Pub Date : 2026-06-01Epub Date: 2026-01-05DOI: 10.1016/j.sigpro.2026.110491
Chengxin Yang , Benoit Champagne , Wei Yi
This paper addresses the optimization problem of transmit beamforming design for area surveillance and multi-target tracking (MTT) in a colocated multiple-input multiple-output (C-MIMO) radar system. We first establish the relationship between the detection probability and the predictive Cramér-Rao lower bound (PCRLB) as performance metrics, and the transmit signal correlation matrix as the design variable. The surveillance area, defined as a circular sector bounded by a polar angle and the intersecting arc, is divided into independent smaller sectors, each corresponding to a different illumination direction of the C-MIMO radar. To maximize the efficient utilization of power resources, we then aim to maximize the number of simultaneously illuminated sectors while achieving desired detection probability and target tracking accuracy. Given that the formulated optimization problem is an intractable non-convex mixed-integer nonlinear problem, we propose a beamforming algorithm based on Quality of Service (QoS) to solve it efficiently. Simulation results indicate that the proposed algorithm is capable of effectively maximizing the illuminated area while consistently meeting the specified detection probability and MTT accuracy requirements.
{"title":"Transmit beamforming design for area surveillance and multi-target tracking in colocated MIMO radar","authors":"Chengxin Yang , Benoit Champagne , Wei Yi","doi":"10.1016/j.sigpro.2026.110491","DOIUrl":"10.1016/j.sigpro.2026.110491","url":null,"abstract":"<div><div>This paper addresses the optimization problem of transmit beamforming design for area surveillance and multi-target tracking (MTT) in a colocated multiple-input multiple-output (C-MIMO) radar system. We first establish the relationship between the detection probability and the predictive Cramér-Rao lower bound (PCRLB) as performance metrics, and the transmit signal correlation matrix as the design variable. The surveillance area, defined as a circular sector bounded by a polar angle and the intersecting arc, is divided into independent smaller sectors, each corresponding to a different illumination direction of the C-MIMO radar. To maximize the efficient utilization of power resources, we then aim to maximize the number of simultaneously illuminated sectors while achieving desired detection probability and target tracking accuracy. Given that the formulated optimization problem is an intractable non-convex mixed-integer nonlinear problem, we propose a beamforming algorithm based on Quality of Service (QoS) to solve it efficiently. Simulation results indicate that the proposed algorithm is capable of effectively maximizing the illuminated area while consistently meeting the specified detection probability and MTT accuracy requirements.</div></div>","PeriodicalId":49523,"journal":{"name":"Signal Processing","volume":"243 ","pages":"Article 110491"},"PeriodicalIF":3.6,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145978342","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 : 2026-06-01Epub Date: 2025-12-20DOI: 10.1016/j.sigpro.2025.110451
Hui Liu , Jicheng Zhu , Hengtai Li , Christian Desrosiers , Caiming Zhang
Multimodal medical image registration and fusion integrate complementary features from different modalities, to enhance diagnostic accuracy and provide comprehensive clinical insights. Existing approaches face critical shortcomings in feature alignment, computational efficiency and clinical interpretability, demanding a novel coupled framework to address these issues. Additionally, the lack of open-source benchmark datasets at the systemic level persists as a major bottleneck. Thus, a novel Imaging Coupled Filtering (ICF), means multi-channel image features coupling filtering, is proposed in this work. First, ICF decomposes source images from different modalities into four feature channels: smoothing, texture, contour and edge. Then, intra-channel fusion strategies are designed to generate fused images. Specifically, in the smoothing channels, we propose a visual saliency decomposition strategy to comprehensively extract energy and partial fiber texture features through multi-scale and multi-dimensional analysis, thereby optimizing the utilization of latent feature information. For the texture channels, we propose a novel texture enhancement operator designed to effectively capture fine details and hierarchical structural information, which enables accurate differentiation of invasion states in adherent lesions. Finally, an imaging coupling mechanism is presented to achieve fused results based on the weights of multi-feature representation. Additionally, we have registered and released 403 groups of multimodal abdominal medical images (Ab-MI) for research purposes. Experiments on Atlas and Ab-MI demonstrate that, compared to six state-of-the-art methods, ICF achieves superior results in terms of visual effects, objective metrics and computational efficiency.
{"title":"Imaging coupled filtering: A unified multi-channel framework for multimodal medical image registration and fusion","authors":"Hui Liu , Jicheng Zhu , Hengtai Li , Christian Desrosiers , Caiming Zhang","doi":"10.1016/j.sigpro.2025.110451","DOIUrl":"10.1016/j.sigpro.2025.110451","url":null,"abstract":"<div><div>Multimodal medical image registration and fusion integrate complementary features from different modalities, to enhance diagnostic accuracy and provide comprehensive clinical insights. Existing approaches face critical shortcomings in feature alignment, computational efficiency and clinical interpretability, demanding a novel coupled framework to address these issues. Additionally, the lack of open-source benchmark datasets at the systemic level persists as a major bottleneck. Thus, a novel Imaging Coupled Filtering (ICF), means multi-channel image features coupling filtering, is proposed in this work. First, ICF decomposes source images from different modalities into four feature channels: smoothing, texture, contour and edge. Then, intra-channel fusion strategies are designed to generate fused images. Specifically, in the smoothing channels, we propose a visual saliency decomposition strategy to comprehensively extract energy and partial fiber texture features through multi-scale and multi-dimensional analysis, thereby optimizing the utilization of latent feature information. For the texture channels, we propose a novel texture enhancement operator designed to effectively capture fine details and hierarchical structural information, which enables accurate differentiation of invasion states in adherent lesions. Finally, an imaging coupling mechanism is presented to achieve fused results based on the weights of multi-feature representation. Additionally, we have registered and released 403 groups of multimodal abdominal medical images (Ab-MI) for research purposes. Experiments on Atlas and Ab-MI demonstrate that, compared to six state-of-the-art methods, ICF achieves superior results in terms of visual effects, objective metrics and computational efficiency.</div></div>","PeriodicalId":49523,"journal":{"name":"Signal Processing","volume":"243 ","pages":"Article 110451"},"PeriodicalIF":3.6,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145842703","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 : 2026-06-01Epub Date: 2025-12-20DOI: 10.1016/j.sigpro.2025.110452
Philippe Flores , Konstantin Usevich , David Brie
In this article, a probability mass function (PMF) estimation method called partial coupled tensor factorization of 3D marginals or PCTF3D is proposed. To tame the inherent PMF estimation curse of dimensionality, PCTF3D’s principle is to couple 3-dimensional data projections – seen as order-3 tensors – to obtain a low-rank tensor approximation of the PMF. The contribution of PCTF3D relies on partial coupling which consists in choosing a limited subset of 3D marginals. While PMF estimation is possible with all marginals, coupling only a subset of marginals like in PCTF3D permits to reduce the computational burden without losing significant estimation performance. A key concept of PCTF3D is the choice of marginals to be coupled: this problem is formulated and studied with hypergraphs. This Part I paper introduces the algorithmic framework of PCTF3D: optimization problem, coupling strategies, numerical experiments and a real data application of PCTF3D. On the other hand, the Part II paper studies coupled tensor uniqueness properties of the model introduced by PCTF3D.
{"title":"Coupled tensor models for probability mass function estimation: Part I, principles and algorithms","authors":"Philippe Flores , Konstantin Usevich , David Brie","doi":"10.1016/j.sigpro.2025.110452","DOIUrl":"10.1016/j.sigpro.2025.110452","url":null,"abstract":"<div><div>In this article, a probability mass function (PMF) estimation method called partial coupled tensor factorization of 3D marginals or PCTF3D is proposed. To tame the inherent PMF estimation curse of dimensionality, PCTF3D’s principle is to couple 3-dimensional data projections – seen as order-3 tensors – to obtain a low-rank tensor approximation of the PMF. The contribution of PCTF3D relies on partial coupling which consists in choosing a limited subset of 3D marginals. While PMF estimation is possible with all marginals, coupling only a subset of marginals like in PCTF3D permits to reduce the computational burden without losing significant estimation performance. A key concept of PCTF3D is the choice of marginals to be coupled: this problem is formulated and studied with hypergraphs. This Part I paper introduces the algorithmic framework of PCTF3D: optimization problem, coupling strategies, numerical experiments and a real data application of PCTF3D. On the other hand, the Part II paper studies coupled tensor uniqueness properties of the model introduced by PCTF3D.</div></div>","PeriodicalId":49523,"journal":{"name":"Signal Processing","volume":"243 ","pages":"Article 110452"},"PeriodicalIF":3.6,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145885929","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 : 2026-06-01Epub Date: 2025-12-15DOI: 10.1016/j.sigpro.2025.110450
Junpeng Hao , Huang Bai , Xiumei Li , Jonatan Lerga , Junmei Sun
Deep learning has demonstrated exceptional learning capabilities, leading to the development various deep unfolding networks for image reconstruction. However, current deep unfolding networks often replace certain steps of traditional optimization algorithms with neural networks, thereby compromising the interpretability of the optimization algorithms. Additionally, each iteration in the unfolding process may result in certain image information loss, negatively impacting image reconstruction quality. This paper proposes a deep unfolding Alternating Direction Method of Multipliers (ADMM) network named LSRA-CSNet for compressive sensing image reconstruction, incorporating a long-short term residual optimization mechanism. The LSRA-CSNet is constructed by stacking multiple stages, with each stage consisting of a Fast ADMM Block (FAB) and a Residual Optimization Block (ROB). In FAB, inspired by the Woodbury matrix identity, we propose a fast version of the ADMM algorithm. Meanwhile, instead of replacing certain steps of the ADMM with neural networks, we leverage CNNs to replace some matrix operations. ROB consists of the Short-Term Residual Refinement Module (SRRM) and the Long-Term Residual Feedback Module (LRFM), which optimize the reconstruction details by leveraging inter-stage image residuals and multi-stage measurement residuals, respectively. Experiments on four datasets show the effectiveness of LSRA-CSNet, demonstrating superior reconstruction accuracy compared to existing CS image reconstruction networks.
{"title":"Deep unfolding ADMM network for CS image reconstruction with long-Short term residuals","authors":"Junpeng Hao , Huang Bai , Xiumei Li , Jonatan Lerga , Junmei Sun","doi":"10.1016/j.sigpro.2025.110450","DOIUrl":"10.1016/j.sigpro.2025.110450","url":null,"abstract":"<div><div>Deep learning has demonstrated exceptional learning capabilities, leading to the development various deep unfolding networks for image reconstruction. However, current deep unfolding networks often replace certain steps of traditional optimization algorithms with neural networks, thereby compromising the interpretability of the optimization algorithms. Additionally, each iteration in the unfolding process may result in certain image information loss, negatively impacting image reconstruction quality. This paper proposes a deep unfolding Alternating Direction Method of Multipliers (ADMM) network named LSRA-CSNet for compressive sensing image reconstruction, incorporating a long-short term residual optimization mechanism. The LSRA-CSNet is constructed by stacking multiple stages, with each stage consisting of a Fast ADMM Block (FAB) and a Residual Optimization Block (ROB). In FAB, inspired by the Woodbury matrix identity, we propose a fast version of the ADMM algorithm. Meanwhile, instead of replacing certain steps of the ADMM with neural networks, we leverage CNNs to replace some matrix operations. ROB consists of the Short-Term Residual Refinement Module (SRRM) and the Long-Term Residual Feedback Module (LRFM), which optimize the reconstruction details by leveraging inter-stage image residuals and multi-stage measurement residuals, respectively. Experiments on four datasets show the effectiveness of LSRA-CSNet, demonstrating superior reconstruction accuracy compared to existing CS image reconstruction networks.</div></div>","PeriodicalId":49523,"journal":{"name":"Signal Processing","volume":"243 ","pages":"Article 110450"},"PeriodicalIF":3.6,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145802317","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}
In practical engineering settings, operating conditions are seldom ideal: input signals are corrupted by noise, desired signals suffer interference, and measurements can be unanticipated truncated. These nonidealities reduce the effectiveness of standard adaptive algorithms and can lead to biased or unstable results. To address these challenges, this paper proposes a robust method called the unanticipated truncation-constrained least total logistic distance metric (UT-CLTLDM). The method combines a maximum likelihood approach with an expectation-maximization framework and a least total squares strategy to handle both input noise and signal truncation effectively. Simulation results show that the proposed algorithm achieves superior estimation accuracy and faster convergence compared to existing methods. Its effectiveness is further validated using chaotic input signals from Chua’s circuit model.
{"title":"Constrained least total logistic distance metric algorithm for unanticipated signal truncation","authors":"Pengwei Wen , Botao Jin , Boyang Qu , Sheng Zhang , Xuzhao Chai","doi":"10.1016/j.sigpro.2025.110478","DOIUrl":"10.1016/j.sigpro.2025.110478","url":null,"abstract":"<div><div>In practical engineering settings, operating conditions are seldom ideal: input signals are corrupted by noise, desired signals suffer interference, and measurements can be unanticipated truncated. These nonidealities reduce the effectiveness of standard adaptive algorithms and can lead to biased or unstable results. To address these challenges, this paper proposes a robust method called the unanticipated truncation-constrained least total logistic distance metric (UT-CLTLDM). The method combines a maximum likelihood approach with an expectation-maximization framework and a least total squares strategy to handle both input noise and signal truncation effectively. Simulation results show that the proposed algorithm achieves superior estimation accuracy and faster convergence compared to existing methods. Its effectiveness is further validated using chaotic input signals from Chua’s circuit model.</div></div>","PeriodicalId":49523,"journal":{"name":"Signal Processing","volume":"243 ","pages":"Article 110478"},"PeriodicalIF":3.6,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145927503","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 : 2026-06-01Epub Date: 2026-01-03DOI: 10.1016/j.sigpro.2026.110490
Khadija Omar Mohammed, Liping Du, Yueyun Chen
Effective spectrum sensing in fading environments faces challenges due to correlated noise, strong multipath effects, and complex non-linear dependencies among received signals. Traditional eigenvalue-based detectors often assume independence or capture only limited forms of dependence, which reduces reliability in realistic conditions. This study proposes an Adaptive Joint Metric Detection Algorithm (AJMDA) that integrates both independent and dependency eigenvalue statistics into a unified framework. The independent metric represents the signal energy through the sum of eigenvalues, while the dependency metric captures the statistical structure using copula modeling with the Cramér–von Mises (CVM) goodness-of-fit test. An adaptive weighting factor balances these two metrics, and a generalized extreme value (GEV) model provides analytical threshold estimation. Simulation results under Rayleigh fading show that AJMDA significantly improves detection performance over classical energy detectors, eigenvalue-based GOF tests, and copula-only methods. At –15 dB SNR, the proposed detectors achieve a 45–50% higher detection probability, and at –10 dB SNR, they maintain a 20–60% gain, depending on the baseline. In ROC analysis, AJMDA achieves 10–25% higher performance at low-to-moderate false-alarm levels, approaching the ideal vertical ROC curve.
衰落环境下的有效频谱感知面临着相关噪声、强多径效应和接收信号之间复杂的非线性依赖关系的挑战。传统的基于特征值的检测器通常假设独立性或只捕获有限形式的依赖性，这降低了现实条件下的可靠性。本文提出了一种自适应联合度量检测算法（AJMDA），该算法将独立和依赖特征值统计集成到一个统一的框架中。独立度量通过特征值的和表示信号能量，而依赖度量使用与cram - von Mises （CVM）拟合优度检验的copula建模来捕获统计结构。自适应加权因子平衡这两个度量，广义极值（GEV）模型提供分析阈值估计。Rayleigh衰落下的仿真结果表明，与经典能量检测器、基于特征值的GOF测试和纯copula方法相比，AJMDA检测性能有显著提高。在-15 dB信噪比下，所提出的检测器实现了45-50%的高检测概率，在-10 dB信噪比下，它们保持了20-60%的增益，具体取决于基线。在ROC分析中，AJMDA在中低虚警水平下的性能提高了10-25%，接近理想的垂直ROC曲线。
{"title":"Adaptive joint-metric detection algorithm for efficient spectrum sensing: A deep-water case study","authors":"Khadija Omar Mohammed, Liping Du, Yueyun Chen","doi":"10.1016/j.sigpro.2026.110490","DOIUrl":"10.1016/j.sigpro.2026.110490","url":null,"abstract":"<div><div>Effective spectrum sensing in fading environments faces challenges due to correlated noise, strong multipath effects, and complex non-linear dependencies among received signals. Traditional eigenvalue-based detectors often assume independence or capture only limited forms of dependence, which reduces reliability in realistic conditions. This study proposes an Adaptive Joint Metric Detection Algorithm (AJMDA) that integrates both independent and dependency eigenvalue statistics into a unified framework. The independent metric represents the signal energy through the sum of eigenvalues, while the dependency metric captures the statistical structure using copula modeling with the Cramér–von Mises (CVM) goodness-of-fit test. An adaptive weighting factor balances these two metrics, and a generalized extreme value (GEV) model provides analytical threshold estimation. Simulation results under Rayleigh fading show that AJMDA significantly improves detection performance over classical energy detectors, eigenvalue-based GOF tests, and copula-only methods. At –15 dB SNR, the proposed detectors achieve a 45–50% higher detection probability, and at –10 dB SNR, they maintain a 20–60% gain, depending on the baseline. In ROC analysis, AJMDA achieves 10–25% higher performance <span><math><mrow><msub><mi>P</mi><mi>d</mi></msub><mspace></mspace></mrow></math></span>at low-to-moderate false-alarm levels, approaching the ideal vertical ROC curve.</div></div>","PeriodicalId":49523,"journal":{"name":"Signal Processing","volume":"243 ","pages":"Article 110490"},"PeriodicalIF":3.6,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145927509","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 : 2026-06-01Epub Date: 2026-01-01DOI: 10.1016/j.sigpro.2025.110482
Saulo Cardoso Barreto, Julien Flamant, Sebastian Miron, David Brie
Matrix-valued images appear in many applications, ranging from polarimetric remote sensing to medical imaging. Such images can be represented as 4th-order tensors, where the first two dimensions correspond to spatial variables and the last two encode the matrix feature in each pixel. To efficiently analyze, decompose, and process these images, this paper considers the block-block terms decomposition (2BTD), a versatile low-rank tensor decomposition model that extends bilinear matrix factorization to 4th-order tensors by representing the latter as the sum of outer products of low-rank matrix blocks. Low-rank assumptions allow for a significantly reduced number of parameters to be estimated and enable the enforcement of key physical constraints on matrix sources. We establish both necessary and sufficient conditions for the uniqueness of the 2BTD model. To enable the use of 2BTD in covariance matrix-valued imaging, we develop an optimization framework that allows efficient handling of non-negativity and symmetry constraints together with low-rank assumptions on matrix blocks. Numerical experiments on synthetic and real data from Diffusion Tensor Imaging (DTI) illustrate the potential of the 2BTD model in matrix-valued imaging, as well as its effectiveness in practical settings.
{"title":"Tensor block-block terms decomposition for matrix-valued imaging applications","authors":"Saulo Cardoso Barreto, Julien Flamant, Sebastian Miron, David Brie","doi":"10.1016/j.sigpro.2025.110482","DOIUrl":"10.1016/j.sigpro.2025.110482","url":null,"abstract":"<div><div>Matrix-valued images appear in many applications, ranging from polarimetric remote sensing to medical imaging. Such images can be represented as 4th-order tensors, where the first two dimensions correspond to spatial variables and the last two encode the matrix feature in each pixel. To efficiently analyze, decompose, and process these images, this paper considers the block-block terms decomposition (2BTD), a versatile low-rank tensor decomposition model that extends bilinear matrix factorization to 4th-order tensors by representing the latter as the sum of outer products of low-rank matrix blocks. Low-rank assumptions allow for a significantly reduced number of parameters to be estimated and enable the enforcement of key physical constraints on matrix sources. We establish both necessary and sufficient conditions for the uniqueness of the 2BTD model. To enable the use of 2BTD in covariance matrix-valued imaging, we develop an optimization framework that allows efficient handling of non-negativity and symmetry constraints together with low-rank assumptions on matrix blocks. Numerical experiments on synthetic and real data from Diffusion Tensor Imaging (DTI) illustrate the potential of the 2BTD model in matrix-valued imaging, as well as its effectiveness in practical settings.</div></div>","PeriodicalId":49523,"journal":{"name":"Signal Processing","volume":"243 ","pages":"Article 110482"},"PeriodicalIF":3.6,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145927507","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 : 2026-06-01Epub Date: 2026-01-03DOI: 10.1016/j.sigpro.2025.110479
Srihari P V, Anik Kumar Paul, Bharath Bhikkaji
This paper considers the Federated learning (FL) in a stochastic approximation (SA) framework. Here, each client i trains a local model using its dataset and periodically transmits the model parameters to a central server, where they are aggregated into a global model parameter and sent back. The clients continue their training by re-initializing their local models with the global model parameters.
Prior works typically assumed constant (and often identical) step sizes (learning rates) across clients for model training. As a consequence the aggregated model converges only in expectation. In this work, client-specific tapering step sizes are used. The global model is shown to track an ODE with a forcing function equal to the weighted sum of the negative gradients of the individual clients. The weights being the limiting ratios of the step sizes, where . Unlike the constant step sizes, the convergence here is with probability one.
In this framework, the clients with the larger p(i) exert a greater influence on the global model than those with smaller p(i), which can be used to favor clients that have rare and uncommon data. Numerical experiments were conducted to validate the convergence and demonstrate the choice of step-sizes for regulating the influence of the clients.
{"title":"Federated learning: A stochastic approximation approach","authors":"Srihari P V, Anik Kumar Paul, Bharath Bhikkaji","doi":"10.1016/j.sigpro.2025.110479","DOIUrl":"10.1016/j.sigpro.2025.110479","url":null,"abstract":"<div><div>This paper considers the Federated learning (FL) in a stochastic approximation (SA) framework. Here, each client <em>i</em> trains a local model using its dataset <span><math><msup><mi>D</mi><mrow><mo>(</mo><mi>i</mi><mo>)</mo></mrow></msup></math></span> and periodically transmits the model parameters <span><math><msubsup><mi>w</mi><mi>n</mi><mrow><mo>(</mo><mi>i</mi><mo>)</mo></mrow></msubsup></math></span> to a central server, where they are aggregated into a global model parameter <span><math><msub><mover><mi>w</mi><mo>¯</mo></mover><mi>n</mi></msub></math></span> and sent back. The clients continue their training by re-initializing their local models with the global model parameters.</div><div>Prior works typically assumed constant (and often identical) step sizes (learning rates) across clients for model training. As a consequence the aggregated model converges only in expectation. In this work, client-specific tapering step sizes <span><math><msubsup><mi>a</mi><mi>n</mi><mrow><mo>(</mo><mi>i</mi><mo>)</mo></mrow></msubsup></math></span> are used. The global model is shown to track an ODE with a forcing function equal to the weighted sum of the negative gradients of the individual clients. The weights being the limiting ratios <span><math><mrow><msup><mi>p</mi><mrow><mo>(</mo><mi>i</mi><mo>)</mo></mrow></msup><mo>=</mo><msub><mi>lim</mi><mrow><mi>n</mi><mo>→</mo><mi>∞</mi></mrow></msub><mfrac><msubsup><mi>a</mi><mi>n</mi><mrow><mo>(</mo><mi>i</mi><mo>)</mo></mrow></msubsup><msubsup><mi>a</mi><mi>n</mi><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow></msubsup></mfrac></mrow></math></span> of the step sizes, where <span><math><mrow><msubsup><mi>a</mi><mi>n</mi><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow></msubsup><mo>≥</mo><msubsup><mi>a</mi><mi>n</mi><mrow><mo>(</mo><mi>i</mi><mo>)</mo></mrow></msubsup><mo>,</mo><mo>∀</mo><mi>n</mi></mrow></math></span>. Unlike the constant step sizes, the convergence here is with probability one.</div><div>In this framework, the clients with the larger <em>p</em><sup>(<em>i</em>)</sup> exert a greater influence on the global model than those with smaller <em>p</em><sup>(<em>i</em>)</sup>, which can be used to favor clients that have rare and uncommon data. Numerical experiments were conducted to validate the convergence and demonstrate the choice of step-sizes for regulating the influence of the clients.</div></div>","PeriodicalId":49523,"journal":{"name":"Signal Processing","volume":"243 ","pages":"Article 110479"},"PeriodicalIF":3.6,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145927505","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 : 2026-06-01Epub Date: 2025-12-20DOI: 10.1016/j.sigpro.2025.110453
Philippe Flores , Konstantin Usevich , David Brie
In this paper, uniqueness properties of a coupled factorization of 3D marginal tensors (or PCTF3D) are studied. The PCTF3D method (detailed in the Part I article) performs estimation of probability mass functions (PMFs) by coupling 3D marginals, seen as order-3 tensors. The core novelty of PCTF3D’s approach relies on the partial coupling which consists in choosing a limited set of 3D marginals to be coupled. PCTF3D uniqueness is examined through the prism of polynomial mappings and their recoverability. A numerical algorithm is proposed for finding the maximal rank for which recoverability is guaranteed. This approach properly accounts for the coupling strategy and simplex constraints. Using the proposed algorithm, the different coupling strategies from Part I are examined with respect to their uniqueness properties. Finally, a new identifiability bound is given for a so-called Cartesian coupling which improves existing sufficient bounds available in the literature.
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Preventing the radar transmitter from being utilized by an adversary as a non-cooperative bistatic illuminator is crucial for advanced surveillance systems. In this paper, a non-cooperative bistatic denial paradigm with coherent frequency diverse array (FDA) transmitter is proposed. The FDA achieves an angle-time/range-dependent beampattern by applying a slight frequency increment among array elements, resulting in transmitted signals that vary across different directions. This inherent anisotropic property decorrelates the target echo and direct-path signal received by the non-cooperative receiver. The signal processing output at the non-cooperative receiver is derived, demonstrating that the anisotropy of the coherent FDA transmitted signal degrades the target signal-to-noise ratio after pulse compression, thereby deteriorating the target detection capability of the non-cooperative receiver. Furthermore, the cross-correlation function (CCF) between the transmitted signals in the target and non-cooperative receiver directions is calculated, and two evaluation criteria, i.e., the peak loss and average loss of the CCF, are defined to quantitatively analyze the denial capability of the coherent FDA transmitter. The influence of FDA transmitter parameters and non-cooperative bistatic geometry on the denial performance is thoroughly investigated. Simulation results validate the effectiveness of the proposed method.
{"title":"Non-cooperative bistatic denial by using coherent FDA radar transmitter","authors":"Qingyun Kan , Jingwei Xu , Yuhong Zhang , Yanhong Xu , Guisheng Liao","doi":"10.1016/j.sigpro.2026.110500","DOIUrl":"10.1016/j.sigpro.2026.110500","url":null,"abstract":"<div><div>Preventing the radar transmitter from being utilized by an adversary as a non-cooperative bistatic illuminator is crucial for advanced surveillance systems. In this paper, a non-cooperative bistatic denial paradigm with coherent frequency diverse array (FDA) transmitter is proposed. The FDA achieves an angle-time/range-dependent beampattern by applying a slight frequency increment among array elements, resulting in transmitted signals that vary across different directions. This inherent anisotropic property decorrelates the target echo and direct-path signal received by the non-cooperative receiver. The signal processing output at the non-cooperative receiver is derived, demonstrating that the anisotropy of the coherent FDA transmitted signal degrades the target signal-to-noise ratio after pulse compression, thereby deteriorating the target detection capability of the non-cooperative receiver. Furthermore, the cross-correlation function (CCF) between the transmitted signals in the target and non-cooperative receiver directions is calculated, and two evaluation criteria, i.e., the peak loss and average loss of the CCF, are defined to quantitatively analyze the denial capability of the coherent FDA transmitter. The influence of FDA transmitter parameters and non-cooperative bistatic geometry on the denial performance is thoroughly investigated. Simulation results validate the effectiveness of the proposed method.</div></div>","PeriodicalId":49523,"journal":{"name":"Signal Processing","volume":"243 ","pages":"Article 110500"},"PeriodicalIF":3.6,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146037937","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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