Multiset Canonical Correlation Analysis (mCCA), also called Generalized Canonical Correlation Analysis (GCCA), is a technique to identify correlated variables across multiple datasets, which can be used for feature extraction in fields like neuroscience, cross-language information retrieval, and recommendation systems, among others. Besides its wide use, there is still a lack of comprehensive understanding of its theory and implementation with different objective functions all under one umbrella. In this paper, we review the five main mCCA methods: sumcor, maxvar, minvar, genvar, and ssqcor. We provide a concise overview of their optimization problems along with their solutions and pseudocodes. After this, we discuss the application of mCCA for estimating underlying latent components in the Joint Blind Source Separation (JBSS) problem and propose the source identification conditions of the different mCCA methods, i.e., the conditions under which they are able to achieve JBSS. We substantiate the proposed theoretical conditions with numerical results and test the statistical efficiency of the methods for finite samples. We observe in our experiments that genvar appears to have the least restrictive source identification conditions and to be more statistically efficient than the other methods. This suggests that genvar is generally the best-performing mCCA method for JBSS except for special cases, which is an important finding, as the most commonly used mCCA methods are maxvar and sumcor.
{"title":"A Comprehensive Guide to Multiset Canonical Correlation Analysis and Its Application to Joint Blind Source Separation","authors":"Isabell Lehmann;Ben Gabrielson;Tanuj Hasija;Tülay Adali","doi":"10.1109/TSP.2025.3623874","DOIUrl":"10.1109/TSP.2025.3623874","url":null,"abstract":"Multiset Canonical Correlation Analysis (mCCA), also called Generalized Canonical Correlation Analysis (GCCA), is a technique to identify correlated variables across multiple datasets, which can be used for feature extraction in fields like neuroscience, cross-language information retrieval, and recommendation systems, among others. Besides its wide use, there is still a lack of comprehensive understanding of its theory and implementation with different objective functions all under one umbrella. In this paper, we review the five main mCCA methods: <monospace>sumcor</monospace>, <monospace>maxvar</monospace>, <monospace>minvar</monospace>, <monospace>genvar</monospace>, and <monospace>ssqcor</monospace>. We provide a concise overview of their optimization problems along with their solutions and pseudocodes. After this, we discuss the application of mCCA for estimating underlying latent components in the Joint Blind Source Separation (JBSS) problem and propose the <italic>source identification conditions</i> of the different mCCA methods, i.e., the conditions under which they are able to achieve JBSS. We substantiate the proposed theoretical conditions with numerical results and test the statistical efficiency of the methods for finite samples. We observe in our experiments that <monospace>genvar</monospace> appears to have the least restrictive source identification conditions and to be more statistically efficient than the other methods. This suggests that <monospace>genvar</monospace> is generally the best-performing mCCA method for JBSS except for special cases, which is an important finding, as the most commonly used mCCA methods are <monospace>maxvar</monospace> and <monospace>sumcor</monospace>.","PeriodicalId":13330,"journal":{"name":"IEEE Transactions on Signal Processing","volume":"74 ","pages":"43-60"},"PeriodicalIF":5.8,"publicationDate":"2025-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=11217411","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145381411","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-10-24DOI: 10.1109/TSP.2025.3623098
Jiabin Lin;Shana Moothedath;Tuan Anh Le
Multi-task representation learning is an emerging machine learning paradigm that integrates data from multiple sources, harnessing task similarities to enhance overall model performance. The application of multi-task learning to real-world settings is hindered due to data scarcity, along with challenges related to scalability and computational resources. To address these challenges, we develop a fast and sample-efficient approach for multi-task active learning with linear representation when the amount of data from source tasks and target tasks is limited. By leveraging the techniques from active learning, we propose an adaptive sampling-based alternating projected gradient descent (GD) and minimization algorithm that iteratively estimates the relevance of each source task to the target task and samples from each source task based on the estimated relevance. We present the convergence guarantees and the sample and time complexities of our algorithm. We evaluated the effectiveness of our algorithm using experiments and compared it with four benchmark algorithms using synthetic and real-world MNIST-C and MovieLens-100K datasets.
{"title":"Provable Active Multi-Task Representation Learning","authors":"Jiabin Lin;Shana Moothedath;Tuan Anh Le","doi":"10.1109/TSP.2025.3623098","DOIUrl":"10.1109/TSP.2025.3623098","url":null,"abstract":"Multi-task representation learning is an emerging machine learning paradigm that integrates data from multiple sources, harnessing task similarities to enhance overall model performance. The application of multi-task learning to real-world settings is hindered due to data scarcity, along with challenges related to scalability and computational resources. To address these challenges, we develop a fast and sample-efficient approach for multi-task active learning with linear representation when the amount of data from source tasks and target tasks is limited. By leveraging the techniques from active learning, we propose an adaptive sampling-based alternating projected gradient descent (GD) and minimization algorithm that iteratively estimates the relevance of each source task to the target task and samples from each source task based on the estimated relevance. We present the convergence guarantees and the sample and time complexities of our algorithm. We evaluated the effectiveness of our algorithm using experiments and compared it with four benchmark algorithms using synthetic and real-world MNIST-C and MovieLens-100K datasets.","PeriodicalId":13330,"journal":{"name":"IEEE Transactions on Signal Processing","volume":"73 ","pages":"5060-5075"},"PeriodicalIF":5.8,"publicationDate":"2025-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145381412","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-10-23DOI: 10.1109/TSP.2025.3624986
Gian Marti;Christoph Studer
Multi-antenna processing enables jammer mitigation through spatial filtering, provided that the receiver knows the spatial characteristics of the jammer interference. Estimating these characteristics is easy for barrage jammers that transmit continuously and with static characteristics, but difficult for more sophisticated jammers. Smart jammers may deliberately suspend transmission when the receiver tries to estimate their spatial characteristics, or they may use time-varying beamforming to continuously change their spatial characteristics. To deal with such smart jammers, we propose MASH (short for MitigAtion via Subspace Hiding), the first method that indiscriminately mitigates all types of jammers. Assume that the transmitter and receiver share a common secret. Based on this secret, the transmitter embeds (with a time-domain transform) its signal in a secret subspace of a higher-dimensional space. The receiver applies a reciprocal transform to the receive signal, which (i) raises the legitimate transmit signal from its secret subspace and (ii) provably transforms any jammer into a barrage jammer, making estimation and mitigation via multi-antenna processing straightforward. Focusing on the massive multi-user MIMO uplink, we present three MASH-based data detectors and show their jammer-resilience via extensive simulations. We also introduce strategies for multi-user communication without a global secret as well as methods that use computationally efficient embedding and raising transforms.
{"title":"Universal MIMO Jammer Mitigation via Subspace Hiding","authors":"Gian Marti;Christoph Studer","doi":"10.1109/TSP.2025.3624986","DOIUrl":"https://doi.org/10.1109/TSP.2025.3624986","url":null,"abstract":"Multi-antenna processing enables jammer mitigation through spatial filtering, provided that the receiver knows the spatial characteristics of the jammer interference. Estimating these characteristics is easy for barrage jammers that transmit continuously and with static characteristics, but difficult for more sophisticated jammers. Smart jammers may deliberately suspend transmission when the receiver tries to estimate their spatial characteristics, or they may use time-varying beamforming to continuously change their spatial characteristics. To deal with such smart jammers, we propose MASH (short for MitigAtion via Subspace Hiding), the first method that indiscriminately mitigates <italic>all</i> types of jammers. Assume that the transmitter and receiver share a common secret. Based on this secret, the transmitter <italic>embeds</i> (with a time-domain transform) its signal in a secret subspace of a higher-dimensional space. The receiver applies a reciprocal transform to the receive signal, which (i) <italic>raises</i> the legitimate transmit signal from its secret subspace and (ii) provably transforms <italic>any</i> jammer into a barrage jammer, making estimation and mitigation via multi-antenna processing straightforward. Focusing on the massive multi-user MIMO uplink, we present three MASH-based data detectors and show their jammer-resilience via extensive simulations. We also introduce strategies for multi-user communication without a global secret as well as methods that use computationally efficient embedding and raising transforms.","PeriodicalId":13330,"journal":{"name":"IEEE Transactions on Signal Processing","volume":"73 ","pages":"5152-5167"},"PeriodicalIF":5.8,"publicationDate":"2025-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145886683","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-10-23DOI: 10.1109/TSP.2025.3624833
Zhenyu Tao;Wei Xu;Xiaohu You
Abstract Digital twin (DT)-driven reinforcement learning (RL) has emerged as a promising paradigm for wireless network optimization, offering safe and efficient training environment for policy exploration. However, in theory existing methods cannot always guarantee real-world performance of DT-trained policies before actual deployment, due to the absence of a universal metric for assessing DT’s ability to support reliable RL training. In this paper, we propose the DT bisimulation metric (DT-BSM), a novel metric based on the Wasserstein distance, to quantify the discrepancy between Markov decision processes (MDPs) in both the DT and the corresponding real-world wireless network environment. We prove that for any DT-trained policy, the sub-optimality of its performance (regret) in the real-world deployment is bounded by a weighted sum of the DT-BSM and its sub-optimality within the MDP in the DT. Then, a modified DT-BSM based on the total variation distance is also introduced to avoid the prohibitive calculation complexity of Wasserstein distance for large-scale wireless network scenarios. Further, to tackle the challenge of obtaining accurate transition probabilities of the MDP in real world for the DT-BSM calculation, we propose an empirical DT-BSM method based on statistical sampling. We prove that the empirical DT-BSM always converges to the desired theoretical one, and quantitatively establish the relationship between the required sample size and the target level of approximation accuracy. Numerical experiments validate this first theoretical finding on the provable and calculable performance bounds for DT-driven RL.
{"title":"Provable Performance Bounds for Digital Twin-Driven Reinforcement Learning in Wireless Networks: A Novel Digital-Twin Bisimulation Metric","authors":"Zhenyu Tao;Wei Xu;Xiaohu You","doi":"10.1109/TSP.2025.3624833","DOIUrl":"https://doi.org/10.1109/TSP.2025.3624833","url":null,"abstract":"Abstract Digital twin (DT)-driven reinforcement learning (RL) has emerged as a promising paradigm for wireless network optimization, offering safe and efficient training environment for policy exploration. However, in theory existing methods cannot always guarantee real-world performance of DT-trained policies before actual deployment, due to the absence of a universal metric for assessing DT’s ability to support reliable RL training. In this paper, we propose the DT bisimulation metric (DT-BSM), a novel metric based on the Wasserstein distance, to quantify the discrepancy between Markov decision processes (MDPs) in both the DT and the corresponding real-world wireless network environment. We prove that for any DT-trained policy, the sub-optimality of its performance (regret) in the real-world deployment is bounded by a weighted sum of the DT-BSM and its sub-optimality within the MDP in the DT. Then, a modified DT-BSM based on the total variation distance is also introduced to avoid the prohibitive calculation complexity of Wasserstein distance for large-scale wireless network scenarios. Further, to tackle the challenge of obtaining accurate transition probabilities of the MDP in real world for the DT-BSM calculation, we propose an empirical DT-BSM method based on statistical sampling. We prove that the empirical DT-BSM always converges to the desired theoretical one, and quantitatively establish the relationship between the required sample size and the target level of approximation accuracy. Numerical experiments validate this first theoretical finding on the provable and calculable performance bounds for DT-driven RL.","PeriodicalId":13330,"journal":{"name":"IEEE Transactions on Signal Processing","volume":"73 ","pages":"4430-4445"},"PeriodicalIF":5.8,"publicationDate":"2025-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145612111","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-10-23DOI: 10.1109/TSP.2025.3624791
Ali Bereyhi;Ben Liang;Gary Boudreau;Ali Afana
Error accumulation is effective for gradient sparsification in distributed settings: initially-unselected gradient entries are eventually selected as their accumulated error exceeds a certain level. The accumulation essentially behaves as a scaling of the learning rate for the selected entries. Although this property prevents the slow-down of lateral movements in distributed gradient descent, it can deteriorate convergence in some settings. This work proposes a novel sparsification scheme that controls the learning rate scaling of error accumulation. The development of this scheme follows two major steps: first, gradient sparsification is formulated as an inverse probability (inference) problem, and the Bayesian optimal sparsification mask is derived as a maximum-a-posteriori estimator. Using the prior distribution inherited from Top-$ k $, we derive a new sparsification algorithm which can be interpreted as a regularized form of Top-$ k $. We call this algorithm regularized Top-$ k $ (RegTop-$ k $). It utilizes past aggregated gradients to evaluate posterior statistics of the next aggregation. It then prioritizes the local accumulated gradient entries based on these posterior statistics. We validate our derivation through various numerical experiments. In distributed linear regression, it is observed that while Top-$ k $ remains at a fixed distance from the global optimum, RegTop-$ k $ converges to the global optimum at significantly higher compression ratios. We further demonstrate the generalization of this observation by employing RegTop-$ k $ in distributed training of ResNet-18 on CIFAR-10, as well as fine-tuning of multiple computer vision models on the ImageNette dataset. Our numerical results confirm that as the compression ratio increases, RegTop-$ k $ sparsification noticeably outperforms Top-$ k $.
在分布式设置下，误差积累对于梯度稀疏化是有效的：初始未选择的梯度项最终被选择，因为它们的累积误差超过了一定的水平。累积本质上表现为所选条目的学习率的缩放。虽然这种特性可以防止在分布式梯度下降中横向运动的减速，但在某些情况下它会降低收敛性。本工作提出了一种新的稀疏化方案，该方案控制了错误积累的学习率缩放。该方案的发展遵循两个主要步骤：首先，将梯度稀疏化表述为一个反概率（推理）问题，并推导出贝叶斯最优稀疏化掩模作为最大后验估计量。利用继承自Top-$ k $的先验分布，导出了一种新的稀疏化算法，该算法可以解释为Top-$ k $的正则化形式。我们称这种算法为正则化Top-$ k $ （RegTop-$ k $）。它利用过去的聚合梯度来评估下一个聚合的后验统计。然后，它根据这些后验统计对局部累积梯度条目进行优先级排序。我们通过各种数值实验验证了我们的推导。在分布线性回归中，可以观察到Top-$ k $与全局最优保持固定距离，而RegTop-$ k $在显著更高的压缩比下收敛到全局最优。通过在CIFAR-10上使用RegTop-$ k $对ResNet-18进行分布式训练，以及在ImageNette数据集上对多个计算机视觉模型进行微调，我们进一步证明了这一观察结果的泛化。我们的数值结果证实，随着压缩比的增加，RegTop-$ k $的稀疏性明显优于Top-$ k $。
{"title":"Regularized Top-$ k $: A Bayesian Framework for Gradient Sparsification","authors":"Ali Bereyhi;Ben Liang;Gary Boudreau;Ali Afana","doi":"10.1109/TSP.2025.3624791","DOIUrl":"https://doi.org/10.1109/TSP.2025.3624791","url":null,"abstract":"Error accumulation is effective for gradient sparsification in distributed settings: initially-unselected gradient entries are eventually selected as their accumulated error exceeds a certain level. The accumulation essentially behaves as a scaling of the learning rate for the selected entries. Although this property prevents the slow-down of lateral movements in distributed gradient descent, it can deteriorate convergence in some settings. This work proposes a novel sparsification scheme that controls the learning rate scaling of error accumulation. The development of this scheme follows two major steps: first, gradient sparsification is formulated as an inverse probability (inference) problem, and the Bayesian optimal sparsification mask is derived as a maximum-a-posteriori estimator. Using the prior distribution inherited from <sc>Top</small>-<inline-formula><tex-math>$ k $</tex-math></inline-formula>, we derive a new sparsification algorithm which can be interpreted as a regularized form of <sc>Top</small>-<inline-formula><tex-math>$ k $</tex-math></inline-formula>. We call this algorithm <italic>regularized</i> <sc>Top</small>-<inline-formula><tex-math>$ k $</tex-math></inline-formula> (<sc>RegTop-</small><inline-formula><tex-math>$ k $</tex-math></inline-formula>). It utilizes past aggregated gradients to evaluate posterior statistics of the next aggregation. It then prioritizes the local accumulated gradient entries based on these posterior statistics. We validate our derivation through various numerical experiments. In distributed linear regression, it is observed that while <sc>Top</small>-<inline-formula><tex-math>$ k $</tex-math></inline-formula> remains at a fixed distance from the global optimum, <sc>RegTop</small>-<inline-formula><tex-math>$ k $</tex-math></inline-formula> converges to the global optimum at significantly higher compression ratios. We further demonstrate the generalization of this observation by employing <sc>RegTop</small>-<inline-formula><tex-math>$ k $</tex-math></inline-formula> in distributed training of ResNet-18 on CIFAR-10, as well as fine-tuning of multiple computer vision models on the ImageNette dataset. Our numerical results confirm that as the compression ratio increases, <sc>RegTop</small>-<inline-formula><tex-math>$ k $</tex-math></inline-formula> sparsification noticeably outperforms <sc>Top</small>-<inline-formula><tex-math>$ k $</tex-math></inline-formula>.","PeriodicalId":13330,"journal":{"name":"IEEE Transactions on Signal Processing","volume":"73 ","pages":"4463-4478"},"PeriodicalIF":5.8,"publicationDate":"2025-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145674855","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Network optimization remains fundamental in wireless communications, with Artificial Intelligence (AI)-based solutions gaining widespread adoption. As Sixth-Generation (6G) communication networks pursue full-scenario coverage, optimization in complex extreme environments presents unprecedented challenges. The dynamic nature of these environments, combined with physical constraints, makes it difficult for AI solutions such as Deep Reinforcement Learning (DRL) to obtain effective reward feedback for the training process. However, many existing DRL-based network optimization studies overlook this challenge through idealized environment settings. Inspired by the powerful capabilities of Generative AI (GenAI), especially diffusion models, in capturing complex latent distributions, we introduce a novel Diffusion Model-based Reward Shaping Scheme (DRESS) to achieve robust network optimization. By conditioning on observed environmental states and executed actions, DRESS leverages diffusion models’ multi-step denoising process to refine latent representations progressively, generating meaningful auxiliary reward signals that capture patterns of network systems. Moreover, DRESS is designed for seamless integration with any DRL framework, allowing DRESS-aided DRL (DRESSed-DRL) to enable stable and efficient DRL training even under extreme network environments. Experimental results demonstrate that DRESSed-DRL achieves about $1.5{rm{x}}$ times faster convergence than its original version in sparse-reward wireless environments and significant performance improvements in multiple general DRL benchmark environments compared to baseline methods. The code of DRESS is available at https://github.com/NICE-HKU/DRESS.
{"title":"DRESS: Diffusion Model-Based Reward Shaping Scheme for Intelligent Networks","authors":"Feiran You;Hongyang Du;Xiangwang Hou;Yong Ren;Kaibin Huang","doi":"10.1109/TSP.2025.3623239","DOIUrl":"https://doi.org/10.1109/TSP.2025.3623239","url":null,"abstract":"Network optimization remains fundamental in wireless communications, with Artificial Intelligence (AI)-based solutions gaining widespread adoption. As Sixth-Generation (6G) communication networks pursue full-scenario coverage, optimization in complex extreme environments presents unprecedented challenges. The dynamic nature of these environments, combined with physical constraints, makes it difficult for AI solutions such as Deep Reinforcement Learning (DRL) to obtain effective reward feedback for the training process. However, many existing DRL-based network optimization studies overlook this challenge through idealized environment settings. Inspired by the powerful capabilities of Generative AI (GenAI), especially diffusion models, in capturing complex latent distributions, we introduce a novel <underline>D</u>iffusion Model-based <underline>Re</u>ward <underline>S</u>haping <underline>S</u>cheme (DRESS) to achieve robust network optimization. By conditioning on observed environmental states and executed actions, DRESS leverages diffusion models’ multi-step denoising process to refine latent representations progressively, generating meaningful auxiliary reward signals that capture patterns of network systems. Moreover, DRESS is designed for seamless integration with any DRL framework, allowing DRESS-aided DRL (DRESSed-DRL) to enable stable and efficient DRL training even under extreme network environments. Experimental results demonstrate that DRESSed-DRL achieves about <inline-formula><tex-math>$1.5{rm{x}}$</tex-math></inline-formula> times faster convergence than its original version in sparse-reward wireless environments and significant performance improvements in multiple general DRL benchmark environments compared to baseline methods. The code of DRESS is available at <uri>https://github.com/NICE-HKU/DRESS</uri>.","PeriodicalId":13330,"journal":{"name":"IEEE Transactions on Signal Processing","volume":"73 ","pages":"4285-4300"},"PeriodicalIF":5.8,"publicationDate":"2025-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145560686","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-10-20DOI: 10.1109/TSP.2025.3623496
Marco Fontana;Ángel F. García-Fernández;Simon Maskell
This paper presents a Poisson multi-Bernoulli mixture (PMBM) filter for multi-target filtering based on sensor measurements that are sets of trajectories in the last two-time step window. The proposed filter, the trajectory measurement PMBM (TM-PMBM) filter, propagates a PMBM density on the set of target states. In prediction, the filter obtains the PMBM density on the set of trajectories over the last two time steps. This density is then updated with the set of trajectory measurements. After the update step, the PMBM posterior on the set of two-step trajectories is marginalised to obtain a PMBM density on the set of target states. The filter provides a closed-form solution for multi-target filtering based on sets of trajectory measurements, estimating the set of target states at the end of each time window. Additionally, the paper proposes computationally lighter alternatives to the TM-PMBM filter by deriving a Poisson multi-Bernoulli (PMB) density through Kullback-Leibler divergence minimisation in an augmented space with auxiliary variables. The performance of the proposed filters are evaluated in a simulation study.
{"title":"Poisson Multi-Bernoulli Mixture Filter for Trajectory Measurements","authors":"Marco Fontana;Ángel F. García-Fernández;Simon Maskell","doi":"10.1109/TSP.2025.3623496","DOIUrl":"https://doi.org/10.1109/TSP.2025.3623496","url":null,"abstract":"This paper presents a Poisson multi-Bernoulli mixture (PMBM) filter for multi-target filtering based on sensor measurements that are sets of trajectories in the last two-time step window. The proposed filter, the trajectory measurement PMBM (TM-PMBM) filter, propagates a PMBM density on the set of target states. In prediction, the filter obtains the PMBM density on the set of trajectories over the last two time steps. This density is then updated with the set of trajectory measurements. After the update step, the PMBM posterior on the set of two-step trajectories is marginalised to obtain a PMBM density on the set of target states. The filter provides a closed-form solution for multi-target filtering based on sets of trajectory measurements, estimating the set of target states at the end of each time window. Additionally, the paper proposes computationally lighter alternatives to the TM-PMBM filter by deriving a Poisson multi-Bernoulli (PMB) density through Kullback-Leibler divergence minimisation in an augmented space with auxiliary variables. The performance of the proposed filters are evaluated in a simulation study.","PeriodicalId":13330,"journal":{"name":"IEEE Transactions on Signal Processing","volume":"73 ","pages":"4301-4314"},"PeriodicalIF":5.8,"publicationDate":"2025-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145560687","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Independent vector analysis (IVA) is an attractive solution to address the problem of joint blind source separation (JBSS), that is, the simultaneous extraction of latent sources from several datasets implicitly sharing some information. Among IVA approaches, we focus here on the celebrated IVA-G model, that describes observed data through the mixing of independent Gaussian source vectors across the datasets. IVA-G algorithms usually seek the values of demixing matrices that maximize the joint likelihood of the datasets, estimating the sources using these demixing matrices. Instead, we write the likelihood of the data with respect to both the demixing matrices and the precision matrices of the source estimates. This allows us to formulate a cost function whose mathematical properties enable the use of a proximal alternating algorithm based on closed form operators with provable convergence to a critical point. After establishing the convergence properties of the new algorithm, we illustrate its desirable performance in separating sources with covariance structures that represent varying degrees of difficulty for JBSS.
{"title":"An Effective Iterative Solution for Independent Vector Analysis With Convergence Guarantees","authors":"Clément Cosserat;Ben Gabrielson;Emilie Chouzenoux;Jean-Christophe Pesquet;Tülay Adali","doi":"10.1109/TSP.2025.3620539","DOIUrl":"https://doi.org/10.1109/TSP.2025.3620539","url":null,"abstract":"Independent vector analysis (IVA) is an attractive solution to address the problem of joint blind source separation (JBSS), that is, the simultaneous extraction of latent sources from several datasets implicitly sharing some information. Among IVA approaches, we focus here on the celebrated IVA-G model, that describes observed data through the mixing of independent Gaussian source vectors across the datasets. IVA-G algorithms usually seek the values of demixing matrices that maximize the joint likelihood of the datasets, estimating the sources using these demixing matrices. Instead, we write the likelihood of the data with respect to both the demixing matrices and the precision matrices of the source estimates. This allows us to formulate a cost function whose mathematical properties enable the use of a proximal alternating algorithm based on closed form operators with provable convergence to a critical point. After establishing the convergence properties of the new algorithm, we illustrate its desirable performance in separating sources with covariance structures that represent varying degrees of difficulty for JBSS.","PeriodicalId":13330,"journal":{"name":"IEEE Transactions on Signal Processing","volume":"73 ","pages":"4718-4733"},"PeriodicalIF":5.8,"publicationDate":"2025-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145778116","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-10-20DOI: 10.1109/TSP.2025.3623455
Wei Chen;Qingfeng Xia;Jiahui Sun;Zhanchuan Cai
Conventional wavelet systems often face intrinsic limitations in simultaneously achieving orthogonality, vanishing moments, regularity and boundary control. This paper proposes a novel complete orthogonal basis system $text{OTP-}k$ (Orthogonal Truncated Power functions of degree $k$) on $L^{2}[0,1]$. The truncated power (TP) functions attain superior flexibility by incorporating nodes while retaining the essential characteristics of conventional power functions. We reveal a critical feature of TP functions: their capacity to explicitly decompose signals into dominant and residual components. Building upon this theoretical insight, we integrate the multi-resolution analysis (MRA) framework into the TP functions paradigm, thereby constructing an orthogonal wavelet-like basis. Notably, the $text{OTP-}k$ basis supports parametrically adjustable vanishing moments through degree modification of $k$, ensures mathematically verifiable smoothness continuity, and demonstrates superior time-frequency localization characteristics. This work rigorously establishes the theoretical foundations, construction methodology, and computational implementation strategies for $text{OTP-}k$. Through systematic evaluations of Electroencephalogram (EEG) and gravitational wave (GW) signal reconstruction and denoising, benchmarked against traditional wavelet bases, we validate the significant potential of the $text{OTP-}k$ basis in signal processing.
{"title":"From Truncated Power Functions To Orthogonal Wavelet-Like Basis: Principle, Implementation and Applications","authors":"Wei Chen;Qingfeng Xia;Jiahui Sun;Zhanchuan Cai","doi":"10.1109/TSP.2025.3623455","DOIUrl":"https://doi.org/10.1109/TSP.2025.3623455","url":null,"abstract":"Conventional wavelet systems often face intrinsic limitations in simultaneously achieving orthogonality, vanishing moments, regularity and boundary control. This paper proposes a novel complete orthogonal basis system <inline-formula><tex-math>$text{OTP-}k$</tex-math></inline-formula> (Orthogonal Truncated Power functions of degree <inline-formula><tex-math>$k$</tex-math></inline-formula>) on <inline-formula><tex-math>$L^{2}[0,1]$</tex-math></inline-formula>. The truncated power (TP) functions attain superior flexibility by incorporating nodes while retaining the essential characteristics of conventional power functions. We reveal a critical feature of TP functions: their capacity to explicitly decompose signals into dominant and residual components. Building upon this theoretical insight, we integrate the multi-resolution analysis (MRA) framework into the TP functions paradigm, thereby constructing an orthogonal wavelet-like basis. Notably, the <inline-formula><tex-math>$text{OTP-}k$</tex-math></inline-formula> basis supports parametrically adjustable vanishing moments through degree modification of <inline-formula><tex-math>$k$</tex-math></inline-formula>, ensures mathematically verifiable smoothness continuity, and demonstrates superior time-frequency localization characteristics. This work rigorously establishes the theoretical foundations, construction methodology, and computational implementation strategies for <inline-formula><tex-math>$text{OTP-}k$</tex-math></inline-formula>. Through systematic evaluations of Electroencephalogram (EEG) and gravitational wave (GW) signal reconstruction and denoising, benchmarked against traditional wavelet bases, we validate the significant potential of the <inline-formula><tex-math>$text{OTP-}k$</tex-math></inline-formula> basis in signal processing.","PeriodicalId":13330,"journal":{"name":"IEEE Transactions on Signal Processing","volume":"73 ","pages":"4226-4239"},"PeriodicalIF":5.8,"publicationDate":"2025-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145560685","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-10-17DOI: 10.1109/TSP.2025.3602387
Mahdi Khojastehnia;Ioannis Lambadaris;Ramy H. Gohary;Sergey Loyka
We consider a multiple-input multiple-output (MIMO) channel, in which the transmit antennas are partitioned into groups, each with a per-group power constraint (PGPC) and a total power constraint (TPC). We considered two cases: (i) right unitary-invariant, including Rayleigh, fading MIMO channels with perfect channel state information at the receiver (CSI-R), and (ii) massive MIMO channels with perfect CSI at the transmitter and the receiver (CSI-TR). For both cases, we show that the rate-optimal input covariance matrix is diagonal, implying reduced design complexity and independent signaling on each antenna. We derive closed-form expressions for the diagonal entries, i.e., the powers allocated to each antenna. For CSI-R channels, we derive a criterion to identify groups with active PGPCs. Majorization theory and Schur-concavity are used to obtain the optimal power allocations. For CSI-TR channels, we use the Karush-Kuhn-Tucker conditions to show that the PGPCs result in a ceiling profile, causing the rate-optimal power allocations to deviate from standard water-filling. Compared to numerical algorithms, our closed-form expressions are significantly more efficient to compute and guarantee globally optimality. Our analytical findings are validated via numerical experiments.
{"title":"Rate-Optimal Power Allocation for MIMO Channels Under Joint Total and Per-Group Power Constraints","authors":"Mahdi Khojastehnia;Ioannis Lambadaris;Ramy H. Gohary;Sergey Loyka","doi":"10.1109/TSP.2025.3602387","DOIUrl":"10.1109/TSP.2025.3602387","url":null,"abstract":"We consider a multiple-input multiple-output (MIMO) channel, in which the transmit antennas are partitioned into groups, each with a per-group power constraint (PGPC) and a total power constraint (TPC). We considered two cases: (i) right unitary-invariant, including Rayleigh, fading MIMO channels with perfect channel state information at the receiver (CSI-R), and (ii) massive MIMO channels with perfect CSI at the transmitter and the receiver (CSI-TR). For both cases, we show that the rate-optimal input covariance matrix is diagonal, implying reduced design complexity and independent signaling on each antenna. We derive closed-form expressions for the diagonal entries, i.e., the powers allocated to each antenna. For CSI-R channels, we derive a criterion to identify groups with active PGPCs. Majorization theory and Schur-concavity are used to obtain the optimal power allocations. For CSI-TR channels, we use the Karush-Kuhn-Tucker conditions to show that the PGPCs result in a ceiling profile, causing the rate-optimal power allocations to deviate from standard water-filling. Compared to numerical algorithms, our closed-form expressions are significantly more efficient to compute and guarantee globally optimality. Our analytical findings are validated via numerical experiments.","PeriodicalId":13330,"journal":{"name":"IEEE Transactions on Signal Processing","volume":"73 ","pages":"4315-4330"},"PeriodicalIF":5.8,"publicationDate":"2025-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145310867","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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