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MMSE-Based MDL Method for Robust Estimation of Number of Sources Without Eigendecomposition

IEEE TRANSACTIONS ON SIGNAL processing 2009年第10期57卷 4135-4142页

作者： Huang, Lei Long, Teng Mao, Erke So, H. C. Beijing Inst Technol Dept Elect Engn Beijing 100081 Peoples R China City Univ Hong Kong Dept Elect Engn Kowloon Hong Kong Peoples R China

It is well known that the conventional eigenvalue-based minimum description length (MDL) approach for source number estimation suffers from high computational load and performs optimally only in the presence of spatially and temporally white noise. To improve the robustness of the MDL methodology, we propose to utilize the minimum mean square error (MMSE) of the multistage Wiener filter to calculate the required description length for encoding the observed data, instead of relying on the eigenvalues of the data covariance matrix. As there is no need to calculate the covariance matrix and its eigenvalue decomposition, our derived MMSE-based MDL (mMDL) method is also more computationally efficient than the traditional counterparts. Numerical examples are included to demonstrate the robustness of the mMDL detector in nonuniform noise.

关键词： Eigenvalue decomposition (EVD) minimum description length (MDL) multistage Wiener filter (MSWF) sensor array processing source number estimation

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Optimal Sample Complexity for Blind Gain and Phase Calibration

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IEEE TRANSACTIONS ON SIGNAL processing 2016年第21期64卷 5549-5556页

作者： Li, Yanjun Lee, Kiryung Bresler, Yoram Univ Illinois Coordinated Sci Lab Urbana IL 61801 USA Univ Illinois Dept Elect & Comp Engn Urbana IL 61801 USA Georgia Inst Technol Sch Elect & Comp Engn Atlanta GA 30332 USA

Blind gain and phase calibration (BGPC) is a structured bilinear inverse problem, which arises in many applications, including inverse rendering in computational relighting (albedo estimation with unknown lighting), blind phase and gain calibration in sensor array processing, and multichannel blind deconvolution. The fundamental question of the uniqueness of the solutions to such problems has been addressed only recently. In a previous paper, we proposed studying the identifiability in bilinear inverse problems up to transformation groups. In particular, we studied several special cases of blind gain and phase calibration, including the cases of subspace and joint sparsity models on the signals, and gave sufficient and necessary conditions for identifiability up to certain transformation groups. However, there were gaps between the sample complexities in the sufficient conditions and the necessary conditions. In this paper, under a mild assumption that the signals and models are generic, we bridge the gaps by deriving tight sufficient conditions with optimal or near optimal sample complexities.

关键词： Blind gain and phase calibration inverse rendering multichannel blind deconvolution SAR autofocus sensor array processing

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Identifiability in Bilinear Inverse Problems With Applications to Subspace or Sparsity-Constrained Blind Gain and Phase Calibration

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IEEE TRANSACTIONS ON INFORMATION THEORY 2017年第2期63卷 822-842页

作者： Li, Yanjun Lee, Kiryung Bresler, Yoram Univ Illinois Dept Elect & Comp Engn Coordinated Sci Lab Champaign IL 61801 USA Georgia Inst Technol Sch Elect & Comp Engn Atlanta GA 30332 USA

Bilinear inverse problems (BIPs), the resolution of two vectors given their image under a bilinear mapping, arise in many applications. Without further constraints, BIPs are usually ill-posed. In practice, the properties of natural signals are exploited to solve BIPs. For example, subspace constraints or sparsity constraints are imposed to reduce the search space. These approaches have shown some success in practice. However, there are few results on uniqueness in BIPs. For most BIPs, the fundamental question of under what condition the problem admits a unique solution is yet to be answered. For example, blind gain and phase calibration (BGPC) is a structured BIP, which arises in many applications, including inverse rendering in computational relighting (albedo estimation with unknown lighting), blind phase and gain calibration in sensor array processing, and multichannel blind deconvolution (MBD). It is interesting to study the uniqueness of such problems. In this paper, we define identifiability of a BIP up to a group of transformations. We derive necessary and sufficient conditions for such identifiability, i.e., the conditions under which the solutions can be uniquely determined up to the transformation group. These conditions take the form of dividing the identifiability of the pair of unknown variables into the individual identifiability of each variable. Although verifying these individual conditions requires problem-specific procedures, this framework is universally applicable to all BIPs. Applying these results to BGPC, we derive sufficient conditions for unique recovery under several scenarios, including subspace, joint sparsity, and sparsity models. For BGPC with joint sparsity or sparsity constraints, we develop a procedure to compute the transformation groups corresponding to inherent ambiguities. We also give necessary conditions in the form of tight lower bounds on sample complexities, and demonstrate the tightness of these bounds by numerical experim

关键词： Ambiguity blind gain and phase calibration equivalence class inverse rendering multichannel blind deconvolution SAR autofocus sensor array processing transformation group uniqueness

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A new subspace identification algorithm for high-resolution DOA estimation

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IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION 2002年第10期50卷 1382-1390页

作者： McCloud, ML Scharf, LL Magis Networks Inc San Diego CA 92130 USA Colorado State Univ Ft Collins CO 80523 USA

In this paper, we propose a new direction of arrival (DOA) estimator for sensor-array processing. The estimator is based on a linear algebraic connection between the standard subspace model of the array correlation matrix and a special signal-plus-interference model, which we develop in this paper. The estimator we propose is a signal subspace scaled MUSIC algorithm, which we call SSMUSIC. It is not a subspace weighted MUSIC, because the scaling depends on the eigenstructure of the estimated signal subspace. SSMUSIC has the advantage of simultaneously estimating the DOA and the power of each source. We employ a second-order perturbation analysis of the estimator and derive stochastic representations for its bias and squared-error. We compare the new DOA estimator with the MUSIC estimator, based on these representations. Numerical results demonstrate the superior performance of SSMUSIC relative to MUSIC and the validity of the perturbation results.

关键词： bearing response function direction of arrival (DOA) MUSIC sensor array processing subspace processing

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Efficient Dipole Parameter Estimation in EEG Systems With Near-ML Performance

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IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING 2012年第5期59卷 1339-1348页

作者： Wu, Shun Chi Swindlehurst, A. Lee Wang, Po T. Nenadic, Zoran Univ Calif Irvine Dept Elect Engn & Comp Sci Irvine CA 92697 USA Univ Calif Irvine Dept Biomed Engn Irvine CA 92697 USA

Source signals that have strong temporal correlation can pose a challenge for high-resolution EEG source localization algorithms. In this paper, we present two methods that are able to accurately locate highly correlated sources in situations where other high-resolution methods such as multiple signal classification and linearly constrained minimum variance beamforming fail. These methods are based on approximations to the optimal maximum likelihood (ML) approach, but offer significant computational advantages over ML when estimates of the equivalent EEG dipole orientation and moment are required in addition to the source location. The first method uses a two-stage approach in which localization is performed assuming an unstructured dipole moment model, and then the dipole orientation is obtained by using these estimates in a second step. The second method is based on the use of the noise subspace fitting concept, and has been shown to provide performance that is asymptotically equivalent to the direct ML method. Both techniques lead to a considerably simpler optimization than ML since the estimation of the source locations and dipole moments is decoupled. Examples using data from simulations and auditory experiments are presented to illustrate the performance of the algorithms.

关键词： Electroencephalography (EEG) magnetoencephalography (MEG) sensor array processing source localization

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A low-complexity estimator for incoherently distributed sources with narrow or wide spread angles

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SIGNAL processing 2007年第5期87卷 1058-1065页

作者： Li, Gang Xu, Jia Peng, Ying-Ning Xia, Xiang-Gen Tsinghua Univ Dept Elect Engn Beijing 100084 Peoples R China Radar Acad Airforce Wuhan 430010 Peoples R China Univ Delaware Dept Elect & Comp Engn Newark DE 19716 USA

In this paper, a concept of contrast of eigenvalues (COE) is introduced to describe the diversity of the eigenvalues of signal covariance matrix. Based on the COE, a novel algorithm is proposed to estimate the central direction of arrival (DOA) and the angular spread of an incoherently distributed (ID) source. Using the proposed method, it is shown that the parameters of not only the narrowly but also the widely spread sources may be accurately obtained with low computational cost. The numerical examples are given to examine the performance of the COE-based estimator under various environments and show that it is indeed effective for both narrowly and widely spread ID sources. (c) 2006 Elsevier B.V. All rights reserved.

关键词： sensor array processing parameter estimation distributed source

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A sparse signal reconstruction perspective for source localization with sensor arrays

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IEEE TRANSACTIONS ON SIGNAL processing 2005年第8期53卷 3010-3022页

作者： Malioutov, D Çetin, M Willsky, AS MIT Dept Elect Engn & Comp Sci Cambridge MA 02139 USA

We present a source localization method based on a sparse representation of sensor measurements with an overcomplete basis composed of samples from the array manifold. We enforce sparsity by imposing penalties based on the l(1)-norm. A number of recent theoretical results on sparsifying properties of l(1) penalties justify this choice. Explicitly enforcing the sparsity of the representation is motivated by a desire to obtain a sharp estimate of the spatial spectrum that exhibits super-resolution. We propose to use the singular value decomposition (SVD) of the data matrix to summarize multiple time or frequency samples. Our formulation leads to an optimization problem, which we solve efficiently in a second-order cone (SOC) programming framework by an interior point implementation. We propose a grid refinement method to mitigate the effects of limiting estimates to a grid of spatial locations and introduce an automatic selection criterion for the regularization parameter involved in our approach. We demonstrate the effectiveness of the method on simulated data by plots of spatial spectra and by comparing the estimator variance to the Cramar-Rao bound (CRB). We observe that our approach has a number of advantages over other source localization techniques, including increased resolution, improved robustness to noise, limitations in data quantity, and correlation of the sources, as well as not requiring an accurate initialization.

关键词： direction-of-arrival estimation overcomplete representation sensor array processing source localization sparse representation superresolution

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Design of chemical sensor arrays for monitoring disposal sites on the ocean floor

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IEEE JOURNAL OF OCEANIC ENGINEERING 1998年第4期23卷 334-343页

作者： Jeremic, A Nehorai, A Univ Illinois Dept Elect Engn & Comp Sci Chicago IL 60607 USA

We develop methods for automatic environmental monitoring of disposal sites on the deep ocean door using chemical sensor arrays and statistical hypothesis testing. Such sites have been proposed to relocate dredge materials from harbors and shipping channels. The transport of pollutants is modeled as a diffusion process, and the measurement and statistical models are derived by exploiting the spatial and temporal evolution of the associated concentration distribution. We derive two detectors, the generalized likelihood ratio (GLR) test and the mean detector, and determine their performance in terms of the probabilities of false alarm and detection. The results are applied to the design of chemical sensor arrays satisfying criteria specified in terms of these probabilities, and to optimally select a number of sensors and time samples. Numerical examples are used to demonstrate the applicability of our results.

关键词： chemical sensing environmental monitoring pollutant detection sensor array processing

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Blind identification of FIR MIMO channels by decorrelating subchannels

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IEEE TRANSACTIONS ON SIGNAL processing 2003年第5期51卷 1143-1155页

作者： Hua, YB An, SJ Xiang, Y Univ Calif Riverside Dept Elect Engn Riverside CA 92521 USA Univ Melbourne Dept Elect & Elect Engn Parkville Vic 3010 Australia

We study blind identification and equalization of finite impulse response (FIR) and multi-input and multi-output (MIMO) channels driven by colored signals. We first show a sufficient condition for an FIR MIMO channel to be identifiable up to a scaling and permutation using the second-order statistics of the channel output. This condition is that the channel matrix is irreducible (but not necessarily column-reduced), and the input signals are mutually uncorrelated and of distinct power spectra. We also show that this condition is necessary in the sense that no single part of the condition can be further weakened without another part being strengthened. While the above condition is a strong result that sets a fundamental limit of blind identification, there does not yet exist a working algorithm under that condition. In the second part of this paper, we show that a method called blind identification via decorrelating subchannels (BIDS) can uniquely identify an FIR MIMO channel if a) the channel matrix is nonsingular (almost everywhere) and column-wise coprime and (b) the input signals are mutually uncorrelated and of sufficiently diverse power spectra. The BIDS method requires a weaker condition on the channel matrix than that required,by most existing methods for the same problem.

关键词： adaptive signal processing blind system identification blind channel deconvolution colored sources decorrelation MIMO channels sensor array processing

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array response kernels for EEG and MEG in multilayer ellipsoidal geometry

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IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING 2008年第3期55卷 1103-1111页

作者： Gutierrez, David Nehorai, Arye Ctr Invest & Estudios Avanzados CINVESTAV Unidad Monterrey Apodaca 66600 NL Mexico Washington Univ Dept Elect & Comp Engn St Louis MO 63139 USA

We present forward modeling solutions in the form of array response kernels for electroencephalography (EEG) and magnetoencephalography (MEG), assuming that a multilayer ellipsoidal geometry approximates the anatomy of the head and a dipole current models the source. The use of an ellipsoidal geometry is useful in cases for which incorporating the anisotropy of the head is important but a better model cannot be defined. The structure of our forward solutions facilitates the analysis of the inverse problem by factoring the lead field into a product of the current dipole source and a kernel containing the information corresponding to the head geometry and location of the source and sensors. This factorization allows the inverse problem to be approached as an explicit function of just the location parameters, which reduces the complexity of the estimation solution search. Our forward solutions have the potential of facilitating the solution of the inverse problem, as they provide algebraic representations suitable for numerical implementation. The applicability of our models is illustrated with numerical examples on real EEG/MEG data of N20 responses. Our results show that the residual data after modeling the N20 response using a dipole for the source and an ellipsoidal geometry for the head is in average lower than the residual remaining when a spherical geometry is used for the same estimated dipole.

关键词： dipole source signal electroencephalography (EEG) ellipsoidal head model magnetoencephalography (MEG) N20 response sensor array processing

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