By Topic

Signal Processing, IEEE Transactions on

Issue 7 • Date April1, 2013

Filter Results

Displaying Results 1 - 25 of 36
  • Front Cover

    Page(s): C1
    Save to Project icon | Request Permissions | PDF file iconPDF (215 KB)  
    Freely Available from IEEE
  • IEEE Transactions on Signal Processing publication information

    Page(s): C2
    Save to Project icon | Request Permissions | PDF file iconPDF (136 KB)  
    Freely Available from IEEE
  • Table of Contents

    Page(s): 1577 - 1578
    Save to Project icon | Request Permissions | PDF file iconPDF (228 KB)  
    Freely Available from IEEE
  • Table of Contents

    Page(s): 1579 - 1580
    Save to Project icon | Request Permissions | PDF file iconPDF (230 KB)  
    Freely Available from IEEE
  • Energy-Efficient, Heterogeneous Sensor Selection for Physical Activity Detection in Wireless Body Area Networks

    Page(s): 1581 - 1594
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (3175 KB) |  | HTML iconHTML  

    In this paper, the problem of efficient operation of an energy-constrained, heterogeneous Wireless Body Area Network (WBAN) to optimize an activity detection application is addressed. WBANs constitute a new class of wireless sensor networks that enable diverse applications in healthcare, entertainment, sports, military and emergency situations. A typical WBAN consists of a few, heterogeneous sensors wirelessly coupled to an energy-constrained fusion center which, according to observations of a real-world prototype WBAN, imposes critical restrictions on system lifetime. To address this issue, a novel stochastic control framework is introduced, which considers both sensor heterogeneity and application requirements, for achieving the two-fold goal: energy savings with satisfactory detection performance. An optimal dynamic programming algorithm for the sensor selection problem is also derived. Important properties of the cost functionals are derived and used to design three approximation algorithms, which offer near optimal performance with significant complexity reduction. Simulations on real-world data show energy gains as high as 68% in comparison to an equal allocation scheme with probability of detection error on the order of 10-4. View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Adaptive Universal Linear Filtering

    Page(s): 1595 - 1604
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (2292 KB) |  | HTML iconHTML  

    We consider the problem of online estimation of an arbitrary real-valued signal corrupted by zero-mean noise using linear estimators. The estimator is required to iteratively predict the underlying signal based on the current and several last noisy observations, and its performance is measured by the mean-square-error. We design and analyze an algorithm for this task whose total square-error on any interval of the signal is equal to that of the best fixed filter in hindsight with respect to the interval plus an additional term whose dependence on the total signal length is only logarithmic. This bound is asymptotically tight, and resolves the question of Moon and Wiessman [“Universal FIR MMSE filtering,” IEEE Trans. Signal Process., vol. 57, no. 3, pp. 1068-1083, 2009]. Furthermore, the algorithm runs in linear time in terms of the number of filter coefficients. Previous constructions required at least quadratic time. View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Multi-Block Joint Optimization for the Peak-to-Average Power Ratio Reduction of FBMC-OQAM Signals

    Page(s): 1605 - 1613
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (2223 KB) |  | HTML iconHTML  

    Recently, the filter bank multicarrier with offset quadrature amplitude modulation (FBMC-OQAM) has attracted increasing attention. However, most peak-to-average power ratio (PAPR) reduction schemes developed for orthogonal frequency division multiplexing (OFDM) signals are not effective for FBMC-OQAM signals, due to the overlapping structure of FBMC-OQAM signals. In this paper, we propose an improved partial transmit sequence (PTS) scheme by employing multi-block joint optimization (MBJO) for the PAPR reduction of FBMC-OQAM signals, called as MBJO-PTS scheme. In PTS scheme, one data block is divided into several subblocks and each subblock is multiplied by a phase rotation factor for the subblock. The PTS scheme searches over all combinations of allowed phase factors to lower the PAPR. Unlike existing PAPR reduction schemes of independently optimizing the data blocks, the MBJO-based scheme exploits the overlapping structure of the FBMC-OQAM signal and jointly optimizes multiple data blocks. Moreover, we develop two algorithms for the optimization problem in the MBJO-PTS scheme, including a dynamic programming (DP) algorithm to guarantee the optimal solution and avoid exhaustive search. Theoretical analysis and simulations show that the proposed MBJO-PTS scheme could provide a significant PAPR reduction in the FBMC-OQAM system, by exploiting the overlapping structure of the FBMC-OQAM signal. Employing the proposed DP algorithm, the FBMC-OQAM system with the proposed MBJO-PTS scheme even outperforms the OFDM system with the conventional PTS scheme by 0.9 dB at CCDF of 10-3 in PAPR reduction, under the same number of subcarriers, modulation type and PTS parameters given in Section V. View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Non-Parametric High-Resolution SAR Imaging

    Page(s): 1614 - 1624
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (2999 KB) |  | HTML iconHTML  

    The development of high-resolution two-dimensional spectral estimation techniques is of notable interest in synthetic aperture radar (SAR) imaging. Typically, data-independent techniques are exploited to form the SAR images, although such approaches will suffer from limited resolution and high sidelobe levels. Recent work on data-adaptive approaches have shown that both the iterative adaptive approach (IAA) and the sparse learning via iterative minimization (SLIM) algorithm offer excellent performance with high-resolution and low side lobe levels for both complete and incomplete data sets. Regrettably, both algorithms are computationally intensive if applied directly to the phase history data to form the SAR images. To help alleviate this, efficient implementations have also been proposed. In this paper, we further this work, proposing yet further improved implementation strategies, including approaches using the segmented IAA approach and the approximative quasi-Newton technique. Furthermore, we introduce a combined IAA-MAP algorithm as well as a hybrid IAA- and SLIM-based estimation scheme for SAR imaging. The effectiveness of the SAR imaging algorithms and the computational complexities of their fast implementations are demonstrated using the simulated Slicy data set and the experimentally measured GOTCHA data set. View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • How Can Online Schedules Improve Communication and Estimation Tradeoff?

    Page(s): 1625 - 1631
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1781 KB) |  | HTML iconHTML  

    We consider remote state estimation and investigate the tradeoff between the sensor-to-estimator communication rate and the remote estimation quality. It is well known that if the communication rate is one, e.g., the sensor communicates with the remote estimator at each time, then the remote estimation quality is the best. It degrades when the communication rate drops. We present one optimal offline schedule and two online schedules and show that the two online schedules provide better tradeoff between the communication rate and the estimation quality than the optimal offline schedule. Simulation examples demonstrate that significant communication savings can be achieved under the two online schedules which only introduce small increment of the estimation errors. View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Vectorial Phase Retrieval of 1-D Signals

    Page(s): 1632 - 1643
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (2910 KB) |  | HTML iconHTML  

    Reconstruction of signals from measurements of their spectral intensities, also known as the phase retrieval problem, is of fundamental importance in many scientific fields. In this paper we present a novel framework, denoted as vectorial phase retrieval, for reconstruction of pairs of signals from spectral intensity measurements of the two signals and of their interference. We show that this new framework can alleviate some of the theoretical and computational challenges associated with classical phase retrieval from a single signal. First, we prove that for compactly supported signals, in the absence of measurement noise, this new setup admits a unique solution. Next, we present a statistical analysis of vectorial phase retrieval and derive a computationally efficient algorithm to solve it. Finally, we illustrate via simulations, that our algorithm can accurately reconstruct signals even at considerable noise levels. View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Discrete Signal Processing on Graphs

    Page(s): 1644 - 1656
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (2577 KB) |  | HTML iconHTML  

    In social settings, individuals interact through webs of relationships. Each individual is a node in a complex network (or graph) of interdependencies and generates data, lots of data. We label the data by its source, or formally stated, we index the data by the nodes of the graph. The resulting signals (data indexed by the nodes) are far removed from time or image signals indexed by well ordered time samples or pixels. DSP, discrete signal processing, provides a comprehensive, elegant, and efficient methodology to describe, represent, transform, analyze, process, or synthesize these well ordered time or image signals. This paper extends to signals on graphs DSP and its basic tenets, including filters, convolution, z-transform, impulse response, spectral representation, Fourier transform, frequency response, and illustrates DSP on graphs by classifying blogs, linear predicting and compressing data from irregularly located weather stations, or predicting behavior of customers of a mobile service provider. View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Source Transmit Antenna Selection for MIMO Decode-and-Forward Relay Networks

    Page(s): 1657 - 1662
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1457 KB) |  | HTML iconHTML  

    Transmit antenna selection (TAS) is usually applied to multiple-input multiple-output (MIMO) systems because it does not require additional radio frequency (RF) chains which are quite expensive. In MIMO decode-and-forward (DF) relay networks, both source-destination and source-relay-destination paths should be simultaneously considered to find an effective source TAS (STAS). In this paper, a new STAS is proposed based on both channel state information and transmission scheme for the MIMO DF relay networks. It is also shown that the proposed STAS which selects MSS antennas among MS transmit antennas at the source can achieve full diversity regardless of the value of MSS. Simulation results show that the proposed STAS has better average bit error probability (BEP) performance than other STASs. Also, the proposed STAS with MSS=1 has lower cost, complexity, overhead, and BEP than the STAS with MSS > 1 using full-rate full-diversity space-time block codes with the same total transmit power. View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Particle Smoothing Algorithms for Variable Rate Models

    Page(s): 1663 - 1675
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (2825 KB) |  | HTML iconHTML  

    Standard state-space methods assume that the latent state evolves uniformly over time, and can be modeled with a discrete-time process synchronous with the observations. This may be a poor representation of some systems in which the state evolution displays discontinuities in its behavior. For such cases, a variable rate model may be more appropriate; the system dynamics are conditioned on a set of random changepoints which constitute a marked point process. In this paper, new particle smoothing algorithms are presented for use with conditionally linear-Gaussian and conditionally deterministic dynamics. These are demonstrated on problems in financial modelling and target tracking. Results indicate that the smoothing approximations provide more accurate and more diverse representations of the state posterior distributions. View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Distance Estimation Using Wrapped Phase Measurements in Noise

    Page(s): 1676 - 1688
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (2968 KB) |  | HTML iconHTML  

    Measuring a distance using phase measurements is a common practice in many areas of engineering. Almost inevitably these measurements are accompanied by noise, and are always subject to ambiguity resulting from the phase of modulo 2π. In the presence of phase ambiguity, where for instance the unknown distance is far longer than the wavelength of the signal carrying the phase measurement, the distance cannot be uniquely determined. One way to resolve this phase ambiguity is to measure the signal phase at multiple frequencies, converting the phase ambiguity problem into one of solving a family of Diophantine equations. Typically, under some reasonable assumptions, the Diophantine problems can be solved using the Chinese Reminder Theorem as documented in the literature. However, the existing algorithms can experience significant computational overhead for a given application because an exhaustive search is required. In this paper, a novel method addressing the phase ambiguity issue using lattice theoretic ideas is proposed and a closed-form algorithm is presented for the estimation of the number of wavelengths in the unknown distance using the phase measurements taken at multiple wavelengths. The algorithm is extremely efficient as the Diophantine equations are solved without searching. The unknown distance can then be estimated via a maximum likelihood method using the unwrapped phase measurement. A statistical bound of the measurement noise which ensures that the number of whole wavelengths in the unknown distance can be found with a probability close to unity is derived. The robustness, efficiency and estimation accuracy of the proposed method are demonstrated by the simulated results presented. View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • A Family of Shrinkage Adaptive-Filtering Algorithms

    Page(s): 1689 - 1697
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (2265 KB) |  | HTML iconHTML  

    A family of adaptive-filtering algorithms that uses a variable step size is proposed. A variable step size is obtained by minimizing the energy of the noise-free a posteriori error signal which is obtained by using a known L1-L2 minimization formulation. Based on this methodology, a shrinkage affine projection (SHAP) algorithm, a shrinkage least-mean-squares (SHLMS) algorithm, and a shrinkage normalized least-mean-squares (SHNLMS) algorithm are proposed. The SHAP algorithm yields a significantly reduced steady-state misalignment as compared to the conventional affine projection (AP), variable-step-size AP, and set-membership AP algorithms for the same convergence speed although the improvement is achieved at the cost of an increase in the average computational effort per iteration in the amount of 11% to 14%. The SHLMS algorithm yields a significantly reduced steady-state misalignment and faster convergence as compared to the conventional LMS and variable-step-size LMS algorithms. Similarly, the SHNLMS algorithm yields a significantly reduced steady-state misalignment and faster convergence as compared to the conventional normalized least-mean-squares (NLMS) and set-membership NLMS algorithms. View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Intrinsic Spectral Analysis

    Page(s): 1698 - 1710
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1972 KB) |  | HTML iconHTML  

    It has long been posited that the space of speech sounds is inherently low dimensional, the result of a relatively small number of degrees of freedom involved in the human vocal apparatus. We attempt to formalize this notion by analyzing a simple physical model of the vocal tract and demonstrating that it produces transfer functions whose spectra are restricted to low dimensional manifolds embedded in an infinite dimensional space of square integrable functions. While source convolution and channel distortion precludes analytic recovery of the articulatory configuration from the observed signal, we present a data-driven unsupervised learning algorithm called Intrinsic Spectral Analysis designed to recover from a stream of unannotated and unsegmented audio a set of nonlinear basis functions for the speech manifold. Projecting a traditional spectrogram onto this nonlinear basis defines a novel acoustic representation that is demonstrated to have phonological significance, improved phonetic separability, inherent speaker independence, and complementarity with standard acoustic front-ends. View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Degrees of Freedom for MIMO Two-Way X Relay Channel

    Page(s): 1711 - 1720
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (2580 KB) |  | HTML iconHTML  

    We study the degrees of freedom (DOF) of a multiple-input multiple-output (MIMO) two-way X relay channel, where there are two groups of source nodes and one relay node, each equipped with multiple antennas, and each of the two source nodes in one group exchanges independent messages with the two source nodes in the other group via the relay node. It is assumed that every source node is equipped with M antennas while the relay is equipped with N antennas. We first show that the upper bound on the total DOF for this network is 2min{2M, N} and then focus on the case of N ≤ 2M so that the DOF is upper bounded by twice the number of antennas at the relay. By applying signal alignment for network coding and joint transceiver design for interference cancellation, we show that this upper bound can be achieved when N ≤ [8M/5]. We also show that with signal alignment only but no joint transceiver design, the upper bound is achievable when N ≤ [4M/3]. Simulation results are provided to corroborate the theoretical results and to demonstrate the performance of the proposed scheme in the finite signal-to-noise ratio regime. View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Attribute Fusion in a Latent Process Model for Time Series of Graphs

    Page(s): 1721 - 1732
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (3050 KB) |  | HTML iconHTML  

    Hypothesis testing on time series of attributed graphs has applications in diverse areas, e.g., social network analysis (wherein vertices represent individual actors or organizations), connectome inference (wherein vertices are neurons or brain regions) and text processing (wherein vertices represent authors or documents). We consider the problem of anomaly/change point detection given the latent process model for time series of graphs with categorical attributes on the edges presented in [N. H. Lee and C. E. Priebe, “A latent process model for time series of attributed random graphs,” Statist. Inference Stoch. Process., vol. 14, pp. 231-253, 2011]. Various attributed graph invariants are considered, and their power for detection as a function of a linear fusion parameter is presented. Our main result is that inferential performance in mathematically tractable first-order and second-order approximation models does provide guidance for methodological choices applicable to the exact (realistic but intractable) model. Furthermore, to the extent that the exact model is realistic, we may tentatively conclude that approximation model investigations have some bearing on real data applications. View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Optimal Perturbation Control of General Topology Molecular Networks

    Page(s): 1733 - 1742
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (2643 KB) |  | HTML iconHTML  

    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. View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • On Convergence of Kronecker Graphical Lasso Algorithms

    Page(s): 1743 - 1755
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (3716 KB) |  | HTML iconHTML  

    This paper studies iteration convergence of Kronecker graphical lasso (KGLasso) algorithms for estimating the covariance of an i.i.d. Gaussian random sample under a sparse Kronecker-product covariance model and MSE convergence rates. The KGlasso model, originally called the transposable regularized covariance model by Allen [“Transposable regularized covariance models with an application to missing data imputation,” Ann. Appl. Statist., vol. 4, no. 2, pp. 764-790, 2010], implements a pair of $ell_1$ penalties on each Kronecker factor to enforce sparsity in the covariance estimator. The KGlasso algorithm generalizes Glasso, introduced by Yuan and Lin [“Model selection and estimation in the Gaussian graphical model,” Biometrika, vol. 94, pp. 19-35, 2007] and Banerjee [“Model selection through sparse maximum likelihood estimation for multivariate Gaussian or binary data,” J. Mach. Learn. Res., vol. 9, pp. 485-516, Mar. 2008], to estimate covariances having Kronecker product form. It also generalizes the unpenalized ML flip-flop (FF) algorithm of Dutilleul [“The MLE algorithm for the matrix normal distribution,” J. Statist. Comput. Simul., vol. 64, pp. 105-123, 1999] and Werner [“On estimation of covariance matrices with Kronecker product structure,” IEEE Trans. Signal Process., vol. 56, no. 2, pp. 478-491, Feb. 2008] to estimation of sparse Kronecker factors. We establish that the KGlasso iterates converge pointwise to a local maximum of the penalized likelihood function. We derive high dimensional rates of convergence to the true covariance as both the number of samples and the number of variables go to infinity. Our results establish that KGlasso has significantly faster asymptotic convergence than Glasso and FF. Simulations are presented that validate the results of our analysis. For example, for a sparse 10 000 ×10 000 covariance matrix equal to the Kronecker product of two 100- × 100 matrices, the root mean squared error of the inverse covariance estimate using FF is 2 times larger than that obtainable using KGlasso for sample size of n=100. View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • DMT MIMO IC Rate Maximization in DSL With Combined Signal and Spectrum Coordination

    Page(s): 1756 - 1769
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (3109 KB) |  | HTML iconHTML  

    Theoretical research has demonstrated that the achievable gains in data rate with dynamic spectrum management, i.e., signal coordination or spectrum coordination, are substantial for digital subscriber line (DSL) networks. Work on these two fronts has progressed steadily and, more often than not, independently. In this paper, we combine the two types of coordination for a mixed DSL scenario, in which some of the infrastructure required for full two-sided signal coordination is available, but not all. This scenario, which is referred to as the discrete multitone multiple-input, multiple-output interference channel (DMT MIMO IC), consists of multiple interfering users, each operating a distinct subset of DSL lines as a MIMO system. Coordination is done both on the signal level (with per user MIMO techniques) and on the spectrum level (with multi-user power allocation). We propose two algorithms for the DMT MIMO IC weighted rate maximization problem. In the first algorithm, we profit from recent work showing the close relation between the weighted rate sum maximization problem and the weighted MMSE minimization problem. We show that with a simple extension, we can adapt the previous work to the scenario of interest. In the second algorithm, the signal and spectrum coordination parts are solved separately. For the signal coordination part, we obtain multiple independent single tone MIMO IC's, which allows us to leverage on the previous work on the topic. For the spectrum coordination part, one of the interesting results of our analysis is a generalization of the distributed spectrum balancing (DSB) power allocation formula for the DMT MIMO IC scenario. Simulation results demonstrate that both algorithms obtain significant gains when compared to pure spectrum coordination algorithms. View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • MSE-Based Source and Relay Precoder Design for Cognitive Multiuser Multi-Way Relay Systems

    Page(s): 1770 - 1785
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (4568 KB) |  | HTML iconHTML  

    We consider joint design of source and relay precoders in a cognitive multiuser multi-way relay system, which supports simultaneous transmission of multiple secondary users concurrently with primary network with the help of a relay station. The design criterion is minimum mean-square error (MMSE) of all secondary users under a transmit power constraint for each transmitting node and a constraint on the interference to primary network assuming complete knowledge of the channel state information is available. To solve this non-convex optimization problem, an iterative algorithm is proposed to iteratively solve the precoding matrices at secondary source nodes and relay node, and the decoding matrices at secondary nodes, where each subproblem is convex. To reduce the computational complexity, a matrix distance based non-iterative algorithm which can be implemented in a distributed manner is also proposed. Given the fact that perfect channel state information is usually non-realistic, a robust precoder design is also proposed to address this problem. Simulation results show the effectiveness of our proposed algorithms. View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Uniqueness Analysis of Non-Unitary Matrix Joint Diagonalization

    Page(s): 1786 - 1796
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (2310 KB) |  | HTML iconHTML  

    Matrix Joint Diagonalization (MJD) is a powerful approach for solving the Blind Source Separation (BSS) problem. It relies on the construction of matrices which are diagonalized by the unknown demixing matrix. Their joint diagonalizer serves as a correct estimate of this demixing matrix only if it is uniquely determined. Thus, a critical question is under what conditions is a joint diagonalizer unique. In the present work we fully answer this question about the identifiability of MJD based BSS approaches and provide a general result on uniqueness conditions of matrix joint diagonalization. It unifies all existing results which exploit the concepts of non-circularity, non-stationarity, non-whiteness, and non-Gaussianity. As a corollary, we propose a solution for complex BSS, which can be formulated in closed form in terms of an eigen and a singular value decomposition of two matrices. View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Shrinkage Approach for Spatiotemporal EEG Covariance Matrix Estimation

    Page(s): 1797 - 1808
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (2843 KB) |  | HTML iconHTML  

    The characterization of the background activity in electroencephalography (EEG) is of interest in many problems, such as in the study of the brain rhythms and in the solution of the inverse problem for source localization. In most cases the background activity is modeled as a random process, and a basic characterization is done via the second order moments of the process, i.e., the spatiotemporal covariance. The general spatiotemporal covariance matrix of the background activity in EEG is extremely large. To reduce its dimensionality it is generally decomposed as a Kronecker product of a spatial and a temporal covariance matrices. They are generally estimated from the data using sample estimators, which have numerical and statistical problems when the number of trials is small. We present a shrinkage estimator for both EEG spatial and temporal covariance matrices of the background activity. We show that this estimator outperforms the commonly used ones when the quantity of available data is low. We find sufficient conditions for the consistency of the shrinkage estimator and present some results concerning its numerical stability. We compare several shrinkage approaches and show how to improve the estimator by incorporating known structure in the covariance matrix based on background activity models. Results using simulated and real EEG data support our approach. View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • On Intrinsic Cramér-Rao Bounds for Riemannian Submanifolds and Quotient Manifolds

    Page(s): 1809 - 1821
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (3640 KB) |  | HTML iconHTML  

    We study Cramér-Rao bounds (CRB's) for estimation problems on Riemannian manifolds. In [S. T. Smith, “Covariance, Subspace, and Intrinsic Cramér-Rao bounds,” IEEE Trans. Signal Process., vol. 53, no. 5, 1610-1630, 2005], the author gives intrinsic CRB's in the form of matrix inequalities relating the covariance of estimators and the Fisher information of estimation problems. We focus on estimation problems whose parameter space is a Riemannian submanifold or a Riemannian quotient manifold of a parent space P, that is, estimation problems on manifolds with either deterministic constraints or ambiguities. The CRB's in the aforementioned reference would be expressed w.r.t. bases of the tangent spaces to P̅. In some cases though, it is more convenient to express covariance and Fisher information w.r.t. bases of the tangent spaces to P. We give CRB's w.r.t. such bases expressed in terms of the geodesic distances on the parameter space. The bounds are valid even for singular Fisher information matrices. In two examples, we show how the CRB's for synchronization problems (including a type of sensor network localization problem) differ in the presence or absence of anchors, leading to bounds for estimation on either submanifolds or quotient manifolds with very different interpretations. View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.

Aims & Scope

IEEE Transactions on Signal Processing covers novel theory, algorithms, performance analyses and applications of techniques for the processing, understanding, learning, retrieval, mining, and extraction of information from signals

Full Aims & Scope

Meet Our Editors

Editor-in-Chief
Zhi-Quan (Tom) Luo
University of Minnesota