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Shape From Moments  An Estimation Theory Perspective
 IEEE TRANSACTIONS ON SIGNAL PROCESSING ON
, 2004
"... This paper discusses the problem of recovering a planar polygon from its measured complex moments. These moments correspond to an indicator function defined over the polygon's support. Previous work on this problem gave necessary and sufficient conditions for such successful recovery process ..."
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Cited by 23 (2 self)
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This paper discusses the problem of recovering a planar polygon from its measured complex moments. These moments correspond to an indicator function defined over the polygon's support. Previous work on this problem gave necessary and sufficient conditions for such successful recovery process and focused mainly on the case of exact measurements being given. In this paper
RankRevealing "TopDown" ULV Factorizations
, 1997
"... Rankrevealing ULV and URV factorizations are useful tools to determine the rank and to compute bases for nullspaces of a matrix. However, in the practical ULV (resp. URV) factorization each left (resp. right) null vector is recomputed from its corresponding right (resp. left) null vector via trian ..."
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Cited by 7 (0 self)
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Rankrevealing ULV and URV factorizations are useful tools to determine the rank and to compute bases for nullspaces of a matrix. However, in the practical ULV (resp. URV) factorization each left (resp. right) null vector is recomputed from its corresponding right (resp. left) null vector via triangular solves. Triangular solves are required at initial factorization, refinement and updating. As a result, algorithms based on these factorizations may be expensive, especially on parallel computers where triangular solves are expensive. In this paper we propose an alternative approach. Our new rankrevealing ULV factorization, which we call "topdown" ULV factorization (TDULV factorization) is based on right null vectors of lower triangular matrices and therefore no triangular solves are required. Right null vectors are easy to estimate accurately using condition estimators such as incremental condition estimator (ICE). The TDULV factorization is shown to be equivalent to the URV fact...
Total Least Squares Algorithms Based on RankRevealing Complete Orthogonal Decompositions
, 1996
"... The total least squares (TLS) method has proven to be effective in many applications which involve a subproblem requiring the solution of a system of linear equations with a numerically rankdeficient coefficient matrix. The TLS method typically requires a singular value decomposition, but practi ..."
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Cited by 4 (1 self)
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The total least squares (TLS) method has proven to be effective in many applications which involve a subproblem requiring the solution of a system of linear equations with a numerically rankdeficient coefficient matrix. The TLS method typically requires a singular value decomposition, but practical considerations call for more efficient, yet reliable, methods. We discuss how efficient and reliable complete orthogonal decompositions can be used in TLS problems.
SubspaceBased Noise Reduction for Speech Signals via Diagonal and Triangular Matrix Decompositions: Survey and Analysis
, 2007
"... We survey the definitions and use of rankrevealing matrix decompositions in singlechannel noise reduction algorithms for speech signals. Our algorithms are based on the rankreduction paradigm and, in particular, signal subspace techniques. The focus is on practical working algorithms, using both ..."
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Cited by 4 (1 self)
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We survey the definitions and use of rankrevealing matrix decompositions in singlechannel noise reduction algorithms for speech signals. Our algorithms are based on the rankreduction paradigm and, in particular, signal subspace techniques. The focus is on practical working algorithms, using both diagonal (eigenvalue and singular value) decompositions and rankrevealing triangular decompositions (ULV, URV, VSV, ULLV, and ULLIV). In addition, we show how the subspacebased algorithms can be analyzed and compared by means of simple FIR filter interpretations. The algorithms are illustrated with working Matlab code and applications in speech processing.
Simultaneous Principal Component Extraction with Application to Adaptive Blind Multiuser Detection
 EURASIP Journal on Applied Signal Processing
, 2002
"... SIPEXG is a fast converging, robust, gradientbased PCA algorithm that has been recently proposed by the authors. Its superior performance in synthetic and real data compared with its benchmark counterparts makes it a viable alternative in applications where subspace methods are employed. Blind mul ..."
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Cited by 3 (3 self)
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SIPEXG is a fast converging, robust, gradientbased PCA algorithm that has been recently proposed by the authors. Its superior performance in synthetic and real data compared with its benchmark counterparts makes it a viable alternative in applications where subspace methods are employed. Blind multiuser detection is one such area, where subspace methods, recently developed by researchers, have proven effective. In this paper, the SIPEXG algorithm is presented in detail, convergence proofs are derived, and the performance is demonstrated in standard subspace problems. These subspace problems include direction of arrival estimation for incoming signals impinging on a linear array of sensors, nonstationary random process subspace tracking, and adaptive blind multiuser detection. I.
AN EFFICIENT, ROBUST, AND FAST CONVERGING PRINCIPAL COMPONENTS EXTRACTION ALGORITHM: SIPEXG
"... Principal Components Analysis (PCA) is a very important statistical tool in signal processing, which has found successful applications in numerous engineering problems as well as other fields. In general, an online algorithm to adapt the PCA network to determine the principal projections of the inp ..."
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Principal Components Analysis (PCA) is a very important statistical tool in signal processing, which has found successful applications in numerous engineering problems as well as other fields. In general, an online algorithm to adapt the PCA network to determine the principal projections of the input data is desired. The authors have recently introduced a fast, robust, and efficient PCA algorithm called SIPEXG without detailed comparisons and analysis of performance. In this paper, we investigate the performance of SIPEXG through Monte Carlo runs on synthetic data and on realistic problems where PCA is applied. These problems include direction of arrival estimation and subspace Wiener filtering. 1
Downdating a RankRevealing URV Decomposition
, 1995
"... . The rankrevealing URV decomposition is a useful tool for the subspace tracking problem in digital signal processing. Updating the decomposition is a stable process. However, downdating a rankrevealing URV decomposition could be unstable because the R factor is illconditioned. In this paper, we ..."
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. The rankrevealing URV decomposition is a useful tool for the subspace tracking problem in digital signal processing. Updating the decomposition is a stable process. However, downdating a rankrevealing URV decomposition could be unstable because the R factor is illconditioned. In this paper, we review some existing downdating algorithms for the fullrank URV decomposition in the absence of U and develop a new combined algorithm. We also show that the combined algorithm has relational stability. For the rankrevealing URV decomposition, we review a twostep method that applies fullrank downdating algorithms to the signal and noise parts separately. We compare several combinations of the fullrank algorithms and demonstrate good performance of our combined algorithm. Key words. rankrevealing factorization, downdating, URV decomposition AMS(MOS) subject classifications. 65F20, 65F25, 65F30 August 31, 1995 1. Introduction. The rankrevealing URV decomposition [12] is a useful too...
TwoDimensional Spatial Smoothing For Multipath Coherent Signal Identification And Separation
"... The existing spatial smoothing (SS) technique, although it is effective in decorrelating coherent signals, is considered applicable only to uniformly spaced linear arrays which are very sensitive to the directionsofarrival (DOA's) and can be used to estimate azimuth angles only. To significan ..."
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The existing spatial smoothing (SS) technique, although it is effective in decorrelating coherent signals, is considered applicable only to uniformly spaced linear arrays which are very sensitive to the directionsofarrival (DOA's) and can be used to estimate azimuth angles only. To significantly improve the robustness of DOA estimation and of beamforming and to estimate both azimuth and elevation angles in a 3D multipath mobile radio environment, we developed techniques for applying SS to arrays of nonlinear geometry. We found and proved the necessary and sufficient conditions on an array configuration for applying SS. This array must have an orientational invariance structure with an ambiguity free center array, and the number of subarrays must be larger than or equal to the size of the largest group of coherent signals. We also studied the cause of ambiguities in a multipath environment. We found the necessary and sufficient conditions for a threesensor array manifold to be ambigu...
EURASIP Journal on Applied Signal Processing 2004:13, 2034–2041 c ○ 2004 Hindawi Publishing Corporation Recursive Principal Components Analysis Using Eigenvector Matrix Perturbation
, 2004
"... Principal components analysis is an important and wellstudied subject in statistics and signal processing. The literature has an abundance of algorithms for solving this problem, where most of these algorithms could be grouped into one of the following three approaches: adaptation based on Hebbian ..."
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Principal components analysis is an important and wellstudied subject in statistics and signal processing. The literature has an abundance of algorithms for solving this problem, where most of these algorithms could be grouped into one of the following three approaches: adaptation based on Hebbian updates and deflation, optimization of a secondorder statistical criterion (like reconstruction error or output variance), and fixed point update rules with deflation. In this paper, we take a completely different approach that avoids deflation and the optimization of a cost function using gradients. The proposed method updates the eigenvector and eigenvalue matrices simultaneously with every new sample such that the estimates approximately track their true values as would be calculated from the current sample estimate of the data covariance matrix. The performance of this algorithm is compared with that of traditional methods like Sanger’s rule and APEX, as well as a structurally similar matrix perturbationbased method.