Pub Date : 2025-01-13DOI: 10.1109/TSP.2025.3527755
Pei-Duo Yu;Chee Wei Tan
Identifying the source of epidemic-like spread in networks is crucial for removing internet viruses or finding the source of rumors in online social networks. The challenge lies in tracing the source from a snapshot observation of infected nodes. How do we accurately pinpoint the source? Utilizing snapshot data, we apply a probabilistic approach, focusing on the graph boundary and the observed time, to detect sources via an effective maximum likelihood algorithm. A novel starlike tree approximation extends applicability to general graphs, demonstrating versatility. Unlike previous works that rely heavily on structural properties alone, our method also incorporates temporal data for more precise source detection. We highlight the utility of the Gamma function for analyzing the ratio of the likelihood being the source between nodes asymptotically. Comprehensive evaluations confirm algorithmic effectiveness in diverse network scenarios, advancing source detection in large-scale network analysis and information dissemination strategies.
{"title":"Unraveling the Viral Spread of Misinformation: Maximum-Likelihood Estimation and Starlike Tree Approximation in Markovian Spreading Models","authors":"Pei-Duo Yu;Chee Wei Tan","doi":"10.1109/TSP.2025.3527755","DOIUrl":"10.1109/TSP.2025.3527755","url":null,"abstract":"Identifying the source of epidemic-like spread in networks is crucial for removing internet viruses or finding the source of rumors in online social networks. The challenge lies in tracing the source from a snapshot observation of infected nodes. How do we accurately pinpoint the source? Utilizing snapshot data, we apply a probabilistic approach, focusing on the graph boundary and the observed time, to detect sources via an effective maximum likelihood algorithm. A novel starlike tree approximation extends applicability to general graphs, demonstrating versatility. Unlike previous works that rely heavily on structural properties alone, our method also incorporates temporal data for more precise source detection. We highlight the utility of the Gamma function for analyzing the ratio of the likelihood being the source between nodes asymptotically. Comprehensive evaluations confirm algorithmic effectiveness in diverse network scenarios, advancing source detection in large-scale network analysis and information dissemination strategies.","PeriodicalId":13330,"journal":{"name":"IEEE Transactions on Signal Processing","volume":"73 ","pages":"446-461"},"PeriodicalIF":4.6,"publicationDate":"2025-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142974841","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 : 2025-01-10DOI: 10.1109/TSP.2024.3522179
Junren Chen;Michael K. Ng;Zhaoqiang Liu
The problem of recovering a signal <inline-formula><tex-math>$boldsymbol{x}inmathbb{R}^{n}$</tex-math></inline-formula> from a quadratic system <inline-formula><tex-math>${y_{i}=boldsymbol{x}^{top}boldsymbol{A}_{i}boldsymbol{x}, i=1,ldots,m}$</tex-math></inline-formula> with full-rank matrices <inline-formula><tex-math>$boldsymbol{A}_{i}$</tex-math></inline-formula> frequently arises in applications such as unassigned distance geometry and sub-wavelength imaging. With i.i.d. standard Gaussian matrices <inline-formula><tex-math>$boldsymbol{A}_{i}$</tex-math></inline-formula>, this paper addresses the high-dimensional case where <inline-formula><tex-math>$mll n$</tex-math></inline-formula> by incorporating prior knowledge of <inline-formula><tex-math>$boldsymbol{x}$</tex-math></inline-formula>. First, we consider a <inline-formula><tex-math>$k$</tex-math></inline-formula>-sparse <inline-formula><tex-math>$boldsymbol{x}$</tex-math></inline-formula> and introduce the thresholded Wirtinger flow (TWF) algorithm that does not require the sparsity level <inline-formula><tex-math>$k$</tex-math></inline-formula>. TWF comprises two steps: the spectral initialization that identifies a point sufficiently close to <inline-formula><tex-math>$boldsymbol{x}$</tex-math></inline-formula> (up to a sign flip) when <inline-formula><tex-math>$m=O(k^{2}log n)$</tex-math></inline-formula>, and the thresholded gradient descent which, when provided a good initialization, produces a sequence linearly converging to <inline-formula><tex-math>$boldsymbol{x}$</tex-math></inline-formula> with <inline-formula><tex-math>$m=O(klog n)$</tex-math></inline-formula> measurements. Second, we explore the generative prior, assuming that <inline-formula><tex-math>$boldsymbol{x}$</tex-math></inline-formula> lies in the range of an <inline-formula><tex-math>$L$</tex-math></inline-formula>-Lipschitz continuous generative model with <inline-formula><tex-math>$k$</tex-math></inline-formula>-dimensional inputs in an <inline-formula><tex-math>$ell_{2}$</tex-math></inline-formula>-ball of radius <inline-formula><tex-math>$r$</tex-math></inline-formula>. With an estimate correlated with the signal, we develop the projected gradient descent (PGD) algorithm that also comprises two steps: the projected power method that provides an initial vector with <inline-formula><tex-math>$Obig{(}sqrt{klog(L)/m}big{)}$</tex-math></inline-formula> <inline-formula><tex-math>$ell_{2}$</tex-math></inline-formula>-error given <inline-formula><tex-math>$m=O(klog(Lnr))$</tex-math></inline-formula> measurements, and the projected gradient descent that refines the <inline-formula><tex-math>$ell_{2}$</tex-math></inline-formula>-error to <inline-formula><tex-math>$O(delta)$</tex-math></inline-formula> at a geometric rate when <inline-formula><tex-math>$m=O(klogfrac{Lrn}{delta^{2}})$</tex-math></inline-formula>. Experimental results corroborate our theoretical findings and show that: (i) our approach for the sparse case nota
{"title":"Solving Quadratic Systems With Full-Rank Matrices Using Sparse or Generative Priors","authors":"Junren Chen;Michael K. Ng;Zhaoqiang Liu","doi":"10.1109/TSP.2024.3522179","DOIUrl":"10.1109/TSP.2024.3522179","url":null,"abstract":"The problem of recovering a signal <inline-formula><tex-math>$boldsymbol{x}inmathbb{R}^{n}$</tex-math></inline-formula> from a quadratic system <inline-formula><tex-math>${y_{i}=boldsymbol{x}^{top}boldsymbol{A}_{i}boldsymbol{x}, i=1,ldots,m}$</tex-math></inline-formula> with full-rank matrices <inline-formula><tex-math>$boldsymbol{A}_{i}$</tex-math></inline-formula> frequently arises in applications such as unassigned distance geometry and sub-wavelength imaging. With i.i.d. standard Gaussian matrices <inline-formula><tex-math>$boldsymbol{A}_{i}$</tex-math></inline-formula>, this paper addresses the high-dimensional case where <inline-formula><tex-math>$mll n$</tex-math></inline-formula> by incorporating prior knowledge of <inline-formula><tex-math>$boldsymbol{x}$</tex-math></inline-formula>. First, we consider a <inline-formula><tex-math>$k$</tex-math></inline-formula>-sparse <inline-formula><tex-math>$boldsymbol{x}$</tex-math></inline-formula> and introduce the thresholded Wirtinger flow (TWF) algorithm that does not require the sparsity level <inline-formula><tex-math>$k$</tex-math></inline-formula>. TWF comprises two steps: the spectral initialization that identifies a point sufficiently close to <inline-formula><tex-math>$boldsymbol{x}$</tex-math></inline-formula> (up to a sign flip) when <inline-formula><tex-math>$m=O(k^{2}log n)$</tex-math></inline-formula>, and the thresholded gradient descent which, when provided a good initialization, produces a sequence linearly converging to <inline-formula><tex-math>$boldsymbol{x}$</tex-math></inline-formula> with <inline-formula><tex-math>$m=O(klog n)$</tex-math></inline-formula> measurements. Second, we explore the generative prior, assuming that <inline-formula><tex-math>$boldsymbol{x}$</tex-math></inline-formula> lies in the range of an <inline-formula><tex-math>$L$</tex-math></inline-formula>-Lipschitz continuous generative model with <inline-formula><tex-math>$k$</tex-math></inline-formula>-dimensional inputs in an <inline-formula><tex-math>$ell_{2}$</tex-math></inline-formula>-ball of radius <inline-formula><tex-math>$r$</tex-math></inline-formula>. With an estimate correlated with the signal, we develop the projected gradient descent (PGD) algorithm that also comprises two steps: the projected power method that provides an initial vector with <inline-formula><tex-math>$Obig{(}sqrt{klog(L)/m}big{)}$</tex-math></inline-formula> <inline-formula><tex-math>$ell_{2}$</tex-math></inline-formula>-error given <inline-formula><tex-math>$m=O(klog(Lnr))$</tex-math></inline-formula> measurements, and the projected gradient descent that refines the <inline-formula><tex-math>$ell_{2}$</tex-math></inline-formula>-error to <inline-formula><tex-math>$O(delta)$</tex-math></inline-formula> at a geometric rate when <inline-formula><tex-math>$m=O(klogfrac{Lrn}{delta^{2}})$</tex-math></inline-formula>. Experimental results corroborate our theoretical findings and show that: (i) our approach for the sparse case nota","PeriodicalId":13330,"journal":{"name":"IEEE Transactions on Signal Processing","volume":"73 ","pages":"477-492"},"PeriodicalIF":4.6,"publicationDate":"2025-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142961228","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 : 2025-01-10DOI: 10.1109/TSP.2025.3528252
Yunchuan Zhang;Sangwoo Park;Osvaldo Simeone
In many applications, ranging from logistics to engineering, a designer is faced with a sequence of optimization tasks for which the objectives are in the form of black-box functions that are costly to evaluate. Furthermore, higher-fidelity evaluations of the optimization objectives often entail a larger cost. Existing multi-fidelity black-box optimization strategies select candidate solutions and fidelity levels with the goal of maximizing the information about the optimal value or the optimal solution for the current task. Assuming that successive optimization tasks are related, this paper introduces a novel information-theoretic acquisition function that balances the need to acquire information about the current task with the goal of collecting information transferable to future tasks. The proposed method transfers across tasks distributions over parameters of a Gaussian process surrogate model by implementing particle-based variational Bayesian updates. Theoretical insights based on the analysis of the expected regret substantiate the benefits of acquiring transferable knowledge across tasks. Furthermore, experimental results across synthetic and real-world examples reveal that the proposed acquisition strategy that caters to future tasks can significantly improve the optimization efficiency as soon as a sufficient number of tasks is processed.
{"title":"Multi-Fidelity Bayesian Optimization With Across-Task Transferable Max-Value Entropy Search","authors":"Yunchuan Zhang;Sangwoo Park;Osvaldo Simeone","doi":"10.1109/TSP.2025.3528252","DOIUrl":"10.1109/TSP.2025.3528252","url":null,"abstract":"In many applications, ranging from logistics to engineering, a designer is faced with a sequence of optimization tasks for which the objectives are in the form of black-box functions that are costly to evaluate. Furthermore, higher-fidelity evaluations of the optimization objectives often entail a larger cost. Existing multi-fidelity black-box optimization strategies select candidate solutions and fidelity levels with the goal of maximizing the information about the optimal value or the optimal solution for the current task. Assuming that successive optimization tasks are related, this paper introduces a novel information-theoretic acquisition function that balances the need to acquire information about the current task with the goal of collecting information transferable to future tasks. The proposed method transfers across tasks distributions over parameters of a Gaussian process surrogate model by implementing particle-based variational Bayesian updates. Theoretical insights based on the analysis of the expected regret substantiate the benefits of acquiring transferable knowledge across tasks. Furthermore, experimental results across synthetic and real-world examples reveal that the proposed acquisition strategy that caters to future tasks can significantly improve the optimization efficiency as soon as a sufficient number of tasks is processed.","PeriodicalId":13330,"journal":{"name":"IEEE Transactions on Signal Processing","volume":"73 ","pages":"418-432"},"PeriodicalIF":4.6,"publicationDate":"2025-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142961197","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 : 2025-01-10DOI: 10.1109/TSP.2025.3528217
Jiawei Zhang;Cheng Jin;Yuantao Gu
Momentum accelerated stochastic gradient descent (SGDM) has gained significant popularity in several signal processing and machine learning tasks. Despite its widespread success, the step size of SGDM remains a critical hyperparameter affecting its performance and often requires manual tuning. Recently, some works have introduced the Polyak step size to SGDM and provided corresponding convergence analysis. However, the convergence guarantee of existing Polyak step sizes for SGDM are limited to convex objectives and lack theoretical support for more widely applicable non-convex problems. To bridge this gap, we design a novel Polyak adaptive step size for SGDM. The proposed algorithm, termed SGDM-APS, incorporates a moving average form tailored for the momentum mechanism in SGDM. We establish the convergence guarantees of SGDM-APS for both convex and non-convex objectives, providing theoretical analysis of its effectiveness. To the best of our knowledge, SGDM-APS is the first Polyak step size for SGDM with general convergence guarantee. Our analysis can also be extended to constant step size SGDM, enriching the theoretical comprehension of the classic SGDM algorithm. Through extensive experiments on diverse benchmarks, we demonstrate that SGDM-APS achieves competitive convergence rates and generalization performance compared to several popular optimization algorithms.
{"title":"Adaptive Polyak Step-Size for Momentum Accelerated Stochastic Gradient Descent With General Convergence Guarantee","authors":"Jiawei Zhang;Cheng Jin;Yuantao Gu","doi":"10.1109/TSP.2025.3528217","DOIUrl":"10.1109/TSP.2025.3528217","url":null,"abstract":"Momentum accelerated stochastic gradient descent (SGDM) has gained significant popularity in several signal processing and machine learning tasks. Despite its widespread success, the step size of SGDM remains a critical hyperparameter affecting its performance and often requires manual tuning. Recently, some works have introduced the Polyak step size to SGDM and provided corresponding convergence analysis. However, the convergence guarantee of existing Polyak step sizes for SGDM are limited to convex objectives and lack theoretical support for more widely applicable non-convex problems. To bridge this gap, we design a novel Polyak adaptive step size for SGDM. The proposed algorithm, termed SGDM-APS, incorporates a moving average form tailored for the momentum mechanism in SGDM. We establish the convergence guarantees of SGDM-APS for both convex and non-convex objectives, providing theoretical analysis of its effectiveness. To the best of our knowledge, SGDM-APS is the first Polyak step size for SGDM with general convergence guarantee. Our analysis can also be extended to constant step size SGDM, enriching the theoretical comprehension of the classic SGDM algorithm. Through extensive experiments on diverse benchmarks, we demonstrate that SGDM-APS achieves competitive convergence rates and generalization performance compared to several popular optimization algorithms.","PeriodicalId":13330,"journal":{"name":"IEEE Transactions on Signal Processing","volume":"73 ","pages":"462-476"},"PeriodicalIF":4.6,"publicationDate":"2025-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142961606","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 : 2025-01-09DOI: 10.1109/tsp.2025.3526989
Haoxiang Ye, Qing Ling
{"title":"Generalization Error Matters in Decentralized Learning Under Byzantine Attacks","authors":"Haoxiang Ye, Qing Ling","doi":"10.1109/tsp.2025.3526989","DOIUrl":"https://doi.org/10.1109/tsp.2025.3526989","url":null,"abstract":"","PeriodicalId":13330,"journal":{"name":"IEEE Transactions on Signal Processing","volume":"46 1","pages":""},"PeriodicalIF":5.4,"publicationDate":"2025-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142940142","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 : 2025-01-09DOI: 10.1109/TSP.2025.3525663
Jin Li;Wei Xing Zheng;Long Yang
This paper proposes a blind equalization algorithm for dispersive wireless communication systems that employ high throughput quadrature amplitude modulation signals under both Gaussian and impulsive noise environments. A novel cost function that combines the modulus match error function with the negative Gaussian kernel function is established to efficiently obtain the weight vector associated with the blind equalizer. Some preferable properties of the novel cost function are presented. Intensive studies show that the proposed cost function efficiently reduces the maladjustment caused by the modulus mismatch error and efficiently suppresses the negative influence resulting from large errors. Moreover, an efficient successive approximation method for minimizing the established cost function is proposed for fast searching of the optimal weight vector. Very importantly, it is proved that the proposed successive approximation method possesses superlinear convergence. Finally, extensive simulations are provided to demonstrate that the proposed blind equalizer has better performances than the existing methods under both Gaussian and impulsive noise circumstances in terms of equalization quality and equalization efficiency.
{"title":"Fast Converging Algorithm for Blind Equalization With Gaussian and Impulsive Noises","authors":"Jin Li;Wei Xing Zheng;Long Yang","doi":"10.1109/TSP.2025.3525663","DOIUrl":"10.1109/TSP.2025.3525663","url":null,"abstract":"This paper proposes a blind equalization algorithm for dispersive wireless communication systems that employ high throughput quadrature amplitude modulation signals under both Gaussian and impulsive noise environments. A novel cost function that combines the modulus match error function with the negative Gaussian kernel function is established to efficiently obtain the weight vector associated with the blind equalizer. Some preferable properties of the novel cost function are presented. Intensive studies show that the proposed cost function efficiently reduces the maladjustment caused by the modulus mismatch error and efficiently suppresses the negative influence resulting from large errors. Moreover, an efficient successive approximation method for minimizing the established cost function is proposed for fast searching of the optimal weight vector. Very importantly, it is proved that the proposed successive approximation method possesses superlinear convergence. Finally, extensive simulations are provided to demonstrate that the proposed blind equalizer has better performances than the existing methods under both Gaussian and impulsive noise circumstances in terms of equalization quality and equalization efficiency.","PeriodicalId":13330,"journal":{"name":"IEEE Transactions on Signal Processing","volume":"73 ","pages":"372-385"},"PeriodicalIF":4.6,"publicationDate":"2025-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142940143","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 : 2025-01-07DOI: 10.1109/TSP.2025.3525951
Steven Kay;Kaushallya Adhikari;Bo Tang
We introduce a nonparametric data-driven classifier that harnesses the statistical properties of the data through the cumulant generating function of the training data. Its implementation is straightforward, requiring only a single tuning parameter. Moreover, it ensures global solutions due to inherent convex optimization. The classifier is explainable, where unexpected or poor results can be interpreted and ameliorated. We derive the properties of the classification statistic, offering insightful observations. We apply the classifier to real-world datasets. The simulation results demonstrate the efficacy of the proposed classifier in signal classification, even in scenarios with mismatched training and testing datasets. Moreover, the results demonstrate that the CGFC has lower computational complexity compared to neural networks.
{"title":"A Nonparametric Data-Driven Classifier Based on the Cumulant Generating Function","authors":"Steven Kay;Kaushallya Adhikari;Bo Tang","doi":"10.1109/TSP.2025.3525951","DOIUrl":"10.1109/TSP.2025.3525951","url":null,"abstract":"We introduce a nonparametric data-driven classifier that harnesses the statistical properties of the data through the cumulant generating function of the training data. Its implementation is straightforward, requiring only a single tuning parameter. Moreover, it ensures global solutions due to inherent convex optimization. The classifier is explainable, where unexpected or poor results can be interpreted and ameliorated. We derive the properties of the classification statistic, offering insightful observations. We apply the classifier to real-world datasets. The simulation results demonstrate the efficacy of the proposed classifier in signal classification, even in scenarios with mismatched training and testing datasets. Moreover, the results demonstrate that the CGFC has lower computational complexity compared to neural networks.","PeriodicalId":13330,"journal":{"name":"IEEE Transactions on Signal Processing","volume":"73 ","pages":"519-533"},"PeriodicalIF":4.6,"publicationDate":"2025-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=10830543","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142936171","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 : 2025-01-01DOI: 10.1109/TSP.2024.3524568
Xiang-Yu Wang;Xiao-Peng Li;Nicholas D. Sidiropoulos;Hing Cheung So
Tensor completion aims at filling in the missing elements of an incomplete tensor based on its partial observations, which is a popular approach for image inpainting. Most existing methods for visual data recovery can be categorized into traditional optimization-based and neural network-based methods. The former usually adopt a low-rank assumption to handle this ill-posed problem, enjoying good interpretability and generalization. However, as visual data are only approximately low rank, handcrafted low-rank priors may not capture the complex details properly, limiting the recovery performance. For neural network-based methods, despite their impressive performance in image inpainting, sufficient training data are required for parameter learning, and their generalization ability on the unseen data is a concern. In this paper, combining the advantages of these two distinct approaches, we propose a tensor Completion neural Network (CNet) for visual data completion. The CNet is comprised of two parts, namely, the encoder and decoder. The encoder is designed by exploiting the CANDECOMP/PARAFAC decomposition to produce a low-rank embedding of the target tensor, whose mechanism is interpretable. To compensate the drawback of the low-rank constraint, a decoder consisting of several convolutional layers is introduced to refine the low-rank embedding. The CNet only uses the observations of the incomplete tensor to recover its missing entries and thus is free from large training datasets. Extensive experiments in inpainting color images, grayscale video sequences, hyperspectral images, color video sequences, and light field images are conducted to showcase the superiority of CNet over state-of-the-art methods in terms of restoration performance.
{"title":"Tensor Completion Network for Visual Data","authors":"Xiang-Yu Wang;Xiao-Peng Li;Nicholas D. Sidiropoulos;Hing Cheung So","doi":"10.1109/TSP.2024.3524568","DOIUrl":"10.1109/TSP.2024.3524568","url":null,"abstract":"Tensor completion aims at filling in the missing elements of an incomplete tensor based on its partial observations, which is a popular approach for image inpainting. Most existing methods for visual data recovery can be categorized into traditional optimization-based and neural network-based methods. The former usually adopt a low-rank assumption to handle this ill-posed problem, enjoying good interpretability and generalization. However, as visual data are only approximately low rank, handcrafted low-rank priors may not capture the complex details properly, limiting the recovery performance. For neural network-based methods, despite their impressive performance in image inpainting, sufficient training data are required for parameter learning, and their generalization ability on the unseen data is a concern. In this paper, combining the advantages of these two distinct approaches, we propose a tensor <bold>C</b>ompletion neural <bold>Net</b>work (CNet) for visual data completion. The CNet is comprised of two parts, namely, the encoder and decoder. The encoder is designed by exploiting the CANDECOMP/PARAFAC decomposition to produce a low-rank embedding of the target tensor, whose mechanism is interpretable. To compensate the drawback of the low-rank constraint, a decoder consisting of several convolutional layers is introduced to refine the low-rank embedding. The CNet only uses the observations of the incomplete tensor to recover its missing entries and thus is free from large training datasets. Extensive experiments in inpainting color images, grayscale video sequences, hyperspectral images, color video sequences, and light field images are conducted to showcase the superiority of CNet over state-of-the-art methods in terms of restoration performance.","PeriodicalId":13330,"journal":{"name":"IEEE Transactions on Signal Processing","volume":"73 ","pages":"386-400"},"PeriodicalIF":4.6,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142911637","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 : 2024-12-23DOI: 10.1109/TSP.2024.3522300
Shenglin Song;Erliang Zhang
This paper deals with frequency domain parametric identification of ARMAX models when the input is corrupted by white noise. By means of a multivariate ARMA representation, the ARMAX model within the errors-in-variables (EIV) framework is identified by a successive two-stage approach, and all the parameter estimates of the dynamic EIV model are further jointly tuned to achieve minimum variance among unbiased estimators using second-order statistics of input-output data. Sufficient conditions are constructed to obtain the identifiability of the EIV-ARMAX model as well as the multivariate ARMA process. The consistency of the estimator is analyzed, and the uncertainty bound of the estimate is also provided and compared with the Cramér-Rao lower bound. The performance of the proposed method is demonstrated via numerical and real examples.
{"title":"Identification of ARMAX Models With Noisy Input: A Parametric Frequency Domain Solution","authors":"Shenglin Song;Erliang Zhang","doi":"10.1109/TSP.2024.3522300","DOIUrl":"10.1109/TSP.2024.3522300","url":null,"abstract":"This paper deals with frequency domain parametric identification of ARMAX models when the input is corrupted by white noise. By means of a multivariate ARMA representation, the ARMAX model within the errors-in-variables (EIV) framework is identified by a successive two-stage approach, and all the parameter estimates of the dynamic EIV model are further jointly tuned to achieve minimum variance among unbiased estimators using second-order statistics of input-output data. Sufficient conditions are constructed to obtain the identifiability of the EIV-ARMAX model as well as the multivariate ARMA process. The consistency of the estimator is analyzed, and the uncertainty bound of the estimate is also provided and compared with the Cramér-Rao lower bound. The performance of the proposed method is demonstrated via numerical and real examples.","PeriodicalId":13330,"journal":{"name":"IEEE Transactions on Signal Processing","volume":"73 ","pages":"292-304"},"PeriodicalIF":4.6,"publicationDate":"2024-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142879692","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 : 2024-12-23DOI: 10.1109/TSP.2024.3520909
Tianyi Jia;Xiaochuan Ke;Hongwei Liu;K. C. Ho;Hongtao Su
The sensor position uncertainties and synchronization offsets can cause substantial performance degradation if the sensors are not properly calibrated. This paper investigates the localization of a constant velocity moving target and the self-calibration of sensors using a sequence of range and azimuth measurements observed at successive instants. A theoretical study by the Cramer-Rao Lower Bound (CRLB) reveals that the sensor positions can only be self-calibrated when there are at least two sensors and synchronization offsets can be handled by joint estimation. A low complexity sequential closed-form solution is proposed to estimate the target position and velocity first, and the coordinates of each sensor and synchronization offset afterward. While less intuitive, the analysis shows that the closed-form solutions for both the target and sensor parameters can reach the CRLB accuracy under small Gaussian noise. We also develop a semidefinite programming (SDP) solution by semidefinite relaxation (SDR) for joint localization and calibration from the Maximum Likelihood formulation, which exhibits higher noise tolerance than the closed-form solution. Simulations validate the analysis and the performance of the proposed methods.
{"title":"Target Localization and Sensor Self-Calibration of Position and Synchronization by Range and Angle Measurements","authors":"Tianyi Jia;Xiaochuan Ke;Hongwei Liu;K. C. Ho;Hongtao Su","doi":"10.1109/TSP.2024.3520909","DOIUrl":"10.1109/TSP.2024.3520909","url":null,"abstract":"The sensor position uncertainties and synchronization offsets can cause substantial performance degradation if the sensors are not properly calibrated. This paper investigates the localization of a constant velocity moving target and the self-calibration of sensors using a sequence of range and azimuth measurements observed at successive instants. A theoretical study by the Cramer-Rao Lower Bound (CRLB) reveals that the sensor positions can only be self-calibrated when there are at least two sensors and synchronization offsets can be handled by joint estimation. A low complexity sequential closed-form solution is proposed to estimate the target position and velocity first, and the coordinates of each sensor and synchronization offset afterward. While less intuitive, the analysis shows that the closed-form solutions for both the target and sensor parameters can reach the CRLB accuracy under small Gaussian noise. We also develop a semidefinite programming (SDP) solution by semidefinite relaxation (SDR) for joint localization and calibration from the Maximum Likelihood formulation, which exhibits higher noise tolerance than the closed-form solution. Simulations validate the analysis and the performance of the proposed methods.","PeriodicalId":13330,"journal":{"name":"IEEE Transactions on Signal Processing","volume":"73 ","pages":"340-355"},"PeriodicalIF":4.6,"publicationDate":"2024-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142879693","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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