{"title":"WSS Processes and Wiener Filters on Digraphs","authors":"Mohammad Bagher Iraji;Mohammad Eini;Arash Amini","doi":"10.1109/TSP.2024.3510434","DOIUrl":"10.1109/TSP.2024.3510434","url":null,"abstract":"In this paper, we generalize the concepts of kernels, weak stationarity and white noise from undirected to directed graphs (digraphs) based on the Jordan decomposition of the shift operator. We characterize two types of kernels (type-I and type-II) and their corresponding localization operators for digraphs. We analytically study the interplay of these types of kernels with the concept of stationarity, specially the filtering properties. We also generalize graph Wiener filters and the related optimization framework to digraphs. For the special case of Gaussian processes, we show that the Wiener filtering again coincides with the MAP estimator. We further investigate the linear minimum mean-squared error (LMMSE) estimator for the non-Gaussian cases; the corresponding optimization problem simplifies to a Lyapunov matrix equation. We propose an algorithm to solve the Wiener optimization using proximal splitting methods. Finally, we provide simulation results to verify the provided theory.","PeriodicalId":13330,"journal":{"name":"IEEE Transactions on Signal Processing","volume":"73 ","pages":"1-11"},"PeriodicalIF":4.6,"publicationDate":"2024-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142776539","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}
{"title":"Generalized Bilinear Factorization via Hybrid Vector Message Passing","authors":"Hao Jiang;Xiaojun Yuan;Qinghua Guo","doi":"10.1109/TSP.2024.3509413","DOIUrl":"10.1109/TSP.2024.3509413","url":null,"abstract":"Generalized bilinear factorization (GBF), in which two matrices are recovered from noisy and typically compressed measurements of their product, arises in various applications such as blind channel-and-signal estimation, image completion, and compressed video foreground and background separation. In this paper, we formulate the GBF problem by unifying several existing bilinear inverse problems, and establish a novel hybrid vector message passing (HVMP) algorithm for GBF. The GBF-HVMP algorithm integrates expectation propagation (EP) and variational message passing (VMP) via variational free energy minimization, and exchanges matrix-variable messages in closed form. GBF-HVMP is advantageous over its counterparts in several aspects. For example, a matrix-variable message can characterize the correlations between the elements of the matrix, which is not possible in scalar-variable message passing; the hybrid of EP and VMP yields closed-form Gaussian messages associated with the bilinear constraints inherent in the GBF problem. We show that damping is unnecessary for GBF-HVMP to ensure convergence. We also show that GBF-HVMP performs close to the replica bound, and significantly outperforms state-of-the-art approaches in terms of both normalized mean squared error (NMSE) performance and computational complexity.","PeriodicalId":13330,"journal":{"name":"IEEE Transactions on Signal Processing","volume":"72 ","pages":"5675-5690"},"PeriodicalIF":4.6,"publicationDate":"2024-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142760268","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}
{"title":"Narrowband Interference Cancellation for OFDM Based on Deep Learning and Compressed Sensing","authors":"Yue Hu, Songkang Huang, Lei Zhao, Ming Jiang","doi":"10.1109/tsp.2024.3510623","DOIUrl":"https://doi.org/10.1109/tsp.2024.3510623","url":null,"abstract":"","PeriodicalId":13330,"journal":{"name":"IEEE Transactions on Signal Processing","volume":"26 1","pages":""},"PeriodicalIF":5.4,"publicationDate":"2024-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142760269","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}
{"title":"Enhancing Missing Data Imputation of Non-Stationary Oscillatory Signals With Harmonic Decomposition","authors":"Joaquin Ruiz;Hau-Tieng Wu;Marcelo A. Colominas","doi":"10.1109/TSP.2024.3508468","DOIUrl":"10.1109/TSP.2024.3508468","url":null,"abstract":"Dealing with time series with missing values, including those afflicted by low quality or over-saturation, presents a significant signal processing challenge. The task of recovering these missing values, known as imputation, has led to the development of several algorithms. However, we have observed that the efficacy of these algorithms tends to diminish when the time series exhibits non-stationary oscillatory behavior. In this paper, we introduce a novel algorithm, coined Harmonic Level Interpolation (\u0000<monospace>HaLI</monospace>\u0000), which enhances the performance of existing imputation algorithms for oscillatory time series. After running any chosen imputation algorithm, \u0000<monospace>HaLI</monospace>\u0000 leverages the \u0000<italic>harmonic decomposition</i>\u0000 based on the \u0000<italic>adaptive non-harmonic model</i>\u0000 of the initial imputation to improve the imputation accuracy for oscillatory time series. Experimental assessments conducted on synthetic and real signals consistently highlight that \u0000<monospace>HaLI</monospace>\u0000 enhances the performance of existing imputation algorithms. The algorithm is made publicly available as a readily employable Matlab code for other researchers to use.","PeriodicalId":13330,"journal":{"name":"IEEE Transactions on Signal Processing","volume":"72 ","pages":"5581-5592"},"PeriodicalIF":4.6,"publicationDate":"2024-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142753504","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}
Mert Kayaalp;Yunus İnan;Visa Koivunen;Ali H. Sayed
{"title":"Causal Influence in Federated Edge Inference","authors":"Mert Kayaalp;Yunus İnan;Visa Koivunen;Ali H. Sayed","doi":"10.1109/TSP.2024.3507715","DOIUrl":"10.1109/TSP.2024.3507715","url":null,"abstract":"In this paper, we consider a setting where heterogeneous agents with connectivity are performing inference using unlabeled streaming data. Observed data are only partially informative about the target variable of interest. In order to overcome the uncertainty, agents cooperate with each other by exchanging their local inferences with and through a fusion center. To evaluate how each agent influences the overall decision, we adopt a causal framework in order to distinguish the actual influence of agents from mere correlations within the decision-making process. Various scenarios reflecting different agent participation patterns and fusion center policies are investigated. We derive expressions to quantify the causal impact of each agent on the joint decision, which could be beneficial for anticipating and addressing atypical scenarios, such as adversarial attacks or system malfunctions. We validate our theoretical results with numerical simulations and a real-world application of multi-camera crowd counting.","PeriodicalId":13330,"journal":{"name":"IEEE Transactions on Signal Processing","volume":"72 ","pages":"5604-5615"},"PeriodicalIF":4.6,"publicationDate":"2024-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142752853","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}
{"title":"Penalized Likelihood Approach to Covariance Matrix Estimation From Data With Cell Outliers","authors":"Petre Stoica;Prabhu Babu","doi":"10.1109/TSP.2024.3507819","DOIUrl":"10.1109/TSP.2024.3507819","url":null,"abstract":"In a recent paper we have proposed an approach for estimating the covariance matrix from a multivariate data set \u0000<inline-formula><tex-math>${mathbf{y}(t)}$</tex-math></inline-formula>\u0000 that may contain outliers. If \u0000<inline-formula><tex-math>$mathbf{y}(t)$</tex-math></inline-formula>\u0000 is flagged as outlying by this approach, then the entire vector \u0000<inline-formula><tex-math>$mathbf{y}(t)$</tex-math></inline-formula>\u0000 is considered to contain no useful information and it is discarded. However, in some applications the data contains cell outliers, that is to say, not all elements of \u0000<inline-formula><tex-math>$mathbf{y}(t)$</tex-math></inline-formula>\u0000 are outlying but only some of them. One then wants to eliminate only the cell outliers from the data, rather than the entire vector \u0000<inline-formula><tex-math>$mathbf{y}(t)$</tex-math></inline-formula>\u0000. In this paper, we propose a penalized maximum likelihood approach to outlier detection and covariance matrix estimation from data with cell outliers. Specifically we estimate the positions of the outliers in the data set, for a given estimate of the covariance matrix, by maximizing the penalized likelihood of the data with the penalty being derived from a property of the likelihood ratio and the false discovery rate (FDR) principle. We alternate this step with a majorization-minimization (MM) technique that estimates the covariance matrix for given outlier positions. The MM is more flexible than the expectation maximization (EM) algorithm commonly used for estimating the covariance matrix from data with missing cells, as the former can be utilized in cases in which the latter is not usable. The closest competitor of our approach is the cellMCD (minimum covariance determinant) method, compared with which the proposed approach has a number of advantages described in the introduction and the numerical study section.","PeriodicalId":13330,"journal":{"name":"IEEE Transactions on Signal Processing","volume":"72 ","pages":"5616-5627"},"PeriodicalIF":4.6,"publicationDate":"2024-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142752854","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}
{"title":"Arithmetic Vs. Expected Mean of Probabilistic Asynchronous Affine Inference","authors":"Georgios Apostolakis;Aggelos Bletsas","doi":"10.1109/TSP.2024.3507572","DOIUrl":"10.1109/TSP.2024.3507572","url":null,"abstract":"Distributed execution of algorithms over various terminals is a topic that regains increasing popularity; when tolerance to failures is also required, asynchronous operation is brought to the light, while probabilistic asynchronous operation can model the probability of failure for each terminal. This work focuses on the probabilistic asynchronous affine update model, applicable in a wide range of inference algorithms, possibly executed over distributed terminals. The existing literature focuses on the asymptotic properties of the expected mean. Instead, this work offers the asymptotic analysis for the arithmetic mean, utilized for discovering fixed points, as it is the only quantity that can be practically offered experimentally. It is shown that the asymptotic behavior of the arithmetic mean is different than the expected mean's and a sufficient condition is provided for convergence of the arithmetic mean to a fixed point. The lack of necessity for this condition is explained and the subcases, where the arithmetic mean converges, diverges or has an unpredictable behavior, are distinguished. Additionally, cases where the individual iterations never converge (e.g., oscillate infinitely) but their arithmetic mean does and offers fixed point, are also highlighted. This is another concrete example of the arithmetic mean utility. Applications of the affine model are also briefly discussed. Finally, simulations corroborate theoretical findings for various affine model setups.","PeriodicalId":13330,"journal":{"name":"IEEE Transactions on Signal Processing","volume":"72 ","pages":"5593-5603"},"PeriodicalIF":4.6,"publicationDate":"2024-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142752852","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}
You Xu;Guanghua Liu;Xiaotong Lu;Chao Xie;Lixia Xiao;Tao Jiang
{"title":"Double Sparse Structure-Enhanced mmWave NLOS Imaging Under Multiangle Relay Surface","authors":"You Xu;Guanghua Liu;Xiaotong Lu;Chao Xie;Lixia Xiao;Tao Jiang","doi":"10.1109/TSP.2024.3505938","DOIUrl":"10.1109/TSP.2024.3505938","url":null,"abstract":"Non-line-of-sight (NLOS) mmWave imaging technology reconstructs the contour features of hidden targets by analyzing the indirect reflected signals of the relay surface, which has been a hot topic in disaster reserve and autonomous driving. However, due to the differences in the reflecting characteristics of multiangle relay surfaces, traditional multipath utilization methods inevitably suffer from disturbance, and obtaining high-quality images remains a challenging task. In this paper, we propose a double sparse structure enhanced mmWave NLOS imaging framework. First, we establish an automotive-squint synthetic aperture radar (AS-SAR) model under multiangle relay surface and analyze the multiangle image characteristics. Subsequently, we introduce a double sparse structure to transform the image reconstruction problem into a hybrid convex regularization problem, and theoretically derive the minimum lower bounds of sample complexity and estimation error. Then, based on the fast iterative threshold shrinkage framework, we propose a time-domain double sparse thresholding algorithm (TD-DSTA), in which the double sparse operator is optimized by alternating direction multiplication. In addition, we propose a two-dimensional frequency domain method based on the approximate-operator to reduce the computational complexity. Finally, we evaluate the performance of the proposed method through quantitative and qualitative analysis in the NLOS multiangle relay surfaces scenario. Simulation and real experimental results verify the superiority of the proposed method in NLOS image reconstruction.","PeriodicalId":13330,"journal":{"name":"IEEE Transactions on Signal Processing","volume":"72 ","pages":"5628-5643"},"PeriodicalIF":4.6,"publicationDate":"2024-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142753466","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}
{"title":"Nonparametric Bellman Mappings for Reinforcement Learning: Application to Robust Adaptive Filtering","authors":"Yuki Akiyama;Minh Vu;Konstantinos Slavakis","doi":"10.1109/TSP.2024.3505266","DOIUrl":"10.1109/TSP.2024.3505266","url":null,"abstract":"This paper designs novel nonparametric Bellman mappings in reproducing kernel Hilbert spaces (RKHSs) for reinforcement learning (RL). The proposed mappings benefit from the rich approximating properties of RKHSs, adopt no assumptions on the statistics of the data owing to their nonparametric nature, require no knowledge on transition probabilities of Markov decision processes, and may operate without any training data. Moreover, they allow for sampling on-the-fly via the design of trajectory samples, re-use past test data via experience replay, effect dimensionality reduction by random Fourier features, and enable computationally lightweight operations to fit into efficient online or time-adaptive learning. The paper offers also a variational framework to design the free parameters of the proposed Bellman mappings, and shows that appropriate choices of those parameters yield several popular Bellman-mapping designs. As an application, the proposed mappings are employed to offer a novel solution to the problem of countering outliers in adaptive filtering. More specifically, with no prior information on the statistics of the outliers and no training data, a policy-iteration algorithm is introduced to select online, per time instance, the “optimal” coefficient \u0000<inline-formula><tex-math>$p$</tex-math></inline-formula>\u0000 in the least-mean-\u0000<inline-formula><tex-math>$p$</tex-math></inline-formula>\u0000-power-error method. Numerical tests on synthetic data showcase, in most of the cases, the superior performance of the proposed solution over several RL and non-RL schemes.","PeriodicalId":13330,"journal":{"name":"IEEE Transactions on Signal Processing","volume":"72 ","pages":"5644-5658"},"PeriodicalIF":4.6,"publicationDate":"2024-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142753479","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}
Zhiyu Liu;Zhi Han;Yandong Tang;Xi-Le Zhao;Yao Wang
{"title":"Low-Tubal-Rank Tensor Recovery via Factorized Gradient Descent","authors":"Zhiyu Liu;Zhi Han;Yandong Tang;Xi-Le Zhao;Yao Wang","doi":"10.1109/TSP.2024.3504292","DOIUrl":"10.1109/TSP.2024.3504292","url":null,"abstract":"This paper considers the problem of recovering a tensor with an underlying low-tubal-rank structure from a small number of corrupted linear measurements. Traditional approaches tackling such a problem require the computation of tensor Singular Value Decomposition (t-SVD), which is a computationally intensive process, rendering them impractical for dealing with large-scale tensors. Aiming to address this challenge, we propose an efficient and effective low-tubal-rank tensor recovery method based on a factorization procedure akin to the Burer-Monteiro (BM) method. Precisely, our fundamental approach involves decomposing a large tensor into two smaller factor tensors, followed by solving the problem through factorized gradient descent (FGD). This strategy eliminates the need for t-SVD computation, thereby reducing computational costs and storage requirements. We provide rigorous theoretical analysis to ensure the convergence of FGD under both noise-free and noisy situations. Additionally, it is worth noting that our method does not require the precise estimation of the tensor tubal-rank. Even in cases where the tubal-rank is slightly overestimated, our approach continues to demonstrate robust performance. A series of experiments have been carried out to demonstrate that, as compared to other popular ones, our approach exhibits superior performance in multiple scenarios, in terms of the faster computational speed and the smaller convergence error.","PeriodicalId":13330,"journal":{"name":"IEEE Transactions on Signal Processing","volume":"72 ","pages":"5470-5483"},"PeriodicalIF":4.6,"publicationDate":"2024-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142690968","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}