• IEEE Trans. Signal Process. (IF 5.230) Pub Date : 2019-12-20
Hoi-To Wai; Santiago Segarra; Asuman E. Ozdaglar; Anna Scaglione; Ali Jadbabaie

This paper considers a new framework to detect communities in a graph from the observation of signals at its nodes. We model the observed signals as noisy outputs of an unknown network process, represented as a graph filter that is excited by a set of unknown low-rank inputs/excitations. Application scenarios of this model include diffusion dynamics, pricing experiments, and opinion dynamics. Rather than learning the precise parameters of the graph itself, we aim at retrieving the community structure directly. The paper shows that communities can be detected by applying a spectral method to the covariance matrix of graph signals. Our analysis indicates that the community detection performance depends on an intrinsic ‘low-pass’ property of the graph filter. We also show that the performance can be improved via a low-rank matrix plus sparse decomposition method when the latent parameter vectors are known. Numerical results demonstrate that our approach is effective.

更新日期：2020-01-24
• IEEE Trans. Signal Process. (IF 5.230) Pub Date : 2019-12-11
Puoya Tabaghi; Ivan Dokmanić; Martin Vetterli

Euclidean distance matrices (EDMs) are a major tool for localization from distances, with applications ranging from protein structure determination to global positioning and manifold learning. They are, however, static objects which serve to localize points from a snapshot of distances. If the objects move, one expects to do better by modeling the motion. In this paper, we introduce Kinetic Euclidean Distance Matrices (KEDMs)—a new kind of time-dependent distance matrices that incorporate motion. The entries of KEDMs become functions of time, the squared time-varying distances. We study two smooth trajectory models—polynomial and bandlimited trajectories—and show that these trajectories can be reconstructed from incomplete, noisy distance observations, scattered over multiple time instants. Our main contribution is a semidefinite relaxation, inspired by similar strategies for static EDMs. Similarly to the static case, the relaxation is followed by a spectral factorization step; however, because spectral factorization of polynomial matrices is more challenging than for constant matrices, we propose a new factorization method that uses anchor measurements. Extensive numerical experiments show that KEDMs and the new semidefinite relaxation accurately reconstruct trajectories from noisy, incomplete distance data and that, in fact, motion improves rather than degrades localization if properly modeled. This makes KEDMs a promising tool for problems in geometry of dynamic points sets.

更新日期：2020-01-24
• IEEE Trans. Signal Process. (IF 5.230) Pub Date : 2020-01-06
Fangzhou Wang; Hongbin Li

We consider a hybrid active-passive radar system that employs a wireless source as a passive illuminator of opportunity (IO) and a co-channel active radar transmitter operating in the same frequency band to seek spectral efficiency. The hybrid system can take advantage of the strengths of passive radar (e.g., energy efficiency, bi-/multi-static configuration, and spatial diversity) as well as those of active radar (dedicated transmitter, flexible transmit beam steering, waveform optimized for sensing, etc.). To mitigate the mutual interference and location-induced timing uncertainty between the radar and communication signals, we propose two designs for the joint optimization of the radar waveform and receive filters. The first is a max-min (MM) criterion that optimizes a worst-case performance metric over a timing uncertainty interval, and the other a weighted-sum (WS) criterion that forms a weighted sum of the performance metric at each delay within the delay uncertainty interval. Both design criteria result in nonconvex constrained optimization problems that are solved by sequential convex programming methods. When timing uncertainty vanishes, the two designs become identical and admit a simpler solution. Numerical results are presented to demonstrate the performance of the proposed hybrid schemes in comparison with conventional active-only and passive-only radar systems.

更新日期：2020-01-24
• IEEE Trans. Signal Process. (IF 5.230) Pub Date : 2019-12-20
Péter Kovács; Sándor Fridli; Ferenc Schipp

In this paper we develop an adaptive transform-domain technique based on rational function systems. It is of general importance in several areas of signal theory, including filter design, transfer function approximation, system identification, control theory etc. The construction of the proposed method is discussed in the framework of a general mathematical model called variable projection. First we generalize this method by adding dimension type free parameters. Then we deal with the optimization problem of the free parameters. To this order, based on the well-known particle swarm optimization (PSO) algorithm, we develop the multi-dimensional hyperbolic PSO algorithm. It is designed especially for the rational transforms in question. As a result, the system along with its dimension is dynamically optimized during the process. The main motivation was to increase the adaptivity while keeping the computational complexity manageable. We note that the proposed method is of general nature. As a case study the problem of electrocardiogram (ECG) signal compression is discussed. By means of comparison tests performed on the PhysioNet MIT-BIH Arrhythmia database we demonstrate that our method outperforms other transformation techniques.

更新日期：2020-01-24
• IEEE Trans. Signal Process. (IF 5.230) Pub Date : 2020-01-06
Jing Bai; Yongchao Wang; Qingjiang Shi

This paper presents an efficient quadratic programming (QP) decoder via the alternating direction method of multipliers (ADMM) technique, called QP-ADMM, for binary low-density parity-check (LDPC) codes. Its main contents are as follows: first, we relax the maximum likelihood (ML) decoding problem to a non-convex quadratic program. Then, we develop an ADMM solving algorithm for the formulated non-convex QP decoding model. In the proposed QP-ADMM decoder, complex Euclidean projections onto the check polytope are eliminated and variables in each updated step can be solved analytically in parallel. Moreover, it is proved that the proposed ADMM algorithm converges to a stationary point of the non-convex QP problem under the assumption of sequence convergence. We also verify that the proposed decoder satisfies the favorable property of the all-zeros assumption . Furthermore, by exploiting the inside structures of the QP model, the complexity of the proposed algorithm in each iteration is shown to be linear in terms of LDPC code length. Simulation results demonstrate the effectiveness of the proposed QP-ADMM decoder.

更新日期：2020-01-24
• IEEE Trans. Signal Process. (IF 5.230) Pub Date : 2020-01-06
Ives Rey-Otero; Jeremias Sulam; Michael Elad

Over the past decade, the celebrated sparse representation model has achieved impressive results in various signal and image processing tasks. A convolutional version of this model, termed convolutional sparse coding (CSC), has been recently reintroduced and extensively studied. CSC brings a natural remedy to the limitation of typical sparse enforcing approaches of handling global and high-dimensional signals by local, patch-based, processing. While the classic field of sparse representations has been able to cater for the diverse challenges of different signal processing tasks by considering a wide range of problem formulations, almost all available algorithms that deploy the CSC model consider the same $\ell _1 - \ell _2$ problem form. As we argue in this paper, this CSC pursuit formulation is also too restrictive as it fails to explicitly exploit some local characteristics of the signal. This work expands the range of formulations for the CSC model by proposing two convex alternatives that merge global norms with local penalties and constraints. The main contribution of this work is the derivation of efficient and provably converging algorithms to solve these new sparse coding formulations.

更新日期：2020-01-24
• IEEE Trans. Signal Process. (IF 5.230) Pub Date : 2020-01-06
Brian P. Day; Aaron Evers; Daniel E. Hack

In continuous wave (CW) radar systems, multiple signal copies impinge the receiver simultaneously. Often, undesired multipath and direct-path copies are many times stronger than potential targets. When applying matched filter signal processing techniques, the undesired signal components can mask weaker targets and decrease performance of post-processing techniques, such as target indication or estimation. In this manuscript, we propose a method of rejecting multipath-scattered returns over a continuous region in range and Doppler. We explore the computational cost of this method and additionally propose an approximate method of rejection which leverages the well-known discrete prolate spheroidal sequences (DPSS)–typically referred to as Slepian sequences–to gain a computational advantage. Results are shown to decrease the effective noise floor when applying matched filtering techniques as well as increase target signal-to-interference-plus-noise ratio (SINR) outside of an undesired multipath region. Comparisons are shown to traditional CW multipath removal in terms of rejection performance and run-time.

更新日期：2020-01-24
• IEEE Trans. Signal Process. (IF 5.230) Pub Date : 2020-01-06
Zahra Sabetsarvestani; Francesco Renna; Franz Kiraly; Miguel Rodrigues

In this paper, we propose an algorithm for source separation with side information where one observes the linear superposition of two source signals plus two additional signals that are correlated with the mixed ones. Our algorithm is based on two ingredients: first, we learn a Gaussian mixture model (GMM) for the joint distribution of a source signal and the corresponding correlated side information signal; second, we separate the signals using standard computationally efficient conditional mean estimators. The paper also puts forth new recovery guarantees for this source separation algorithm. In particular, under the assumption that the signals can be perfectly described by a GMM model, we characterize necessary and sufficient conditions for reliable source separation in the asymptotic regime of low-noise as a function of the geometry of the underlying signals and their interaction. It is shown that if the subspaces spanned by the innovation components of the source signals with respect to the side information signals have zero intersection, provided that we observe a certain number of linear measurements from the mixture, then we can reliably separate the sources; otherwise we cannot. Our proposed framework – which provides a new way to incorporate side information to aid the solution of source separation problems where the decoder has access to linear projections of superimposed sources and side information – is also employed in a real-world art investigation application involving the separation of mixtures of X-ray images. The simulation results showcase the superiority of our algorithm against other state-of-the-art algorithms.

更新日期：2020-01-24
• IEEE Trans. Signal Process. (IF 5.230) Pub Date : 2020-01-06
Leibo Liu; Guiqiang Peng; Pan Wang; Sheng Zhou; Qiushi Wei; Shouyi Yin; Shaojun Wei

Minimum-mean-square-error (MMSE) detection is increasingly relevant for massive multiple-input multiple-output (MIMO) systems. MMSE suffers from high computational complexity and low parallelism because of the increasing number of users and antennas in massive MIMO systems. This paper proposes a recursive conjugate gradient (RCG) method to iteratively estimate signals. First, a recursive conjugate gradient detection algorithm is proposed that achieves high parallelism and low complexity through iteration. Second, a quadrant-certain-based initial method that improves detection accuracy without added complexity is proposed. Third, an approximated log likelihood ratio (LLR) computation method is proposed to achieve simplified calculation. The analyses show that compared with related methods, the proposed RCG algorithm reduces computational complexity and exploits the potential parallelism. RCG is mathematically demonstrated to achieve low approximated error. Based on the RCG method, an architecture is proposed in a 128 × 8 64-QAM massive MIMO system. First, a parallel processing element array with single-sided input is adopted; this array eliminates the throughput limitation. Second, a deeply pipelined user-level method based on the recursive conjugate gradient method is proposed. Third, an approximated architecture is proposed to compute the soft output. The architecture is verified on an FPGA and fabricated on 1.87 × 1.87 mm $^2$ silicon with TSMC 65 nm CMOS technology. The chip achieves 2.69 Mbps/mW and 1.09 Mbps/kG energy efficiency (throughput/power) and area efficiency (throughput/area), respectively, which are 2.39 to 10.60× and 1.15 to 8.81× those of the normalized state-of-the-art designs.

更新日期：2020-01-24
• IEEE Trans. Signal Process. (IF 5.230) Pub Date : 2019-11-20
Saeid Sedighi; Bhavani Shankar Mysore Rama Rao; Björn Ottersten

Co-array-based Direction of Arrival (DoA) estimation using Sparse Linear Arrays (SLAs) has recently gained considerable interest in array processing thanks to its capability of providing enhanced degrees of freedom. Although the literature presents a variety of estimators in this context, none of them are proven to be statistically efficient. This work introduces a novel estimator for the co-array-based DoA estimation employing the Weighted Least Squares (WLS) method. An analytical expression for the large sample performance of the proposed estimator is derived. Then, an optimal weighting is obtained so that the asymptotic performance of the proposed WLS estimator coincides with the Cramér-Rao Bound (CRB), thereby ensuring asymptotic statistical efficiency of resulting WLS estimator. This implies that the proposed WLS estimator has a significantly better performance compared to existing methods. Numerical simulations are provided to validate the analytical derivations and corroborate the improved performance.

更新日期：2020-01-24
• IEEE Trans. Signal Process. (IF 5.230) Pub Date : 2020-01-06
An Liu; Lixiang Lian; Vincent Lau; Guanying Liu; Min-Jian Zhao

Due to the high resolution of angles of arrivals (AoAs) provided by the massive MIMO base station in 5 G wireless systems, it is promising to integrate 5G-based localization technology into autonomous driving to improve the accuracy and robustness of vehicle localization. In this paper, we investigate the problem of 5G cloud-assisted cooperative localization for vehicle platoons. The existing 5G-based localization algorithms focused on single-user localization and are not efficient for the localization of vehicle platoon where the positions of the vehicles are highly correlated. To the best of our knowledge, cloud-assisted cooperative localization tailored to vehicle platoons has not been studied before. To address this challenging problem, we first propose a Gamma-Markov-Group-Sparse (GMGS) model to capture the joint distribution of the vehicle positions in a vehicle platoon. Then we formulate the vehicle platoon cooperative localization as a sparse Bayesian inference (SBI) problem. The existing standard SBI algorithms such as variational Bayesian inference (VBI) and approximate message passing (AMP) cannot be applied to our platoon localization problem due to the complicated GMGS prior and the ill-conditioned measurement matrix. As such, we propose a novel turbo vehicle platoon cooperative localization (Turbo-VPCL) algorithm to fully exploit the correlations of the vehicle positions (as captured by the GMGS prior) under the ill-conditioned measurement matrix. Simulation results verify that the proposed Turbo-VPCL can achieve significant gain over the-state-of-art SBI algorithms.

更新日期：2020-01-24
• IEEE Trans. Signal Process. (IF 5.230) Pub Date : 2019-12-11
Ali Ahmed

This paper considers the blind deconvolution of multiple modulated signals/filters, and an arbitrary filter/signal. Multiple inputs $\boldsymbol{s}_1, \boldsymbol{s}_2, \ldots, \boldsymbol{s}_N =: [\boldsymbol{s}_n]$ are modulated (pointwise multiplied) with random sign sequences $\boldsymbol{r}_1, \boldsymbol{r}_2, \ldots, \boldsymbol{r}_N =: [\boldsymbol{r}_n]$ , respectively, and the resultant inputs $(\boldsymbol{s}_n \odot \boldsymbol{r}_n) \in \mathbb {C}^Q, \ n \in [N]$ are convolved against an arbitrary input $\boldsymbol{h} \in \mathbb {C}^M$ to yield the measurements $\boldsymbol{y}_n = (\boldsymbol{s}_n\odot \boldsymbol{r}_n)\circledast \boldsymbol{h}, \ n \in [N] := 1,2,\ldots,N,$ where $\odot$ and $\circledast$ denote pointwise multiplication, and circular convolution. Given $[\boldsymbol{y}_n]$ , we want to recover the unknowns $[\boldsymbol{s}_n]$ and $\boldsymbol{h}$ . We make a structural assumption that unknowns $[\boldsymbol{s}_n]$ are members of a known $K$ -dimensional (not necessarily random) subspace, and prove that the unknowns can be recovered from sufficiently many observations using a regularized gradient descent algorithm whenever the modulated inputs $\boldsymbol{s}_n \odot \boldsymbol{r}_n$ are long enough, i.e, $Q \gtrsim KN+M$ (to within logarithmic factors, and signal dispersion/coherence parameters). Under the bilinear model, this is the first result on multichannel ( $N\geq 1$ ) blind deconvolution with provable recovery guarantees under near optimal (in the $N=1$ case) sample complexity estimates, and comparatively lenient structural assumptions on the convolved inputs. A neat conclusion of this result is that modulation of a bandlimited signal protects it against an unknown convolutive distortion. We discuss the applications of this result in passive imaging, wireless communication in unknown environment, and image deblurring. A thorough numerical investigation of the theoretical results is also presented using phase transitions, image deblurring experiments, and noise stability plots.

更新日期：2020-01-17
• IEEE Trans. Signal Process. (IF 5.230) Pub Date : 2019-12-20
Matthew R. O’Shaughnessy; Mark A. Davenport; Christopher J. Rozell

Many signal processing applications require estimation of time-varying sparse signals, potentially with the knowledge of an imperfect dynamics model. In this paper, we propose an algorithm for dynamic filtering of time-varying sparse signals based on the sparse Bayesian learning (SBL) framework. The key idea underlying the algorithm, termed SBL-DF, is the incorporation of a signal prediction generated from a dynamics model and estimates of previous time steps into the hyperpriors of the SBL probability model. The proposed algorithm is online, robust to imperfect dynamics models (due to the propagation of dynamics information through higher-order statistics), robust to certain undesirable dictionary properties such as coherence (due to properties of the SBL framework), allows the use of arbitrary dynamics models, and requires the tuning of fewer parameters than many other dynamic filtering algorithms do. We also extend the fast marginal likelihood SBL inference procedure to the informative hyperprior setting to create a particularly efficient version of the SBL-DF algorithm. Numerical simulations show that SBL-DF converges much faster and to more accurate solutions than standard SBL and other dynamical filtering algorithms. In particular, we show that SBL-DF outperforms state of the art algorithms when the dictionary contains the challenging coherence and column scaling structure found in many practical applications.

更新日期：2020-01-17
• IEEE Trans. Signal Process. (IF 5.230) Pub Date : 2019-12-20
Amir Masoud Molaei; Bijan Zakeri; Seyed Mehdi Hosseini Andargoli

In recent years, the sources localization has noticed an increase in research conducted on the problem of mixed far-field sources (FFSs) and near-field sources (NFSs). The main assumption of the existing researches is that the signals should be uncorrelated. Therefore, they cannot be used for multipath environments. The present paper provides a method called components separation algorithm (CSA) for the localization of multiple mixed FFSs and NFSs, including uncorrelated, lowly correlated and coherent signals. Firstly, by constructing one special cumulant matrix, and using a MUSIC-based technique, the noncoherent DOA vector (NDOAV) is extracted. By constructing another special cumulant matrix, and with respect to NDOAV, an estimate of the range, as well as a signal classification is obtained for noncoherent sources. Then, by estimating their kurtosis, the noncoherent component and consequently the coherent one of the second cumulant matrix is obtained. Finally, by introducing a novel approach based on squaring, projection, spatial smoothing, array interpolation transform and coherent component restoring, the parameters of coherent signals in each coherent group are estimated separately. The CSA prevents severe loss of the aperture. Furthermore, it does not require any pairing. The simulation results validate its satisfactory performance in terms of estimation accuracy, resolution, computational complexity, reasonable classification, and also its robustness against lowly correlated sources.

更新日期：2020-01-17
• IEEE Trans. Signal Process. (IF 5.230) Pub Date : 2019-12-20
Xiaodan Shao; Xiaoming Chen; Rundong Jia

Grant-free random access is a promising protocol to support massive access in beyond fifth-generation (B5G) cellular Internet-of-Things (IoT) with sporadic traffic. Specifically, in each coherence interval, the base station (BS) performs joint activity detection and channel estimation (JADCE) before data transmission. Due to the deployment of a large-scale antennas array and the existence of a huge number of IoT devices, JADCE usually has high computational complexity and needs long pilot sequences. To solve these challenges, this paper proposes a dimension reduction method, which projects the original device state matrix to a low-dimensional space by exploiting its sparse and low-rank structure. Then, we develop an optimized design framework with a coupled full column rank constraint for JADCE to reduce the size of the search space. However, the resulting problem is non-convex and highly intractable, for which the conventional convex relaxation approaches are inapplicable. To this end, we propose a logarithmic smoothing method for the non-smoothed objective function and transform the interested matrix to a positive semidefinite matrix, followed by giving a Riemannian trust-region algorithm to solve the problem in complex field. Simulation results show that the proposed algorithm is efficient to a large-scale JADCE problem and requires shorter pilot sequences than the state-of-art algorithms which only exploit the sparsity of device state matrix.

更新日期：2020-01-17
• IEEE Trans. Signal Process. (IF 5.230) Pub Date : 2019-12-11
Daniyal Amir Awan; Renato L. G. Cavalcante; Slawomir Stanczak

Learning of the cell-load in radio access networks (RANs) has to be performed within a short time period. Therefore, we propose a learning framework that is robust against uncertainties resulting from the need for learning based on a relatively small training set. To this end, we incorporate prior knowledge about the cell-load in the learning framework. For example, an inherent property of the cell-load is that it is monotonic in downlink (data) rates. To obtain additional prior knowledge we first study the feasible rate region, i.e., the set of all vectors of user rates that can be supported by the network. We prove that the feasible rate region is compact. Moreover, we show the existence of a Lipschitz function that maps feasible rate vectors to cell-load vectors. With these results in hand, we present a learning technique that guarantees a minimum approximation error in the worst-case scenario by using prior knowledge and a small training sample set. Simulations in the network simulator NS3 demonstrate that the proposed method exhibits better robustness and accuracy than standard learning techniques, especially for small training sample sets.

更新日期：2020-01-10
• IEEE Trans. Signal Process. (IF 5.230) Pub Date : 2019-12-11
Ahmed Douik; Xing Liu; Tarig Ballal; Tareq Y. Al-Naffouri; Babak Hassibi

In the past few years, Global Navigation Satellite Systems (GNSS) based attitude determination has been widely used thanks to its high accuracy, low cost, and real-time performance. This paper presents a novel 3-D GNSS attitude determination method based on Riemannian optimization techniques. The paper first exploits the antenna geometry and baseline lengths to reformulate the 3-D GNSS attitude determination problem as an optimization over a non-convex set. Since the solution set is a manifold, in this manuscript we formulate the problem as an optimization over a Riemannian manifold. The study of the geometry of the manifold allows the design of efficient first and second order Riemannian algorithms to solve the 3-D GNSS attitude determination problem. Despite the non-convexity of the problem, the proposed algorithms are guaranteed to globally converge to a critical point of the optimization problem. To assess the performance of the proposed framework, numerical simulations are provided for the most challenging attitude determination cases: the unaided, single-epoch, and single-frequency scenarios. Numerical results reveal that the proposed algorithms largely outperform state-of-the-art methods for various system configurations with lower complexity than generic non-convex solvers, e.g., interior point methods.

更新日期：2020-01-10
• IEEE Trans. Signal Process. (IF 5.230) Pub Date : 2019-12-11
Yasuhiro Takano; Hsuan-Jung Su; Yoshiaki Shiraishi; Masakatu Morii

Spatial–temporal (ST) subspace-based channel estimation techniques formulated with $\ell 2$ minimum mean square error (MMSE) criterion alleviate the multi-access interference (MAI) problem when the interested signals exhibit low-rank property. However, the conventional $\ell 2$ ST subspace-based methods suffer from mean squared error (MSE) deterioration in unknown interference channels, due to the difficulty to separate the interested signals from the channel covariance matrices (CCMs) contaminated with unknown interference. As a solution to the problem, we propose a new $\ell 1$ regularized ST channel estimation algorithm by applying the expectation-maximization (EM) algorithm to iteratively examine the signal subspace and the corresponding sparse-supports. The new algorithm updates the CCM independently of the slot-dependent $\ell 1$ regularization, which enables it to correctly perform the sparse-independent component analysis (ICA) with a reasonable complexity order. Simulation results shown in this paper verify that the proposed technique significantly improves MSE performance in unknown interference MIMO channels, and hence, solves the BER floor problems from which the conventional receivers suffer.

更新日期：2020-01-10
• IEEE Trans. Signal Process. (IF 5.230) Pub Date : 2019-12-13
Maja Taseska; Toon van Waterschoot; Emanuël A. P. Habets; Ronen Talmon

Frameworks for efficient and accurate data processing often rely on a suitable representation of measurements that capture phenomena of interest. Typically, such representations are high-dimensional vectors obtained by a transformation of raw sensor signals such as time-frequency transform, lag-map, etc. In this work, we focus on representation learning approaches that consider the measurements as the nodes of a weighted graph, with edge weights computed by a given kernel . If the kernel is chosen properly, the eigenvectors of the resulting graph affinity matrix provide suitable representation coordinates for the measurements. Consequently, tasks such as regression, classification, and filtering, can be done more efficiently than in the original domain of the data. In this paper, we address the problem of representation learning from measurements, which besides the phenomenon of interest contain undesired sources of variability. We propose data-driven kernels to learn representations that accurately parametrize the phenomenon of interest, while reducing variations due to other sources of variability. This is a non-linear filtering problem, which we approach under the assumption that certain geometric information about the undesired variables can be extracted from the measurements, e.g., using an auxiliary sensor. The applicability of the proposed kernels is demonstrated in toy problems and in a real signal processing task.

更新日期：2020-01-10
• IEEE Trans. Signal Process. (IF 5.230) Pub Date : 2019-10-02
Xuejing Zhang; Xiang-Gen Xia; Zishu He; Xuepan Zhang

This paper presents two secure transmission algorithms for millimeter-wave wireless communication, which are computationally attractive and have analytical solutions. In the proposed algorithms, we consider phased-array transmission structure and focus on phase shift keying (PSK) modulation. It is found that the traditional constellation synthesis problem can be solved with the aid of polygon construction in the complex plane. A detailed analysis is then carried out and an analytical procedure is developed to obtain a qualified phase solution. For a given synthesis task, it is derived that there exist infinite weight vector solutions under a mild condition. Based on this result, we propose the first secure transmission algorithm by varying the transmitting weight vector at symbol rate, thus resulting exact phases at the intended receiver and producing randomnesses at the undesired eavesdroppers. To improve the security without significantly degrading the symbol detection reliability for target receiver, the second secure transmission algorithm is devised by allowing a relaxed symbol region for the intended receiver. Compared to the first algorithm, the second one incorporates an additional random phase rotation operation to the transmitting weight vector and brings extra disturbance for the undesired eavesdroppers. Different from the existing works that are only feasible for the case of single-path mmWave channels, our proposed algorithms are applicable to more general multi-path channels. Moreover, all the antennas are active in the proposed algorithms and the on-off switching circuit is not needed. Simulations are presented to demonstrate the effectivenesses of the proposed algorithms under various situations.

更新日期：2020-01-10
• IEEE Trans. Signal Process. (IF 5.230) Pub Date : 2019-11-20
Geethu Joseph; Chandra R. Murthy

Dictionary learning (DL) is a well-researched problem, where the goal is to learn a dictionary from a finite set of noisy training signals, such that the training data admits a sparse representation over the dictionary. While several solutions are available in the literature, relatively little is known about their convergence and optimality properties. In this paper, we make progress on this problem by analyzing a Bayesian algorithm for DL. Specifically, we cast the DL problem into the sparse Bayesian learning (SBL) framework by imposing a hierarchical Gaussian prior on the sparse vectors. This allows us to simultaneously learn the dictionary as well as the parameters of the prior on the sparse vectors using the expectation-maximization algorithm. The dictionary update step turns out to be a non-convex optimization problem, and we present two solutions, namely, an alternating minimization (AM) procedure and an Armijo line search (ALS) method. We analytically show that the ALS procedure is globally convergent, and establish the stability of the solution by characterizing its limit points. Further, we prove the convergence and stability of the overall DL-SBL algorithm, and show that the minima of the cost function of the overall algorithm are achieved at sparse solutions. As a concrete example, we consider the application of the SBL-based DL algorithm to image denoising, and demonstrate the efficacy of the algorithm relative to existing DL algorithms.

更新日期：2020-01-10
• IEEE Trans. Signal Process. (IF 5.230) Pub Date : 2019-11-28
Paolo Braca; Augusto Aubry; Leonardo Maria Millefiori; Antonio De Maio; Stefano Marano

Covariance matrix estimation is a crucial task in adaptive signal processing applied to several surveillance systems, including radar and sonar. In this paper we propose a dynamic learning strategy to track both the covariance matrix of data and its structure (class). We assume that, given the class, the posterior distribution of the covariance is described through a mixture of inverse Wishart distributions, while the class evolves according to a Markov chain. Hence, we devise a novel and general filtering strategy, called multi-class inverse Wishart mixture filter, able to capitalize on previous observations so as to accurately track and estimate the covariance. Some case studies are provided to highlight the effectiveness of the proposed technique, which is shown to outperform alternative methods in terms of both covariance estimation accuracy and probability of correct model selection. Specifically, the proposed filter is compared with class-clairvoyant covariance estimators, e.g., the maximum likelihood and the knowledge-based recursive least square filter, and with the model order selection method based on the Bayesian information criterion.

更新日期：2020-01-10
• IEEE Trans. Signal Process. (IF 5.230) Pub Date : 2019-11-06
Charilaos I. Kanatsoulis; Xiao Fu; Nicholas D. Sidiropoulos; Mehmet Akçakaya

Signal sampling and reconstruction is a fundamental engineering task at the heart of signal processing. The celebrated Shannon-Nyquist theorem guarantees perfect signal reconstruction from uniform samples, obtained at a rate twice the maximum frequency present in the signal. Unfortunately a large number of signals of interest are far from being band-limited. This motivated research on reconstruction from sub-Nyquist samples, which mainly hinges on the use of random/incoherent sampling procedures. However, uniform or regular sampling is more appealing in practice and from the system design point of view, as it is far simpler to implement, and often necessary due to system constraints. In this work, we study regular sampling and reconstruction of three- or higher-dimensional signals (tensors). We show that reconstructing a tensor signal from regular samples is feasible. Under the proposed framework, the sample complexity is determined by the tensor rank—rather than the signal bandwidth. This result offers new perspectives for designing practical regular sampling patterns and systems for signals that are naturally tensors, e.g., images and video. For a concrete application, we show that functional magnetic resonance imaging (fMRI) acceleration is a tensor sampling problem, and design practical sampling schemes and an algorithmic framework to handle it. Numerical results show that our tensor sampling strategy accelerates the fMRI sampling process significantly without sacrificing reconstruction accuracy.

更新日期：2020-01-04
• IEEE Trans. Signal Process. (IF 5.230) Pub Date : 2019-11-28
Nguyen Tran; Oleksii Abramenko; Alexander Jung

We study conditions that allow accurate graphical model selection from non-stationary data. The observed data is modelled as a vector-valued zero-mean Gaussian random process whose samples are uncorrelated but have different covariance matrices. This model contains as special cases the standard setting of i.i.d. samples as well as the case of samples forming a stationary time series. More generally, our approach applies to any data for which efficient decorrelation transforms, such as the Fourier transform for stationary time series, are available. By analyzing a conceptually simple model selection method, we derive a sufficient condition on the required sample size for accurate graphical model selection based on non-stationary data.

更新日期：2020-01-04
• IEEE Trans. Signal Process. (IF 5.230) Pub Date : 2019-11-06
Mohsen Ghassemi; Zahra Shakeri; Anand D. Sarwate; Waheed U. Bajwa

This work addresses the problem of learning sparse representations of tensor data using structured dictionary learning. It proposes learning a mixture of separable dictionaries to better capture the structure of tensor data by generalizing the separable dictionary learning model. Two different approaches for learning mixture of separable dictionaries are explored and sufficient conditions for local identifiability of the underlying dictionary are derived in each case. Moreover, computational algorithms are developed to solve the problem of learning mixture of separable dictionaries in both batch and online settings. Numerical experiments are used to show the usefulness of the proposed model and the efficacy of the developed algorithms.

更新日期：2020-01-04
• IEEE Trans. Signal Process. (IF 5.230) Pub Date : 2019-11-28
Mingjin Wang; Feifei Gao; Nir Shlezinger; Mark F. Flanagan; Yonina C. Eldar

Multiple-input multiple-output (MIMO) millimeter wave (mmWave) communication is a key technology for next generation wireless networks. One of the consequences of utilizing a large number of antennas with an increased bandwidth is that array steering vectors vary among different subcarriers. Due to this effect, known as beam squint , the conventional channel model is no longer applicable for mmWave massive MIMO systems. In this paper, we study channel estimation under the resulting non-standard model. To that aim, we first analyze the beam squint effect from an array signal processing perspective, resulting in a model which sheds light on the angle-delay sparsity of mmWave transmission. We next design a compressive sensing based channel estimation algorithm which utilizes the shift-invariant block-sparsity of this channel model. The proposed algorithm jointly computes the off-grid angles, the off-grid delays, and the complex gains of the multi-path channel. We show that the newly proposed scheme reflects the mmWave channel more accurately and results in improved performance compared to traditional approaches. We then demonstrate how this approach can be applied to recover both the uplink as well as the downlink channel in frequency division duplex (FDD) systems, by exploiting the angle-delay reciprocity of mmWave channels.

更新日期：2020-01-04
• IEEE Trans. Signal Process. (IF 5.230) Pub Date : 2019-11-25
Min Xiang; Yili Xia; Danilo P. Mandic

Quaternion adaptive filters have been widely used for processing 3D and 4D phenomena. Deficient length quaternion adaptive filters are explicitly or implicitly used in many practical applications where the length of system impulse response is large or unknown. However, their statistical behaviors are yet to be fully understood. As theoretical results on the class of “full length” quaternion least mean square (QLMS) algorithms do not necessarily apply to their deficient length versions, this article fills this void and analyses the mean and mean square convergence of the deficient length QLMS algorithms, both for the strictly linear and widely linear cases. Transient and steady-state performance is characterised by exploiting the augmented statistics of noncircular quaternion random vectors. A novel decorrelation technique in the quaternion domain is shown to allow for the development of intuitive closed-form solutions for correlated quaternion Gaussian inputs, thus unveiling the relationship between the algorithm behaviour and the noncircularity of quaternion input data. The analysis also provides a general framework whereby the strictly linear and semi-widely linear QLMS algorithms can be seen as “deficient-length” versions of the widely linear QLMS. Numerical simulations validate the accuracy of the theoretical results and support the behaviour of the considered algorithms.

更新日期：2020-01-04
• IEEE Trans. Signal Process. (IF 5.230) Pub Date : 2019-12-06
Xiaoye Wang; Zhaocheng Yang; Jianjun Huang; Rodrigo C. de Lamare

Space-time adaptive processing (STAP) algorithms with coprime arrays can provide good clutter suppression potential with low cost in airborne radar systems as compared with their uniform linear arrays counterparts. However, the performance of these algorithms is limited by the training samples support in practical applications. To address this issue, a robust two-stage reduced-dimension (RD) sparsity-aware STAP algorithm is proposed in this work. In the first stage, an RD virtual snapshot is constructed using all spatial channels but only $m$ adjacent Doppler channels around the target Doppler frequency to reduce the slow-time dimension of the signal. In the second stage, an RD sparse measurement modeling is formulated based on the constructed RD virtual snapshot, where the sparsity of clutter and the prior knowledge of the clutter ridge are exploited to formulate an RD overcomplete dictionary. Moreover, an orthogonal matching pursuit (OMP)-like method is proposed to recover the clutter subspace. In order to set the stopping parameter of the OMP-like method, a robust clutter rank estimation approach is developed. Compared with recently developed sparsity-aware STAP algorithms, the size of the proposed sparse representation dictionary is much smaller, resulting in low complexity. Simulation results show that the proposed algorithm is robust to prior knowledge errors and can provide good clutter suppression performance in low sample support.

更新日期：2020-01-04
• IEEE Trans. Signal Process. (IF 5.230) Pub Date : 2019-12-04
Bin Li; Weisi Guo; Xiang Wang; Yansha Deng; Yueheng Lan; Chenglin Zhao; Arumugam Nallanathan

Molecular communications rely on diffusive propagation to transport information, which is attractive for a variety of nano-scale applications. Due to the long-tail channel response, spatial-temporal coding of information may lead to severe inter-symbol interference (ISI). Classical linear signal processing in wireless communications is usually operating with high complexity and high signal-to-noise ratios, whereas signal processing in molecular communication system requires operating in opposite conditions. In this work, we propose a novel signal processing paradigm inspired by the biological principle, which enables low-complexity signal detection in extremely noisy environments. We first propose a non-linear filter inspired by stochastic resonance, which is found in a variety of biological systems, and it can significantly improve the output SNR by converting noise to useful signals. Then, we design a non-coherent detection method, one which exploits the generally transient trend of observed signals (i.e. quick-rising and slow-decaying) rather than hidden channel state information (CSI), thus excluding CSI estimation and involving only summations. Implementation issues are also discussed, including parameters configuration and adaptive threshold. Numerical results show that the proposed bio-inspired scheme can improve the performance remarkably over classical approaches. Even compared with the optimal linear methods, the required SNR of the proposed scheme can be reduced by 7 dB, which reaffirms why it can be used in noisy biological environments. As the first attempt to design bio-inspired molecular signal detectors, the proposed non-linear processing paradigm may provide the great promise to the emerging nano-machine applications.

更新日期：2020-01-04
• IEEE Trans. Signal Process. (IF 5.230) Pub Date : 2019-11-25
David Ramírez; Ignacio Santamaria; Louis L. Scharf; Steven Van Vaerenbergh

This work presents a generalization of classical factor analysis (FA). Each of $M$ channels carries measurements that share factors with all other channels, but also contains factors that are unique to the channel. Furthermore, each channel carries an additive noise whose covariance is diagonal, as is usual in factor analysis, but is otherwise unknown. This leads to a problem of multi-channel factor analysis with a specially structured covariance model consisting of shared low-rank components, unique low-rank components, and diagonal components. Under a multivariate normal model for the factors and the noises, a maximum likelihood (ML) method is presented for identifying the covariance model, thereby recovering the loading matrices and factors for the shared and unique components in each of the $M$ multiple-input multiple-output (MIMO) channels. The method consists of a three-step cyclic alternating optimization, which can be framed as a block minorization-maximization (BMM) algorithm. Interestingly, the three steps have closed-form solutions and the convergence of the algorithm to a stationary point is ensured. Numerical results demonstrate the performance of the proposed algorithm and its application to passive radar.

更新日期：2020-01-04
• IEEE Trans. Signal Process. (IF 5.230) Pub Date : 2019-11-25
Luana Ruiz; Fernando Gama; Antonio García Marques; Alejandro Ribeiro

Graph signals are signals with an irregular structure that can be described by a graph. Graph neural networks (GNNs) are information processing architectures tailored to these graph signals and made of stacked layers that compose graph convolutional filters with nonlinear activation functions. Graph convolutions endow GNNs with invariance to permutations of the graph nodes’ labels. In this paper, we consider the design of trainable nonlinear activation functions that take into consideration the structure of the graph. This is accomplished by using graph median filters and graph max filters, which mimic linear graph convolutions and are shown to retain the permutation invariance of GNNs. We also discuss modifications to the backpropagation algorithm necessary to train local activation functions. The advantages of localized activation function architectures are demonstrated in four numerical experiments: source localization on synthetic graphs, authorship attribution of 19th century novels, movie recommender systems and scientific article classification. In all cases, localized activation functions are shown to improve model capacity.

更新日期：2020-01-04
• IEEE Trans. Signal Process. (IF 5.230) Pub Date : 2019-12-04
Nitesh Sahu; Prabhu Babu; Arun Kumar; Rajendar Bahl

This paper proposes a novel algorithm to determine the optimal orientation of sensing axes of redundant inertial sensors such as accelerometers and gyroscopes (gyros) for increasing the sensing accuracy. In this paper, we have proposed a novel iterative algorithm to find the optimal sensor configuration. The proposed algorithm utilizes the majorization-minimization (MM) algorithm and the duality principle to find the optimal configuration. Unlike the state-of-the-art approaches which are mainly geometrical in nature and restricted to sensors’ noise being uncorrelated, the proposed algorithm gives the exact orientations of the sensors and can easily deal with the cases of correlated noise. The proposed algorithm has been implemented and tested via numerical simulation in the MATLAB. The simulation results show that the algorithm converges to the optimal configurations and shows the effectiveness of the proposed algorithm.

更新日期：2020-01-04
• IEEE Trans. Signal Process. (IF 5.230) Pub Date : 2019-05-28
Reza Rezaie; X. Rong Li

Conditionally Markov (CM) sequences are powerful mathematical tools for modeling problems. One class of CM sequences is the reciprocal sequence. In application, we need not only CM dynamic models, but also know how to design model parameters. Models of two important classes of nonsingular Gaussian (NG) CM sequences, called $CM_L$ and $CM_F$ models, and a model of the NG reciprocal sequence, called reciprocal $CM_L$ model, were presented in our previous works and their applications were discussed. In this paper, these models are studied in more detail, in particular their parameter design. It is shown that every reciprocal $CM_L$ model can be induced by a Markov model. Then, parameters of each reciprocal $CM_L$ model can be obtained from those of the Markov model. Also, it is shown that an NG $CM_L$ ( $CM_F$ ) sequence can be represented by a sum of an NG Markov sequence and an uncorrelated NG vector. This (necessary and sufficient) representation provides a basis for designing parameters of a $CM_L$ ( $CM_F$ ) model. From the CM viewpoint, a representation is also obtained for NG reciprocal sequences. This representation is simple and reveals an important property of reciprocal sequences. As a result, the significance of studying reciprocal sequences from the CM viewpoint is demonstrated. A full spectrum of dynamic models from a $CM_L$ model to a reciprocal $CM_L$ model is also presented. Some examples are presented for illustration.

更新日期：2020-01-04
• IEEE Trans. Signal Process. (IF 5.230) Pub Date : 2019-12-11
Kangjian Chen; Chenhao Qi; Geoffrey Ye Li

In this paper, a two-step codeword design approach for millimeter wave (mmWave) massive MIMO systems is presented. Ideal codewords are first designed, which ignores the hardware constraints in terms of phase shifter resolution and the number of RF chains. Based on the ideal codewords, practical codewords are then obtained taking the hardware constraints into consideration. For the ideal codeword design in the first step, additional phase is introduced to the beam gain to provide extra degree of freedom. We develop a phase-shifted ideal codeword design (PS-ICD) method, which is based on alternative minimization with each iteration having a closed-form solution and can be extended to design more general beamforming vectors with different beam patterns. Once the ideal codewords are obtained in the first step, the practical codeword design problem in the second step is to approach the ideal codewords by considering the hardware constraints of the hybrid precoding structure in terms of phase shifter resolution and the number of RF chains. We propose a fast search based alternative minimization (FS-AltMin) algorithm that alternatively designs the analog precoder and digital precoder. Simulation results verify the effectiveness of the proposed methods and show that the codewords designed based on the two-step approach outperform those designed by the existing approaches.

更新日期：2020-01-04
• IEEE Trans. Signal Process. (IF 5.230) Pub Date : 2019-11-08
Yicong He; Fei Wang; Yingsong Li; Jing Qin; Badong Chen

Robust matrix completion aims to recover a low-rank matrix from a subset of noisy entries perturbed by complex noises. Traditional matrix completion algorithms are always based on $l_2$ -norm minimization and are sensitive to non-Gaussian noise with outliers. In this paper, we propose a novel robust and fast matrix completion method based on the maximum correntropy criterion (MCC). The correntropy-based error measure is utilized instead of the $l_2$ -based error norm to improve robustness against noise. By using the half-quadratic optimization technique, the correntropy-based optimization can be transformed into a weighted matrix factorization problem. Two efficient algorithms are then derived: an alternating minimization-based algorithm and an alternating gradient descent-based algorithm. These algorithms do not require the singular value decomposition (SVD) to be calculated for each iteration. Furthermore, an adaptive kernel width selection strategy is proposed to accelerate the convergence speed as well as improve the performance. A comparison with existing robust matrix completion algorithms is provided by simulations and shows that the new methods can achieve better performance than the existing state-of-the-art algorithms.

更新日期：2020-01-04
• IEEE Trans. Signal Process. (IF 5.230) Pub Date : 2019-12-04
Wen-Liang Hwang; Andreas Heinecke

We consider deep neural networks with rectifier activations and max-pooling from a signal representation perspective. In this view, such representations mark the transition from using a single linear representation for all signals to utilizing a large collection of affine linear representations that are tailored to particular regions of the signal space. We propose a novel technique to “un-rectify” the nonlinear activations into data-dependent linear equations and constraints, from which we derive explicit expressions for the affine linear operators, their domains and ranges in terms of the network parameters. We show how increasing the depth of the network refines the domain partitioning and derive atomic decompositions for the corresponding affine mappings that process data belonging to the same partitioning region. In each atomic decomposition the connections over all hidden network layers are summarized and interpreted in a single matrix. We apply the decompositions to study the Lipschitz regularity of the networks and give sufficient conditions for network-depth-independent stability of the representation, drawing a connection to compressible weight distributions. Such analyses may facilitate and promote further theoretical insight and exchange from both the signal processing and machine learning communities.

更新日期：2020-01-04
• IEEE Trans. Signal Process. (IF 5.230) Pub Date : 2019-12-11
Qiao Qi; Xiaoming Chen; Derrick Wing Kwan Ng

In this paper, we study the resource allocation design for non-orthogonal multiple access (NOMA)-based cellular massive Internet-of-Things (IoT) enabled with simultaneous wireless information and power transfer (SWIPT). The design is formulated as a non-convex optimization problem, which takes into account practical and adverse factors, e.g., the channel uncertainty during channel state information (CSI) acquisition, the non-linear receiver during energy harvesting (EH) and the imperfect successive information cancellation (SIC) during the information decoding (ID). The originally harmful co-channel interference in massive access is coordinated to strike a balance between efficient information transmission and efficient energy harvesting via spatial beamforming. Subsequently, two robust beamforming algorithms are designed from the aspects of the weighted sum rate maximization and the total power consumption minimization, respectively. It is found that overall performance can be improved by adding BS antennas due to more array gains. Moreover, it is proved that the proposed algorithms can effectively alleviate the influence of adverse practical conditions and achieve the best performance compared to the baseline ones, which demonstrates the effectiveness and robustness of proposed algorithms for cellular massive IoT.

更新日期：2020-01-04
• IEEE Trans. Signal Process. (IF 5.230) Pub Date : 2019-11-25
Rubén Martín-Clemente; Vicente Zarzoso

Principal component analysis (PCA) and Fisher's linear discriminant analysis (LDA) are widespread techniques in data analysis and pattern recognition. Recently, the L1-norm has been proposed as an alternative criterion to classical L2-norm in PCA, drawing considerable research interest on account of its increased robustness to outliers. The present work proves that, combined with a whitening preprocessing step, L1-PCA can perform LDA in an unsupervised manner, i.e., sparing the need for labelled data. Rigorous proof is given in the case of data drawn from a mixture of Gaussians. A number of numerical experiments on synthetic as well as real data confirm the theoretical findings.

更新日期：2020-01-04
• IEEE Trans. Signal Process. (IF 5.230) Pub Date : 2019-12-04
Wei Yi; Suqi Li; Bailu Wang; Reza Hoseinnezhad; Lingjiang Kong

This paper proposes a computationally efficient algorithm for distributed fusion in a sensor network in which multi-Bernoulli (MB) filters are locally running in every sensor node for multi-object tracking. The generalized Covariance Intersection (GCI) fusion rule is employed to fuse multiple MB random finite set densities. The fused density comprises a set of fusion hypotheses that grow exponentially with the number of Bernoulli components. Thus, GCI fusion with MB filters can become computationally intractable in practical applications that involve tracking of even a moderate number of objects. In order to accelerate the multi-sensor fusion procedure, we derive a theoretically sound approximation to the fused density. The number of fusion hypotheses in the resulting density is significantly smaller than the original fused density. It also has a parallelizable structure that allows multiple clusters of Bernoulli components to be fused independently. By carefully clustering Bernoulli components into isolated clusters using the GCI divergence as the distance metric, we propose an alternative to build exactly the approximated density without exhaustively computing all the fusion hypotheses. The combination of the proposed approximation technique and the fast clustering algorithm can enable a novel and fast GCI-MB fusion implementation. Our analysis shows that the proposed fusion method can dramatically reduce the computational and memory requirements with small bounded $L_1$ -error. The Gaussian mixture implementation of the proposed method is also presented. In various numerical experiments, including a challenging scenario with up to forty objects, the efficacy of the proposed fusion method is demonstrated.

更新日期：2020-01-04
• IEEE Trans. Signal Process. (IF 5.230) Pub Date : 2019-12-11
Shanxiang Lyu; Jinming Wen; Jian Weng; Cong Ling

Lattice reduction is a popular preprocessing strategy in multiple-input multiple-output (MIMO) detection. In a quest for developing a low-complexity reduction algorithm for large-scale problems, this paper investigates a new framework called sequential reduction (SR), which aims to reduce the lengths of all basis vectors. The performance upper bounds of the strongest reduction in SR are given when the lattice dimension is no larger than 4. The proposed new framework enables the implementation of a hash-based low-complexity lattice reduction algorithm, which becomes especially tempting when applied to large-scale MIMO detection. Simulation results show that, compared to other reduction algorithms, the hash-based SR algorithm exhibits the lowest complexity while maintaining comparable error performance.

更新日期：2020-01-04
• IEEE Trans. Signal Process. (IF 5.230) Pub Date : 2012-10-23
Jung Kuk Kim,Jeffrey A Fessler,Zhengya Zhang

Iterative image reconstruction can dramatically improve the image quality in X-ray computed tomography (CT), but the computation involves iterative steps of 3D forward- and back-projection, which impedes routine clinical use. To accelerate forward-projection, we analyze the CT geometry to identify the intrinsic parallelism and data access sequence for a highly parallel hardware architecture. To improve the efficiency of this architecture, we propose a water-filling buffer to remove pipeline stalls, and an out-of-order sectored processing to reduce the off-chip memory access by up to three orders of magnitude. We make a floating-point to fixed-point conversion based on numerical simulations and demonstrate comparable image quality at a much lower implementation cost. As a proof of concept, a 5-stage fully pipelined, 55-way parallel separable-footprint forward-projector is prototyped on a Xilinx Virtex-5 FPGA for a throughput of 925.8 million voxel projections/s at 200 MHz clock frequency, 4.6 times higher than an optimized 16-threaded program running on an 8-core 2.8-GHz CPU. A similar architecture can be applied to back-projection for a complete iterative image reconstruction system. The proposed algorithm and architecture can also be applied to hardware platforms such as graphics processing unit and digital signal processor to achieve significant accelerations.

更新日期：2019-11-01
• IEEE Trans. Signal Process. (IF 5.230) Pub Date : 2019-10-09
Yanning Shen,Georgios B Giannakis,Brian Baingana

Structural equation models (SEMs) and vector autoregressive models (VARMs) are two broad families of approaches that have been shown useful in effective brain connectivity studies. While VARMs postulate that a given region of interest in the brain is directionally connected to another one by virtue of time-lagged influences, SEMs assert that directed dependencies arise due to instantaneous effects, and may even be adopted when nodal measurements are not necessarily multivariate time series. To unify these complementary perspectives, linear structural vector autoregressive models (SVARMs) that leverage both instantaneous and time-lagged nodal data have recently been put forth. Albeit simple and tractable, linear SVARMs are quite limited since they are incapable of modeling nonlinear dependencies between neuronal time series. To this end, the overarching goal of the present paper is to considerably broaden the span of linear SVARMs by capturing nonlinearities through kernels, which have recently emerged as a powerful nonlinear modeling framework in canonical machine learning tasks, e.g., regression, classification, and dimensionality reduction. The merits of kernel-based methods are extended here to the task of learning the effective brain connectivity, and an efficient regularized estimator is put forth to leverage the edge sparsity inherent to real-world complex networks. Judicious kernel choice from a preselected dictionary of kernels is also addressed using a data-driven approach. Numerical tests on ECoG data captured through a study on epileptic seizures demonstrate that it is possible to unveil previously unknown directed links between brain regions of interest.

更新日期：2019-11-01
• IEEE Trans. Signal Process. (IF 5.230) Pub Date : 2008-09-05
Z Jane Wang,Zsolt Szabo,Peng Lei,József Varga,K J Ray Liu

The positron emission tomography (PET) imaging technique enables the measurement of receptor distribution or neurotransmitter release in the living brain and the changes of the distribution with time and thus allows quantification of binding sites as well as the affinity of a radioligand. However, quantification of receptor binding studies obtained with PET is complicated by tissue heterogeneity in the sampling image elements (i.e., voxels, pixels). This effect is caused by a limited spatial resolution of the PET scanner. Spatial heterogeneity is often essential in understanding the underlying receptor binding process. Tracer kinetic modeling also often requires an intrusive collection of arterial blood samples. In this paper, we propose a likelihood-based framework in the voxel domain for quantitative imaging with or without the blood sampling of the input function. Radioligand kinetic parameters are estimated together with the input function. The parameters are initialized by a subspace-based algorithm and further refined by an iterative likelihood-based estimation procedure. The performance of the proposed scheme is examined by simulations. The results show that the proposed scheme provides reliable estimation of factor time-activity curves (TACs) and the underlying parametric images. A good match is noted between the result of the proposed approach and that of the Logan plot. Real brain PET data are also examined, and good performance is observed in determining the TACs and the underlying factor images.

更新日期：2019-11-01
• IEEE Trans. Signal Process. (IF 5.230) Pub Date : 2018-05-29
Tamir Bendory,Nicolas Boumal,Chao Ma,Zhizhen Zhao,Amit Singer

We consider the problem of estimating a signal from noisy circularly-translated versions of itself, called multireference alignment (MRA). One natural approach to MRA could be to estimate the shifts of the observations first, and infer the signal by aligning and averaging the data. In contrast, we consider a method based on estimating the signal directly, using features of the signal that are invariant under translations. Specifically, we estimate the power spectrum and the bispectrum of the signal from the observations. Under mild assumptions, these invariant features contain enough information to infer the signal. In particular, the bispectrum can be used to estimate the Fourier phases. To this end, we propose and analyze a few algorithms. Our main methods consist of non-convex optimization over the smooth manifold of phases. Empirically, in the absence of noise, these non-convex algorithms appear to converge to the target signal with random initialization. The algorithms are also robust to noise. We then suggest three additional methods. These methods are based on frequency marching, semidefinite relaxation and integer programming. The first two methods provably recover the phases exactly in the absence of noise. In the high noise level regime, the invariant features approach for MRA results in stable estimation if the number of measurements scales like the cube of the noise variance, which is the information-theoretic rate. Additionally, it requires only one pass over the data which is important at low signal-to-noise ratio when the number of observations must be large.

更新日期：2019-11-01
• IEEE Trans. Signal Process. (IF 5.230) Pub Date : 2018-08-25
Greg Ongie,Sampurna Biswas,Mathews Jacob

We consider the recovery of a continuous domain piecewise constant image from its non-uniform Fourier samples using a convex matrix completion algorithm. We assume the discontinuities/edges of the image are localized to the zero level-set of a bandlimited function. This assumption induces linear dependencies between the Fourier coefficients of the image, which results in a two-fold block Toeplitz matrix constructed from the Fourier coefficients being low-rank. The proposed algorithm reformulates the recovery of the unknown Fourier coefficients as a structured low-rank matrix completion problem, where the nuclear norm of the matrix is minimized subject to structure and data constraints. We show that exact recovery is possible with high probability when the edge set of the image satisfies an incoherency property. We also show that the incoherency property is dependent on the geometry of the edge set curve, implying higher sampling burden for smaller curves. This paper generalizes recent work on the super-resolution recovery of isolated Diracs or signals with finite rate of innovation to the recovery of piecewise constant images.

更新日期：2019-11-01
• IEEE Trans. Signal Process. (IF 5.230) Pub Date : 2011-05-06
Jianqiu Zhang,Xiaobo Zhou,Honghui Wang,Anthony Suffredini,Lin Zhang,Yufei Huang,Stephen Wong

In this paper, we address the issue of peptide ion peak detection for high resolution time-of-flight (TOF) mass spectrometry (MS) data. A novel Bayesian peptide ion peak detection method is proposed for TOF data with resolution of 10 000-15 000 full width at half-maximum (FWHW). MS spectra exhibit distinct characteristics at this resolution, which are captured in a novel parametric model. Based on the proposed parametric model, a Bayesian peak detection algorithm based on Markov chain Monte Carlo (MCMC) sampling is developed. The proposed algorithm is tested on both simulated and real datasets. The results show a significant improvement in detection performance over a commonly employed method. The results also agree with expert's visual inspection. Moreover, better detection consistency is achieved across MS datasets from patients with identical pathological condition.

更新日期：2019-11-01
• IEEE Trans. Signal Process. (IF 5.230) Pub Date : 2010-07-17
Wei Xiong,Tülay Adalı,Yi-Ou Li,Hualiang Li,Vince D Calhoun

We derive the entropy rate formula for a complex Gaussian random process by using a widely linear model. The resulting expression is general and applicable to both circular and noncircular Gaussian processes, since any second-order stationary process can be modeled as the output of a widely linear system driven by a circular white noise. Furthermore, we demonstrate application of the derived formula to an order selection problem. We extend a scheme for independent and identically distributed (i.i.d.) sampling to the complex domain to improve the estimation performance of information-theoretic criteria when samples are correlated. We show the effectiveness of the approach for order selection for simulated and actual functional magnetic resonance imaging (fMRI) data that are inherently complex valued.

更新日期：2019-11-01
• IEEE Trans. Signal Process. (IF 5.230) Pub Date : 2010-07-08
Aliaksei Sandryhaila,Amina Chebira,Christina Milo,Jelena Kovčcević,Markus Püschel

We present a constructive algorithm for the design of real lapped equal-norm tight frame transforms. These transforms can be efficiently implemented through filter banks and have recently been proposed as a redundant counterpart to lapped orthogonal transforms, as well as an infinite-dimensional counterpart to harmonic tight frames. The proposed construction consists of two parts: First, we design a large class of new real lapped orthogonal transforms derived from submatrices of the discrete Fourier transform. Then, we seed these to obtain real lapped tight frame transforms corresponding to tight, equal-norm frames. We identify those frames that are maximally robust to erasures, and show that our construction leads to a large class of new lapped orthogonal transforms as well as new lapped tight frame transforms.

更新日期：2019-11-01
• IEEE Trans. Signal Process. (IF 5.230) Pub Date : 2010-03-12
Yi-Ou Li,Tülay Adalı,Wei Wang,Vince D Calhoun

In this work, we introduce a simple and effective scheme to achieve joint blind source separation (BSS) of multiple datasets using multi-set canonical correlation analysis (M-CCA) [1]. We first propose a generative model of joint BSS based on the correlation of latent sources within and between datasets. We specify source separability conditions, and show that, when the conditions are satisfied, the group of corresponding sources from each dataset can be jointly extracted by M-CCA through maximization of correlation among the extracted sources. We compare source separation performance of the M-CCA scheme with other joint BSS methods and demonstrate the superior performance of the M-CCA scheme in achieving joint BSS for a large number of datasets, group of corresponding sources with heterogeneous correlation values, and complex-valued sources with circular and non-circular distributions. We apply M-CCA to analysis of functional magnetic resonance imaging (fMRI) data from multiple subjects and show its utility in estimating meaningful brain activations from a visuomotor task.

更新日期：2019-11-01
• IEEE Trans. Signal Process. (IF 5.230) Pub Date : 2011-01-01
Yau Wong,Zhiping Lin,Raimund J Ober

In this paper, we consider the problem of the accuracy of estimating the location and other attributes of a moving single molecule whose trajectory is imaged by fluorescence microscopy. As accuracy in parameter estimation is closely related to the Fisher information matrix, we first give a general expression of the Fisher information matrix for the estimated parameters for a single object moving in three-dimensional (3D) space. Explicit Cramér-Rao lower bound (CRLB) expressions are then obtained from the Fisher information matrix for a single object moving in the two-dimensional (2D) focus plane with the object trajectory being either linear or circular. We also investigate how extraneous noise sources, pixelation, parameters of the detection system and parameters of the trajectory affect the limit of the accuracy. The results obtained in this paper provide insights that enable the experimentalists to optimize their experimental setups for tracking single molecules in order to achieve the best possible accuracy. They are also applicable to the general problem of tracking an object using quantum limited detectors.

更新日期：2019-11-01
• IEEE Trans. Signal Process. (IF 5.230) Pub Date : 2014-03-19
E A K Cohen,R J Ober

We present an asymptotic treatment of errors involved in point-based image registration where control point (CP) localization is subject to heteroscedastic noise; a suitable model for image registration in fluorescence microscopy. Assuming an affine transform, CPs are used to solve a multivariate regression problem. With measurement errors existing for both sets of CPs this is an errors-in-variable problem and linear least squares is inappropriate; the correct method being generalized least squares. To allow for point dependent errors the equivalence of a generalized maximum likelihood and heteroscedastic generalized least squares model is achieved allowing previously published asymptotic results to be extended to image registration. For a particularly useful model of heteroscedastic noise where covariance matrices are scalar multiples of a known matrix (including the case where covariance matrices are multiples of the identity) we provide closed form solutions to estimators and derive their distribution. We consider the target registration error (TRE) and define a new measure called the localization registration error (LRE) believed to be useful, especially in microscopy registration experiments. Assuming Gaussianity of the CP localization errors, it is shown that the asymptotic distribution for the TRE and LRE are themselves Gaussian and the parameterized distributions are derived. Results are successfully applied to registration in single molecule microscopy to derive the key dependence of the TRE and LRE variance on the number of CPs and their associated photon counts. Simulations show asymptotic results are robust for low CP numbers and non-Gaussianity. The method presented here is shown to outperform GLS on real imaging data.

更新日期：2019-11-01
• IEEE Trans. Signal Process. (IF 5.230) Pub Date : 2011-10-01

We consider the problem of decomposing a signal into a linear combination of features, each a continuously translated version of one of a small set of elementary features. Although these constituents are drawn from a continuous family, most current signal decomposition methods rely on a finite dictionary of discrete examples selected from this family (e.g., shifted copies of a set of basic waveforms), and apply sparse optimization methods to select and solve for the relevant coefficients. Here, we generate a dictionary that includes auxiliary interpolation functions that approximate translates of features via adjustment of their coefficients. We formulate a constrained convex optimization problem, in which the full set of dictionary coefficients represents a linear approximation of the signal, the auxiliary coefficients are constrained so as to only represent translated features, and sparsity is imposed on the primary coefficients using an L1 penalty. The basis pursuit denoising (BP) method may be seen as a special case, in which the auxiliary interpolation functions are omitted, and we thus refer to our methodology as continuous basis pursuit (CBP). We develop two implementations of CBP for a one-dimensional translation-invariant source, one using a first-order Taylor approximation, and another using a form of trigonometric spline. We examine the tradeoff between sparsity and signal reconstruction accuracy in these methods, demonstrating empirically that trigonometric CBP substantially outperforms Taylor CBP, which in turn offers substantial gains over ordinary BP. In addition, the CBP bases can generally achieve equally good or better approximations with much coarser sampling than BP, leading to a reduction in dictionary dimensionality.

更新日期：2019-11-01
• IEEE Trans. Signal Process. (IF 5.230) Pub Date : 2013-12-11
Yongqiang Wang,Felipe Núñez,Francis J Doyle

Pulse-coupled synchronization is attracting increased attention in the sensor network community. Yet its properties have not been fully investigated. Using statistical analysis, we prove analytically that by controlling the number of connections at each node, synchronization can be guaranteed for generally pulse-coupled oscillators even in the presence of a refractory period. The approach does not require the initial phases to reside in half an oscillation cycle, which improves existing results. We also find that a refractory period can be strategically included to reduce idle listening at nearly no sacrifice to the synchronization probability. Given that reduced idle listening leads to higher energy efficiency in the synchronization process, the strategically added refractory period makes the synchronization scheme appealing to cheap sensor nodes, where energy is a precious system resource. We also analyzed the pulse-coupled synchronization in the presence of unreliable communication links and obtained similar results. QualNet experimental results are given to confirm the effectiveness of the theoretical predictions.

更新日期：2019-11-01
• IEEE Trans. Signal Process. (IF 5.230) Pub Date : 2012-07-10
Yongqiang Wang,Francis J Doyle

Synchronization is crucial to wireless sensor networks. Recently a pulse-coupled synchronization strategy that emulates biological pulse-coupled agents has been used to achieve this goal. We propose to optimize the phase response function such that synchronization rate is maximized. Since the synchronization rate is increased independently of transmission power, energy consumption is reduced, hence extending the life of battery-powered sensor networks. Comparison with existing phase response functions confirms the effectiveness of the method.

更新日期：2019-11-01
• IEEE Trans. Signal Process. (IF 5.230) Pub Date : 2012-06-20
Yongqiang Wang,Felipe Núñez,Francis J Doyle

Synchronization is crucial to wireless sensor networks due to their decentralized structure. We propose an energy-efficient pulse-coupled synchronization strategy to achieve this goal. The basic idea is to reduce idle listening by intentionally introducing a large refractory period in the sensors' cooperation. The large refractory period greatly reduces idle listening in each oscillation period, and is analytically proven to have no influence on the time to synchronization. Hence, it significantly reduces the total energy consumption in a synchronization process. A topology control approach tailored for pulse-coupled synchronization is given to guarantee a k-edge strongly connected interaction topology, which is tolerant to communication-link failures. The topology control approach is totally decentralized and needs no information exchange among sensors, and it is applicable to dynamic network topologies as well. This facilitates a completely decentralized implementation of the synchronization strategy. The strategy is applicable to mobile sensor networks, too. QualNet case studies confirm the effectiveness of the synchronization strategy.

更新日期：2019-11-01
• IEEE Trans. Signal Process. (IF 5.230) Pub Date : 2013-09-13
Nidhal Bouaynaya,Roman Shterenberg,Dan Schonfeld

In this paper, we develop a comprehensive framework for optimal perturbation control of dynamic networks. The aim of the perturbation is to drive the network away from an undesirable steady-state distribution and to force it to converge towards a desired steady-state distribution. The proposed framework does not make any assumptions about the topology of the initial network, and is thus applicable to general-topology networks. We define the optimal perturbation control as the minimum-energy perturbation measured in terms of the Frobenius-norm between the initial and perturbed probability transition matrices of the dynamic network. We subsequently demonstrate that there exists at most one optimal perturbation that forces the network into the desirable steady-state distribution. In the event where the optimal perturbation does not exist, we construct a family of suboptimal perturbations, and show that the suboptimal perturbation can be used to approximate the optimal limiting distribution arbitrarily closely. Moreover, we investigate the robustness of the optimal perturbation control to errors in the probability transition matrix, and demonstrate that the proposed optimal perturbation control is robust to data and inference errors in the probability transition matrix of the initial network. Finally, we apply the proposed optimal perturbation control method to the Human melanoma gene regulatory network in order to force the network from an initial steady-state distribution associated with melanoma and into a desirable steady-state distribution corresponding to a benign cell.

更新日期：2019-11-01
• IEEE Trans. Signal Process. (IF 5.230) Pub Date : 2010-12-01
Minhua Chen,Jorge Silva,John Paisley,Chunping Wang,David Dunson,Lawrence Carin

Nonparametric Bayesian methods are employed to constitute a mixture of low-rank Gaussians, for data x ∈ ℝ N that are of high dimension N but are constrained to reside in a low-dimensional subregion of ℝ N . The number of mixture components and their rank are inferred automatically from the data. The resulting algorithm can be used for learning manifolds and for reconstructing signals from manifolds, based on compressive sensing (CS) projection measurements. The statistical CS inversion is performed analytically. We derive the required number of CS random measurements needed for successful reconstruction, based on easily-computed quantities, drawing on block-sparsity properties. The proposed methodology is validated on several synthetic and real datasets.

更新日期：2019-11-01
• IEEE Trans. Signal Process. (IF 5.230) Pub Date : 2011-10-18
Julien Fleureau,Jean-Claude Nunes,Amar Kachenoura,Laurent Albera,Lotfi Senhadji

A novel Empirical Mode Decomposition (EMD) algorithm, called 2T-EMD, for both mono- and multivariate signals is proposed in this paper. It differs from the other approaches by its computational lightness and its algorithmic simplicity. The method is essentially based on a redefinition of the signal mean envelope, computed thanks to new characteristic points, which offers the possibility to decompose multivariate signals without any projection. The scope of application of the novel algorithm is specified, and a comparison of the 2T-EMD technique with classical methods is performed on various simulated mono- and multivariate signals. The monovariate behaviour of the proposed method on noisy signals is then validated by decomposing a fractional Gaussian noise and an application to real life EEG data is finally presented.

更新日期：2019-11-01
• IEEE Trans. Signal Process. (IF 5.230) Pub Date : 2011-09-16
Andrew Bolstad,Barry D Van Veen,Robert Nowak

This paper addresses the problem of inferring sparse causal networks modeled by multivariate autoregressive (MAR) processes. Conditions are derived under which the Group Lasso (gLasso) procedure consistently estimates sparse network structure. The key condition involves a "false connection score" ψ. In particular, we show that consistent recovery is possible even when the number of observations of the network is far less than the number of parameters describing the network, provided that ψ < 1. The false connection score is also demonstrated to be a useful metric of recovery in nonasymptotic regimes. The conditions suggest a modified gLasso procedure which tends to improve the false connection score and reduce the chances of reversing the direction of causal influence. Computational experiments and a real network based electrocorticogram (ECoG) simulation study demonstrate the effectiveness of the approach.

更新日期：2019-11-01
• IEEE Trans. Signal Process. (IF 5.230) Pub Date : 2011-09-13