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138
A multilinear singular value decomposition
 SIAM J. Matrix Anal. Appl
, 2000
"... Abstract. We discuss a multilinear generalization of the singular value decomposition. There is a strong analogy between several properties of the matrix and the higherorder tensor decomposition; uniqueness, link with the matrix eigenvalue decomposition, firstorder perturbation effects, etc., are ..."
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Cited by 472 (22 self)
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Abstract. We discuss a multilinear generalization of the singular value decomposition. There is a strong analogy between several properties of the matrix and the higherorder tensor decomposition; uniqueness, link with the matrix eigenvalue decomposition, firstorder perturbation effects, etc., are analyzed. We investigate how tensor symmetries affect the decomposition and propose a multilinear generalization of the symmetric eigenvalue decomposition for pairwise symmetric tensors.
Multichannel Blind Identification: From Subspace to Maximum Likelihood Methods
 Proc. IEEE
, 1998
"... this paper is to review developments in blind channel identification and estimation within the estimation theoretical framework. We have paid special attention to the issue of identifiability, which is at the center of all blind channel estimation problems. Various existing algorithms are classified ..."
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Cited by 128 (2 self)
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this paper is to review developments in blind channel identification and estimation within the estimation theoretical framework. We have paid special attention to the issue of identifiability, which is at the center of all blind channel estimation problems. Various existing algorithms are classified into the momentbased and the maximum likelihood (ML) methods. We further divide these algorithms based on the modeling of the input signal. If input is assumed to be random with prescribed statistics (or distributions), the corresponding blind channel estimation schemes are considered to be statistical. On the other hand, if the source does not have a statistical description, or although the source is random but the statistical properties of the source are not exploited, the corresponding estimation algorithms are classified as deterministic. Fig. 2 shows a map for different classes of algorithms and the organization of the paper.
Statistical Tools for Digital Forensics
 In 6th International Workshop on Information Hiding
, 2004
"... A digitally altered photograph, often leaving no visual clues of having been tampered with, can be indistinguishable from an authentic photograph. As a result, photographs no longer hold the unique stature as a definitive recording of events. We describe several statistical techniques for detecting ..."
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Cited by 102 (11 self)
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A digitally altered photograph, often leaving no visual clues of having been tampered with, can be indistinguishable from an authentic photograph. As a result, photographs no longer hold the unique stature as a definitive recording of events. We describe several statistical techniques for detecting traces of digital tampering in the absence of any digital watermark or signature. In particular, we quantify statistical correlations that result from specific forms of digital tampering, and devise detection schemes to reveal these correlations.
Blind System Identification
, 1997
"... Blind system identification is a fundamental signal processing technology aimed to retrieve unknown information of a system from its output only. This technology has a wide range of possible applications such as mobile communications, speech reverberation cancellation and blind image restoration. Th ..."
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Cited by 47 (3 self)
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Blind system identification is a fundamental signal processing technology aimed to retrieve unknown information of a system from its output only. This technology has a wide range of possible applications such as mobile communications, speech reverberation cancellation and blind image restoration. This paper reviews a number of recently developed concepts and techniques for blind system identification which include the concept of blind system identifiability in a deterministic framework, the blind techniques of maximum likelihood and subspace for estimating the system's impulse response, and other techniques for direct estimation of the system input. Keywords: System identification, Blind techniques, Multichannels, Equalization, Source separation. This work has been supported by the Australian Research Council and the Australian Cooperative Research Center for Sensor Signal and Information Processing. y Currently with Motorola Australian Research Centre, 12 Lord Street, Botany 2019, ...
Identification and deconvolution of multichannel linear nonGaussian processes using higher order statistics and inverse filter criteria
 IEEE Trans. Signal Process
, 1997
"... Abstract—This paper is concerned with the problem of estimation and deconvolution of the matrix impulse response function of a multipleinput multipleoutput (MIMO) system given only the measurements of the vector output of the system. The system is assumed to be driven by a temporally i.i.d. and s ..."
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Cited by 47 (1 self)
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Abstract—This paper is concerned with the problem of estimation and deconvolution of the matrix impulse response function of a multipleinput multipleoutput (MIMO) system given only the measurements of the vector output of the system. The system is assumed to be driven by a temporally i.i.d. and spatially independent nonGaussian vector sequence (which is not observed). An iterative, inverse filter criteriabased approach is developed using the thirdorder or the fourthorder normalized cumulants of the inverse filtered data at zero lag. Stationary points of the proposed cost functions are investigated. The approach is input iterative, i.e., the input sequences are extracted and removed one by one. The matrix impulse response is then obtained by cross correlating the extracted inputs with the observed outputs. Identifiability conditions are analyzed. Strong consistency of the proposed approach is also briefly discussed. Computer simulation examples are presented to illustrate the proposed approaches. I.
Multichannel blind deconvolution of nonminimum phase systems using information backpropagation
 in: Proceedings of the Fifth International Conference on Neural Information Processing (ICONIP’99
, 1999
"... Abstract—In this paper, we present a new filter decomposition method for multichannel blind deconvolution of nonminimumphase systems. With this approach, we decompose a doubly finite impulse response filter into a cascade form of two filters: a causal finite impulse response (FIR) filter and an an ..."
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Cited by 21 (13 self)
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Abstract—In this paper, we present a new filter decomposition method for multichannel blind deconvolution of nonminimumphase systems. With this approach, we decompose a doubly finite impulse response filter into a cascade form of two filters: a causal finite impulse response (FIR) filter and an anticausal FIR filter. After introducing a Lie group to the manifold of FIR filters, we discuss geometric properties of the FIR filter manifold. Using the nonholonomic transform, we derive the natural gradient on the FIR manifold. By simplifying the mutual information rate, we present a very simple cost function for blind deconvolution of nonminimumphase systems. Subsequently, the natural gradient algorithms are developed both for the causal FIR filter and for the anticausal FIR filter. Simulations are presented to illustrate the validity and favorable learning performance of the proposed algorithms. Index Terms—Blind deconvolution, independent component analysis, natural gradient, nonmimimumphase systems. I.
Comparative Analysis of Evolving Software Systems Using the Gini Coefficient ∗
"... Software metrics offer us the promise of distilling useful information from vast amounts of software in order to track development progress, to gain insights into the nature of the software, and to identify potential problems. Unfortunately, however, many software metrics exhibit highly skewed, non ..."
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Cited by 20 (2 self)
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Software metrics offer us the promise of distilling useful information from vast amounts of software in order to track development progress, to gain insights into the nature of the software, and to identify potential problems. Unfortunately, however, many software metrics exhibit highly skewed, nonGaussian distributions. As a consequence, usual ways of interpreting these metrics — for example, in terms of “average” values — can be highly misleading. Many metrics, it turns out, are distributed like wealth — with high concentrations of values in selected locations. We propose to analyze software metrics using the Gini coefficient, a higherorder statistic widely used in economics to study the distribution of wealth. Our approach allows us not only to observe changes in software systems efficiently, but also to assess project risks and monitor the development process itself. We apply the Gini coefficient to numerous metrics over a range of software projects, and we show that many metrics not only display remarkably high Gini values, but that these values are remarkably consistent as a project evolves over time. 1.
Subspace methods for blind estimation of timevarying FIR channels
 IEEE Trans. Signal Processing
, 1997
"... Novel linear algorithms are proposed in this paper for estimating timevarying FIR systems, without resorting to higher order statistics. The proposed methods are applicable to systems where each timevarying tap coefficient can be described (with respect to time) as a linear combination of a finite ..."
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Cited by 18 (0 self)
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Novel linear algorithms are proposed in this paper for estimating timevarying FIR systems, without resorting to higher order statistics. The proposed methods are applicable to systems where each timevarying tap coefficient can be described (with respect to time) as a linear combination of a finite number of basis functions. Examples of such channels include almost periodically varying ones (Fourier Series description) or channels locally modeled by a truncated Taylor series or by a wavelet expansion. It is shown that the estimation of the expansion parameters is equivalent to estimating the secondorder parameters of an unobservable FIR singleinputmanyoutput (SIMO) process, which are directly computed (under some assumptions) from the observation data. By exploiting this equivalence, a number of different blind subspace methods are applicable, which have been originally developed in the context of timeinvariant SIMO systems. Identifiability issues are investigated, and some illustrative simulations are presented.
Blind Channel Estimation and Data Detection Using Hidden Markov Models
 IEEE Trans. Signal Processing
, 1997
"... In this correspondence, we propose applying the hidden Markov models (HMM) theory to the problem of blind channel estimation and data detection. The BaumWelch (BW) algorithm, which is able to estimate all the parameters of the model, is enriched by introducing some linear constraints emerging from ..."
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Cited by 17 (1 self)
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In this correspondence, we propose applying the hidden Markov models (HMM) theory to the problem of blind channel estimation and data detection. The BaumWelch (BW) algorithm, which is able to estimate all the parameters of the model, is enriched by introducing some linear constraints emerging from a linear FIR hypothesis on the channel. Additionally, a version of the algorithm that is suitable for timevarying channels is also presented. Performance is analyzed in a GSM environment using standard test channels and is found to be close to that obtained with a nonblind receiver.