Xi-Lin Li

University of Maryland, Baltimore County, Baltimore, Maryland, United States

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Publications (45)103.48 Total impact

  • [Show abstract] [Hide abstract]
    ABSTRACT: Estimating likelihood or entropy rate is one of the key issues in many signal processing problems. Mutual information rate, which leads to the minimization of entropy rate, provides a natural cost for achieving blind source separation (BSS). In many complex-valued BSS applications, the latent sources are non-Gaussian, noncircular, and possess sample dependence. Consequently, an effective estimator of entropy rate that jointly considers all three properities of the sources is required. In this paper, we propose such an entropy rate estimator that assumes the sources are generated by invertible filters. With this new entropy rate estimator, we propose a complex entropy rate bound minimization algorithm. Simulation results show that the new method exploits all three properties effectively.
    ICASSP 2014 - 2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP); 05/2014
  • Xi-Lin Li · Tulay Adali
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    ABSTRACT: We develop an efficient algorithm for noncircular complex independent component analysis (ICA) by optimizing the rows of separation matrix independently using a generalized Householder reflector and Newton method. We apply the new algorithm to the separation of complex generalized Gaussian distributed (GGD) sources, and propose a convenient way to learn the noncircularity of the sources. Simulation results are reported to study the convergence behavior, and confirm the superior performance of the new algorithm.
    IEEE Transactions on Signal Processing 12/2013; 61(24):6423-6430. DOI:10.1109/TSP.2013.2286113 · 3.20 Impact Factor
  • Xi-Lin Li · Tülay Adali
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    ABSTRACT: In this paper, we study the performance of mean square error (MSE) and Gaussian entropy criteria for linear and widely linear complex filtering. The MSE criterion has been extensively studied, and with a widely linear filter form, it can take into account the full second-order statistics of the input signal. However, it cannot exploit the full second-order statistics of the error, and doubles the dimension of the parameter vector to be estimated. In this paper, we introduce the use of Gaussian entropy criterion such that full second-order statistics of the error can be taken into account, and compare the performance of the Gaussian entropy and MSE criteria for a linear and widely linear filter implementation in batch and adaptive implementations. Detailed performance analysis with numerical examples is presented to investigate the relationship and performance differences of the two criteria in diverse scenarios.
    IEEE Transactions on Signal Processing 11/2012; 60(11):5672-5684. DOI:10.1109/TSP.2012.2210889 · 3.20 Impact Factor
  • Xi-Lin Li
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    ABSTRACT: A decoupled relative Newton algorithm is proposed for the matrix optimization problem encountered in blind source separation (BSS) and independent component analysis (ICA). The algorithm decouples the matrix optimization problem into a series of small vector optimization problems. The nonsingularity of separation matrix enables a simple and efficient relative Newton learning algorithm for the vector optimization problems. Simulation results are reported to confirm its superior performance.
    IEEE Signal Processing Letters 09/2012; 19(9):567-570. DOI:10.1109/LSP.2012.2207890 · 1.64 Impact Factor
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    ABSTRACT: We consider the problem of joint blind source separation of multiple datasets and introduce a solution to the problem for complex-valued sources. We pose the problem in an independent vector analysis (IVA) framework and provide a new general IVA implementation using Wirtinger calculus and a decoupled nonunitary optimization algorithm to facilitate Newton-based optimization. Utilizing the noncircular multivariate Gaussian distribution as a source prior enables the full utilization of the complete second-order statistics available in the covariance and pseudo-covariance matrices. The algorithm provides a principled approach for achieving multiset canonical correlation analysis.
    Signal Processing 08/2012; 92(8). DOI:10.1016/j.sigpro.2011.09.034 · 2.24 Impact Factor
  • Matthew Anderson · Tülay Adali · Xi-Lin Li
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    ABSTRACT: In this paper, we consider the joint blind source separation (JBSS) problem and introduce a number of algorithms to solve the JBSS problem using the independent vector analysis (IVA) framework. Source separation of multiple datasets simultaneously is possible when the sources within each and every dataset are independent of one another and each source is dependent on at most one source within each of the other datasets. In addition to source separation, the IVA framework solves an essential problem of JBSS, namely the identification of the dependent sources across the datasets. We propose to use the multivariate Gaussian source prior to achieve JBSS of sources that are linearly dependent across datasets. Analysis within the paper yields the local stability conditions, nonidentifiability conditions, and induced Cramér-Rao lower bound on the achievable interference to source ratio for IVA with multivariate Gaussian source priors. Additionally, by exploiting a novel nonorthogonal decoupling of the IVA cost function we introduce both Newton and quasi-Newton optimization algorithms for the general IVA framework.
    IEEE Transactions on Signal Processing 04/2012; 60(4):1672-1683. DOI:10.1109/TSP.2011.2181836 · 3.20 Impact Factor
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    ABSTRACT: Adaptive filtering has been extensively studied under the assumption that the noise is Gaussian. The most commonly used least-mean-square-error (LMSE) filter is optimal when the noise is Gaussian. However, in many practical applications, the noise can be modeled more accurately using a non-Gaussian distribution. In this correspondence, we consider non-Gaussian distributions for the noise model and show that the filter of using entropy bound minimization (EBM) leads to significant performance gain compared to the LMSE filter. The least mean p-norm (LMP) filter using the $\alpha$-stable distribution to model noise is shown to be the maximum-likelihood solution when using the generalized Gaussian distribution (GGD) to model noise. The GGD model for noise allows us to compute the Cramér–Rao lower bound (CRLB) for the error in estimating the weights. Simulations show that both the EBM and LMP filters achieve the CRLB as the sample size increases. The EBM filter is shown to be less committed with respect to unseen data yielding generally superior performance in online learning when compared to LMP. We also show that, when the noise comes from impulsive $\alpha$ -stable distributions, both the EBM and LMP filters provide better performance than LMSE. In addition, the EBM filter offers the advantage that it does not assume a certain parametric model for the noise, and by proper selection of the measuring functions, it can be adapted to a wide range of noise distributions.
    IEEE Transactions on Signal Processing 04/2012; 60(4):2049-2055. DOI:10.1109/TSP.2011.2182345 · 3.20 Impact Factor
  • Source
    M. Anderson · Xi-Lin Li · P. Rodriguez · T. Adali
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    ABSTRACT: Matrix optimization of cost functions is a common problem. Construction of methods that enable each row or column to be individually optimized, i.e., decoupled, are desirable for a number of reasons. With proper decoupling, the convergence characteristics such as local stability can be improved. Decoupling can enable density matching in applications such as independent component analysis (ICA). Lastly, efficient Newton algorithms become tractable after decoupling. The most common method for decoupling rows is to reduce the optimization space to orthogonal matrices. Such restrictions can degrade performance. We present a decoupling procedure that uses standard vector optimization procedures while still admitting nonorthogonal solutions. We utilize the decoupling procedure to develop a new decoupled ICA algorithm that uses Newton optimization enabling superior performance when the sample size is limited.
    Acoustics, Speech and Signal Processing (ICASSP), 2012 IEEE International Conference on; 03/2012
  • Source
    Xi-Lin Li · Tülay Adali · Matthew Anderson
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    ABSTRACT: One of the most commonly used data analysis tools, principal component analysis (PCA), since is based on variance maximization, assumes a circular model, and hence cannot account for the potential noncircularity of complex data. In this paper, we introduce noncircular PCA (ncPCA), which extends the traditional PCA to the case where there can be both circular and noncircular Gaussian signals in the subspace. We study the properties of ncPCA, introduce an efficient algorithm for its computation, and demonstrate its application to model selection, i.e., the detection of both the signal subspace order and the number of circular and noncircular signals. We present numerical results to demonstrate the advantages of ncPCA over regular PCA when there are noncircular signals in the subspace. At the same time, we note that since a noncircular model has more degrees of freedom than a circular one, there are cases where a circular model might be preferred even though the underlying problem is noncircular. In particular, we show that a circular model is preferred when the signal-to-noise ratio (SNR) is low, number of samples is small, or the degree of noncircularity of the signals is low. Hence, ncPCA inherently provides guidance as to when to take noncircularity into account.
    IEEE Transactions on Signal Processing 11/2011; 59(10-59):4516 - 4528. DOI:10.1109/TSP.2011.2160631 · 3.20 Impact Factor
  • Xi-Lin Li · Tülay Adali · Matthew Anderson
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    ABSTRACT: In this paper, we show that the joint blind source separation (JBSS) problem can be solved by jointly diagonalizing cumulant matrices of any order higher than one, including the correlation matrices and the fourth-order cumulant matrices. We introduce an efficient iterative generalized joint diagonalization algorithm such that a series of orthogonal procrustes problems are solved. We present simulation results to show that the new algorithms can reliably solve the permutation ambiguity in JBSS and that they offer superior performance compared with existing multiset canonical correlation analysis (MCCA) and independent vector analysis (IVA) approaches. Experiment on real-world data for separation of fetal heartbeat in electrocardiogram (ECG) data demonstrates a new application of JBSS, and the success of the new algorithms for a real-world problem.
    Signal Processing 10/2011; 91(10):2314-2322. DOI:10.1016/j.sigpro.2011.04.016 · 2.24 Impact Factor
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    ABSTRACT: In independent component analysis (ICA) of functional magnetic resonance imaging (fMRI) data, extracting a large number of maximally independent components provides a detailed functional segmentation of brain. However, such high-order segmentation does not establish the relationships among different brain networks, and also studying and classifying components can be challenging. In this study, we present a multidimensional ICA (MICA) scheme to achieve automatic component clustering. In our MICA framework, stable components are hierarchically grouped into clusters based on higher order statistical dependence--mutual information--among spatial components, instead of the typically used temporal correlation among time courses. The final cluster membership is determined using a statistical hypothesis testing method. Since ICA decomposition takes into account the modulation of the spatial maps, i.e., temporal information, our ICA-based approach incorporates both spatial and temporal information effectively. Our experimental results from both simulated and real fMRI datasets show that the use of spatial dependence leads to physiologically meaningful connectivity structure of brain networks, which is consistently identified across various ICA model orders and algorithms. In addition, we observe that components related to artifacts, including cerebrospinal fluid, arteries, and large draining veins, are grouped together and encouragingly distinguished from other components of interest.
    IEEE transactions on bio-medical engineering 09/2011; 58(12):3406-17. DOI:10.1109/TBME.2011.2167149 · 2.23 Impact Factor
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    Xue Jiang · Wen-Jun Zeng · Xi-Lin Li
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    ABSTRACT: Estimation of the parameters of a multipath underwater acoustic channel is of great interest for a variety of applications. This paper proposes a high-resolution method for jointly estimating the multipath time delays, Doppler scales, and attenuation amplitudes of a time-varying acoustical channel. The proposed method formulates the estimation of channel parameters into a sparse representation problem. With the [script-l](1)-norm as the measure of sparsity, the proposed method makes use of the basis pursuit (BP) criterion to find the sparse solution. The ill-conditioning can be effectively reduced by the [script-l](1)-norm regularization. Unlike many existing methods that are only applicable to narrowband signals, the proposed method can handle both narrowband and wideband signals. Simulation results are provided to verify the performance and effectiveness of the proposed algorithm, indicating that it has a super-resolution in both delay and Doppler domain, and it is robust to noise.
    The Journal of the Acoustical Society of America 08/2011; 130(2):850-7. DOI:10.1121/1.3609118 · 1.56 Impact Factor
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    Xi-Lin Li · Tülay Adali
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    ABSTRACT: We introduce a new blind source separation (BSS) algorithm for correlated noncircular sources that uses only second-order statistics and fully takes the correlation structure into account. We propose a parametric entropy rate estimator that uses a widely linear autoregressive (AR) model for the sources, and derive the BSS algorithm by minimizing the mutual information of separated time series. We compare the performance of the new algorithm with competing algorithms and demonstrate its superior separation performance as well as its effectiveness in separation of non-Gaussian sources when the identification conditions are met.
    IEEE Transactions on Signal Processing 07/2011; 59(6-59):2969 - 2975. DOI:10.1109/TSP.2011.2114653 · 3.20 Impact Factor
  • Wei Du · Hualiang Li · Xi-Lin Li · V.D. Calhoun · T. Adali
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    ABSTRACT: Independent component analysis (ICA) has proven useful for the analysis of functional magnetic resonance imaging (fMRI) data. In this paper, we compare the performance of three ICA algorithms and show the importance of taking sample correlation information into account. The three ICA algorithms are Infomax, the most widely used algorithm for fMRI analysis, entropy bound minimization (EBM) that adapts to a wide range of source distributions, and full blind source separation (FBSS) which has the ability to incorporate a flexible density model along with sample correlation information. We apply these three ICA algorithms to fMRI data from multiple subjects performing an auditory oddball task (AOD). We show that FBSS leads to significant improvement in the estimation of both the spatial activation and the time courses of several components. More importantly, by taking the correlation information into account, the default mode network (DMN) component, an important one in the study of brain function, is more consistently estimated using FBSS.
    Biomedical Imaging: From Nano to Macro, 2011 IEEE International Symposium on; 05/2011
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    Xi-Lin Li · T. Adali
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    ABSTRACT: In this paper, we study the performance of mean square error (MSE) and Gaussian entropy criteria for linear and widely linear complex filtering. The MSE criterion cannot exploit the full second-order statistics of the error signal. To this end, we propose a new Gaussian entropy criterion to exploit the full second-order statistics of the error signal, and compare the performance of the two criteria in linear and widely linear filters. We show that the minimum Gaussian entropy estimator is also the best linear unbiased estimator (BLUE).
    Information Sciences and Systems (CISS), 2011 45th Annual Conference on; 04/2011
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    Xi-Lin Li · Sai Ma · Vince D. Calhoun · Tülay Adali
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    ABSTRACT: Estimation of the order of functional magnetic resonance imaging (fMRI) data is a crucial step in data-driven methods assuming a multivariate linear model. Use of information theoretic criteria for model order detection was proven useful but the sample dependence in fMRI data limits this usefulness. In this paper, we propose an iterative procedure that jointly estimates the downsampling depth and order of fMRI data, both by using information theoretic criteria. Experimental results on real-world fMRI data show reliable performance of the new method. Order analysis on auditory oddball task (AOD) data of healthy and schizophrenia subjects suggests that model order can be a promising biomarker for mental disorders.
    Proceedings of the 8th IEEE International Symposium on Biomedical Imaging: From Nano to Macro, ISBI 2011, March 30 - April 2, 2011, Chicago, Illinois, USA; 01/2011
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    ABSTRACT: This paper presents a novel algorithm for independent vector analysis (IVA) of Gaussian data sets. Following a maximum likelihood (ML) approach, we show that the cost function to be minimized by the proposed GML-IVA algorithm reduces to an estimate of the mutual information among the different sets of latent variables. The proposed method, which can be seen as a new generalization of canonical correlation analysis (CCA), is based on the sequential solution of different least squares problems obtained from the quadratic approximation of the non-convex IVA cost function. The convergence and performance of the proposed algorithm are illustrated by means of several simulation examples, including an application consisting in the joint blind source separation (J-BSS) of three color images.
    01/2011; DOI:10.1109/MLSP.2011.6064584
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    ABSTRACT: This paper considers the problem of joint blind source separation (J-BSS), which appears in many practical problems such as blind deconvolution or functional magnetic resonance imaging (fMRI). In particular, we establish the necessary and sufficient conditions for the solution of the J-BSS problem by exclusively exploiting the second-order statistics (SOS) of the observations. The identifiability analysis is based on the idea of equivalently distributed sets of latent variables, that is, latent variables with covariance matrices related by means of a diagonal matrix. Interestingly, the identifiability analysis also allows us to introduce a measure of the identifiability degree based on Kullback-Leibler projections. This measure is clearly correlated with the performance of practical SOS-based J-BSS algorithms, which is illustrated by means of numerical examples.
    Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2011, May 22-27, 2011, Prague Congress Center, Prague, Czech Republic; 01/2011
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    Wen-Jun Zeng · Xi-Lin Li · En Cheng
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    ABSTRACT: In this paper, the blind and semiblind channel esti- mation and equalization are investigated for zero-padding single- carrier block transmission (ZP-SCBT) systems using second- order statistics. Unlike the conventional channel estimation techniques, the proposed approach focuses on identifying the inverse of the channel impulse response rather than the channel response itself by skillfully exploiting the redundancy of the zero- padding. One interesting advantage of the proposed blind and semiblind approach is that the number of received blocks needed for blind identification is significantly reduced compared to the subspace method. Moreover, the computational complexity of the proposed approaches is much lower than the existing subspace methods. Simulation results are provided to demonstrate that the performance of the proposed approach is superior to the subspace-based blind methods.
    Proceedings of IEEE International Conference on Communications, ICC 2011, Kyoto, Japan, 5-9 June, 2011; 01/2011
  • Xi-Lin Li · M. Anderson · T. Adali
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    ABSTRACT: The commonly used principal component analysis (PCA) assumes circular Gaussian distribution for the observed complex random variables. This paper extends PCA to the general case where the signals can be noncircular, and introduces a new PCA method called the noncircular PCA (ncPCA). We study the properties of ncPCA and propose an efficient algorithm for its implementation. Numerical results are presented to demonstrate its advantages in signal detection and subspace estimation, in particular when the circularity assumptions on data do not hold.
    Signals, Systems and Computers (ASILOMAR), 2010 Conference Record of the Forty Fourth Asilomar Conference on; 12/2010

Publication Stats

513 Citations
103.48 Total Impact Points

Institutions

  • 2010–2014
    • University of Maryland, Baltimore County
      • Department of Computer Science and Electrical Engineering
      Baltimore, Maryland, United States
  • 2011–2012
    • University of Maryland, Baltimore
      Baltimore, Maryland, United States
  • 2006–2009
    • Tsinghua University
      • Department of Automation
      Peping, Beijing, China