adequately address the challenges of overlapping clusters or ambiguous cluster membership. Additionally, assigning appropriate weights based on the importance of each view is crucial. To address these problems, we propose a self-weighted multi-view fuzzy clustering algorithm that incorporates multiple graph learning. Specifically, we automatically allocate weights corresponding to each view to construct a fused similarity graph matrix. Subsequently, we approximate it as the scaled product of fuzzy membership matrices to directly derive clustering assignments. An iterative optimization algorithm is designed for solving the proposed model. Experiment evaluations conducted on benchmark datasets illustrate that the proposed method outperforms several leading multi-view clustering approaches.

关键词： Clustering algorithms Data mining Benchmark testing Linear programming Computational complexity Training signal processing algorithms Optimization Flowering plants Vectors Fuzzy clustering graph learning multi-view clustering self-weighted

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Learning algorithms and signal processing for Brain-Inspired Computing

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IEEE signal processing MAGAZINE 2019年第6期36卷 12-15页

作者： Simeone, Osvaldo Rajendran, Bipin Gruning, Andre Eleftheriou, Evangelos S. Davies, Mike Deneve, Sophie Huang, Guang-Bin Kings Coll London Dept Engn Informat Engn Res London England New Jersey Inst Technol Newark NJ 07102 USA New Jersey Inst Technol Elect & Comp Engn Newark NJ 07102 USA IBM TJ Watson Res Ctr New York NY USA Univ Surrey Dept Comp Sci Computat Intelligence Surrey England Univ Bern Inst Physiol Bern Switzerland IBM Res Zurich Zurich Switzerland Intels Neuromorph Comp Lab Zurich Switzerland Nanyang Technol Univ Sch Elect & Elect Engn Singapore Singapore

The articles in this special section focuses on machine learning (ML) and signal processing algorithms for bio-inspired computing. The articles bring together key researchers in this area to provide readers of IEEE signal processing Magazine with up-to-date and survey-style articles on algorithmic, hardware, and neuroscience perspectives on the state-of- the-art aspects of this emerging field.

关键词： Special issues and sections Bio-inspired computing signal processing algorithms Neuromorphic engineering Neuroscience Machine learning

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DOA Estimation of Coherent signals Exploiting Forward/Backward Convolutional Kernels

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IEEE signal processing LETTERS 2025年 32卷 876-880页

作者： Zhao, Jun Dong, Xudong Zhang, Han Sun, Meng China Jiliang Univ Coll Informat Engn Hangzhou 310018 Peoples R China Hangzhou Dianzi Univ Coll Commun Engn Hangzhou 310018 Peoples R China Nanjing Univ Posts & Telecommun Coll Commun & Informat Engn Nanjing 210003 Peoples R China Nanjing Univ Aeronaut & Astronaut Coll Elect & Informat Engn Nanjing 210000 Peoples R China

The traditional subspace-based algorithms in the process of coherent direction of arrival (DOA) estimation get in trouble because of the rank loss of the signal covariance matrix. To this end, this paper introduces a forward/backward convolution kernel (FBCK) method, which not only reconstructs the signal covariance matrix and its diagonal elements, but also efficiently solves the signal coherence problem by utilizing the moving array technique. More precisely, the FBCK operation is applied to the signal space matrix at a given instant and utilizes the forward/backward convolution kernel to recover the rank corresponding to the number of signals without loss of the arrays' aperture. In a comparison evaluation with state-of-the-art spatial smoothing methods (including MSSP, SSP, ESS, ESS-SS, SSS and ASS), the proposed FBCK algorithm demonstrates excellent estimation capabilities in terms of snapshot number and signal-to-noise ratio (SNR), thus providing a robust and effective solution for DOA estimation in coherent signal environments.

关键词： Covariance matrices Direction-of-arrival estimation Vectors Estimation signal processing algorithms Convolution Array signal processing Smoothing methods Kernel Sensor arrays Coherent signals DOA estimation convolution kernel signal space matrix

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Fast DFT Computation for signals With Structured Support

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IEEE TRANSACTIONS ON INFORMATION THEORY 2024年第2期70卷 1498-1524页

作者： Pochimireddy, Charantej Reddy Siripuram, Aditya Osgood, Brad Indian Inst Technol Dept Elect Engn Hyderabad 502285 India Stanford Univ Dept Elect Engn Stanford CA 94305 USA

Suppose an N-length signal has known frequency support of size k . Given access to samples of this signal, how fast can we compute the DFT? The answer to this question depends on the structure of the frequency support. We first identify some frequency supports for which (an ideal) O(k \log k) complexity can be achieved, which we refer to as homogeneous sets. We give a generalization of the radix-2 FFT that enables O(k\log k) computation of signals with homogeneous frequency support. We use homogeneous sets as building blocks to construct more complex support structures for which the complexity of O(k log k) is achievable. Applying these ideas, we present an O(k log(2 )k) algorithm for computing the DFT of signals whose frequency support is additively structured. We also present partial converses.

关键词： Discrete Fourier transforms Complexity theory Indexes Additives signal processing algorithms Arithmetic Approximation algorithms fast Fourier transforms algorithm design and analysis signal processing algorithms combinatorial mathematics computational efficiency signal reconstruction signal sampling

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Can Far-Field Beam Training Be Deployed for Cross-Field Beam Alignment in Terahertz UM-MIMO Communications?

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IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS 2024年第10期23卷 14972-14987页

作者： Chen, Yuhang Han, Chong Bjornson, Emil Shanghai Jiao Tong Univ Terahertz Wireless Commun TWC Lab Shanghai 200240 Peoples R China Shanghai Jiao Tong Univ Dept Elect Engn Terahertz Wireless Commun TWC Lab Shanghai 200240 Peoples R China Shanghai Jiao Tong Univ Cooperat Medianet Innovat Ctr CMIC Shanghai 200240 Peoples R China KTH Royal Inst Technol Dept Comp Sci S-16440 Stockholm Sweden

Ultra-massive multiple-input multiple-output (UM-MIMO) is the enabler of Terahertz (THz) communications in next-generation wireless networks. In THz UM-MIMO systems, a new paradigm of cross-field communications spanning from near-field to far-field is emerging, since the near-field range expands with higher frequencies and larger array apertures. Precise beam alignment in cross-field is critical but challenging. Specifically, unlike far-field beams that rely only on the angle domain, the incorporation of dual-domain (angle and distance) training significantly increases overhead. A natural question arises of whether far-field beam training can be deployed for cross-field beam alignment. In this paper, this question is answered, by demonstrating that the far-field training enables sufficient signal-to-noise ratio (SNR) in both far- and near-field scenarios, while exciting all channel dimensions. Based on that, we propose a subarray-coordinated hierarchical (SCH) training with greatly reduced overhead. To further obtain high-precision beam designs, we propose a two-phase angle and distance beam estimator (TPBE). Extensive simulations demonstrate the effectiveness of the proposed methods. Compared to near-field exhaustive search, the SCH possesses 0.2% training overhead. The TPBE achieves 0.16 degrees and 0.01 meters estimation root-mean-squared errors for angle and distance. Furthermore, with the estimated beam directions, a near-optimal SNR with 0.3 dB deviation is attained after beam alignment.

关键词： Training Estimation Terahertz communications signal to noise ratio Channel models Wireless communication signal processing algorithms Terahertz (THz) communications near-field ultra-massive multiple-input multiple-output (UM-MIMO) systems cross far- and near-field

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Effect of Deep Learning Algorithm Incorporating Attention Module Optimization on Assisted Training for Youth Running Sports

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IEEE ACCESS 2024年 12卷 113960-113971页

作者： Han, Chunlong Liu, Pengyu Zhuhai 1 High Sch Pingsha Campus Zhuhai 519000 Peoples R China Guangzhou Acad Fine Arts Guangzhou 510006 Peoples R China

Given the limitations of traditional methods in automatic feature extraction, the study aims to improve the accuracy of posture recognition in adolescent running training through deep learning techniques. This study first constructed a human pose motion model to capture complex pose changes during the motion process. Furthermore, an algorithm framework combining convolutional neural networks and long short-term memory networks was proposed, and optimized by integrating attention modules to enhance the model's ability to capture key action details and improve recognition accuracy. The outcomes indicated that the recognition accuracy of the raw data processed using the convolutional neural network algorithm is 0.93, which is improved to 0.96 after preprocessing, while the accuracy of the long-short-term memory network algorithm is 0.91 on the raw data and 0.95 after preprocessing. The Inception combined with long-short-term memory network algorithm optimised by incorporating the attention module has the highest accuracy of 0.98 on the preprocessed data, while that on the 0.95 on the raw data, and 1.0 on specific actions such as running and riding. It can be found that the attention module significantly improves the recognition accuracy of the algorithm and its ability to recognise complex actions. This study not only improves the way that teenagers train to run, but it also creates new opportunities for the use of deep learning methods in the context of sports-assisted training.

关键词： Training Accuracy Sports Long short term memory Deep learning signal processing algorithms Optimization Pose estimation Assisted training attention deep learning motion pose recognition

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