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Higher-Order Statistics, 1997., Proceedings of the IEEE Signal Processing Workshop on

Date 21-23 July 1997

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  • Proceedings of the IEEE Signal Processing Workshop on Higher-Order Statistics

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    Freely Available from IEEE
  • Author index

    Page(s): 469 - 471
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    Freely Available from IEEE
  • Higher order moment detection of transients in measured shallow-water noise

    Page(s): 405 - 409
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    A comparison between second and fourth order moment detectors is made for three low frequency transient signals embedded in measured ambient shipping noise from a shallow-water area. Detector evaluations must be made over short periods of time because of the nonstationary nature of the noise. Results indicate that the fourth order moment detects better than the second order moment for the two nonGaussian transient signals, but not as well for the more Gaussian transient signal. This suggests that the fourth order moment detector be used in addition to the second order moment detector, rather than as a replacement. The results of detection simulations with independent Gaussian noise are given for comparison to the results with the measured shipping noise. The comparison indicates that gains for the fourth order moment detector over the second order moment detector are higher in the shipping noise than in the Gaussian noise for the two nonGaussian signals View full abstract»

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  • Inverter fed induction machine condition monitoring using the bispectrum

    Page(s): 67 - 71
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    This paper proposes the use of the unnormalised bispectrum as a signal processing tool for the diagnosis of inverter-fed induction machine fault conditions. Increasingly, induction machines are supplied from nonsinusoidal, variable speed sources which increases the complexity and magnitude of the machine cage vibration. In addition, contamination of the vibration signal from both known and unknown sources makes accurate fault detection more difficult. This paper addresses both issues, experimental results are presented and it is shown that the unnormalised bispectrum improves on the diagnostic capability of more conventional second order statistical measures View full abstract»

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  • Higher-order statistics for tissue characterization from ultrasound images

    Page(s): 72 - 76
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    We model tissue as a collection of point scatterers embedded in a uniform media, and show that the higher order statistics (HOS) of the scatterer spacing distribution can be estimated from digitized RF scan line segments and be used in obtaining tissue signatures. Based on our model for tissue microstructure, we estimate resolvable periodicity and correlations among non-periodic scatterers. Using higher-order statistics of the scattered signal, we define as tissue “color” a quantity that describes the scatterer spatial correlations, show how to estimate it from the higher-order correlations of the digitized RF scan line segments, and investigate its potential as a tissue signature View full abstract»

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  • Autoregressive modeling of lung sounds using higher-order statistics: estimation of source and transmission

    Page(s): 4 - 8
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    The use of higher-order statistics in an autoregressive modeling of lung sounds is presented resulting in a characterization of their source and transmission. The lung sound source in the airway is estimated using the prediction error of an all-pole filter based on higher-order statistics (AR-HOS), while the acoustic transmission through the lung parenchyma and chest wall is modeled by the transfer function of the same AR-HOS filter. The parametric bispectrum, using the estimated ai coefficients of the AR-HOS model, is also calculated to elucidate the frequency characteristics of the modeled system. The implementation of this approach on pre-classified lung sound segments in known disease conditions, selected from teaching tapes, was examined. Experiments have shown that a reliable and consistent with current knowledge estimation of lung sound characteristics can be achieved using this method, even in the presence of additive Gaussian noise View full abstract»

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  • Signal-dependent film grain noise removal and generation based on higher-order statistics

    Page(s): 77 - 81
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    In this paper, we propose a new noise filtering scheme that is based on higher-order statistics (HOS) for photographic images corrupted by signal-dependent film grain noise. In addition, reliable estimation of the noise parameter using HOS is proposed. This parameter estimation technique can be used to generate film grain noise which has applications in motion picture and television productions. Simulation results show that the proposed filter perform better than existing methods which are based on second-order statistics View full abstract»

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  • Improving the threshold performance of higher-order direction finding methods via pseudorandomly generated estimator banks

    Page(s): 285 - 289
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    A recently reported estimator bank approach (see IEEE SP Lett., vol.4, p.54, 1997) is extended below to the fourth-order direction finding algorithms. The essence of our approach is to exploit “parallel” underlying eigenstructure based estimators for removing the outliers and improving the direction finding performance in the threshold domain. The pseudorandomly generated weighted fourth-order MUSIC estimators are exploited as underlying techniques for estimator bank. Motivated by the superior performance and reduced computational complexity of beamspace and root modifications of the second-order eigenstructure techniques, beamspace root implementations of fourth-order MUSIC and fourth-order estimator bank are developed. Simulations show dramatical improvements of the threshold performance View full abstract»

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  • Robust time-frequency representations for signals in α-stable noise using fractional lower-order statistics

    Page(s): 415 - 419
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    Characterizing signals jointly in the time and frequency domains through time-frequency representations (TFRs) such as the Wigner-Ville distribution (WVD) is a natural extension of Fourier analysis and gives a more complete representation of signal behavior particularly in the case of non-stationary signals. In the presence of additive impulsive noise, TFRs quickly break down and any information about the desired signal is lost. To combat these effects, we propose in this paper a family of memoryless nonlinearities which have been shown to produce a signal autocorrelation statistic which is well-behaved in the presence of stable noise. The result of this approach is a TFR which is both robust and simple to implement, and has many of the mathematical properties associated with the standard WVD. We illustrate the improvement in performance that can be obtained with several examples View full abstract»

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  • On the modeling of network traffic and fast simulation of rare events using α-stable self-similar processes

    Page(s): 268 - 272
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    We present a new model for aggregated network traffic based on α-stable self-similar processes which captures the burstiness and the long range dependence of the data. We show how the fractional Gaussian noise assumption fails and why our proposed model fits well by comparing real and synthesized network traffic. In addition, we show that we can speed up the simulation times for estimation of rare event probabilities, such as cell losses in ATM switches, by up to three orders of magnitude using α-stable modeling and importance sampling View full abstract»

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  • Detection of a common non-Gaussian signal in two sensors using the bootstrap

    Page(s): 463 - 467
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    Tugnait (1993) has used the cross bispectrum to detect non-Gaussian signals common to two sensors when the noise in each sensor is either mutually independent or has vanishing bispectra. However the detection methods presented assume enough data are available for asymptotic results to apply. If this assumption is not valid then the performance of the detection methods will be degraded. In this paper we propose a detection scheme based on the bootstrap that handles the small data size case. Unlike other bispectrum based techniques, the proposed scheme maintains the nominal test level while achieving high power. Simulation examples are given and the performance of the bootstrap based method is compared with a method proposed by Tugnait View full abstract»

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  • Adaptive separation of an unknown number of sources

    Page(s): 295 - 299
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    The problem of separation of mixed sources is addressed in this paper. To solve this problem, at least as many observations as sources are needed. In particular, the number of sources can be unknown. The separation system is a linear network updated with a stochastic descent algorithm to minimize some separation criterion. A first algorithm separates sources with positive kurtosises while a second one separates sources with negative kurtosises. For both, the performances are independent of the mixture. Besides, in the noisy case, when there are more sensors than sources, the additional outputs merely generate noise View full abstract»

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  • Second-order statistics versus HOS for the estimation of harmonics in additive and multiplicative noise

    Page(s): 122 - 126
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    Second-order statistics (SOS) have been widely used for the detection and estimation of coherent sinusoids in additive wide-band noise. This paper addresses the detection and estimation of harmonics which have been corrupted by both multiplicative and additive noise, HOS are useful in estimating harmonics of zero mean amplitude where SOS generally fail. The paper analyses and compares the performance of SOS and HOS when the harmonic has both coherent and non-coherent powers. We determine thresholds on the coherent-to-non-coherent sine wave power ratio which delimitate the regions of optimality of SOS and HOS. Gaussian as well as non-Gaussian noise sources are studied View full abstract»

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  • MUSICs and Cramer-Rao bound in fourth-order cumulant domain

    Page(s): 290 - 294
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    A unifying asymptotic performance analysis of a class of MUSIC algorithms for direction-of-arrival (DOA) estimation in fourth-order cumulant domain (FOCD-MUSIC) is presented in this paper. A simple and explicit formula for the asymptotic variances of DOA estimation by FOCD-MUSIC's is given. The Cramer-Rao bound for DOA estimation in fourth-order cumulant domain (FOCD-CRB) is also derived. The performances of three typical FOCD-MUSICs and the conventional covariance-based MUSIC are compared. It is shown that the FOCD-MUSICs are inefficient and they are not superior to the conventional MUSIC algorithm in any case. Nevertheless, the FOCD-MUSICs outperform the conventional MUSIC with reduced variances and improved robustness when the spatial sources are closely spaced and the signal-to-noise ratios (SNRs) are relatively low. Simulations are included to validate the analytical results View full abstract»

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  • Higher-order statistics of natural images and their exploitation by operators selective to intrinsic dimensionality

    Page(s): 147 - 151
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    Natural images contain considerable statistical redundancies beyond the level of second-order correlations. To identify the nature of these higher-order dependencies, we analyze the bispectra and trispectra of natural images. Our investigations reveal substantial statistical dependencies between those frequency components which are aligned to each other with respect to orientation. We argue that operators which are selective to local intrinsic dimensionality can optimally exploit such redundancies. We also show that the polyspectral structure we find for natural images helps to understand the hitherto unexplained superiority of orientation-selective filter decompositions over isotropic schemes like the Laplacian pyramid. However any essentially linear scheme can only partially exploit this higher-order redundancy. We therefore propose nonlinear i2D-selective operators which exhibit close resemblance to hypercomplex and end-stopped cells in the visual cortex. The function of these operators can be interpreted as a higher-order whitening of the input signal View full abstract»

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  • Fourier series based nonminimum phase model for second- and higher-order statistical signal processing

    Page(s): 395 - 399
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    In the paper, a parametric Fourier series based model (FSBM) for or as an approximation to an arbitrary nonminimum-phase linear time-invariant (LTI) system is proposed for statistical signal processing applications where a model for LTI systems is needed. Based on the FSBM, a (minimum-phase) linear prediction error (LPE) filter for amplitude estimation of the unknown LTI system together with the Cramer Rao (CR) bounds is presented. Then an iterative algorithm for obtaining the optimum mean-square LPE filter with finite data is presented which is also an approximate maximum likelihood algorithm when the data are Gaussian. Then three iterative algorithms using higher-order statistics with finite non-Gaussian data are presented for estimating parameters of the FSBM followed by some simulation results to support the efficacy of the proposed algorithms. Finally, we draw some conclusions View full abstract»

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  • Linear algebraic approaches for (almost) periodic moving average system identification

    Page(s): 112 - 116
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    This paper addresses the problem of (almost) periodic moving average (APMA) system identification. Two normal equations are established by using time varying higher order cumulants of the measurements, from which two new linear algebraic algorithms are presented for parameter estimation. Simulation examples are given to demonstrate the performance of these new approaches View full abstract»

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  • Blind separation of sources applied to convolutive mixtures in shallow water

    Page(s): 340 - 343
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    In underwater acoustics, the signal received by sensors is a mixture of different elementary sources, filtered by the environment. In blind separation of sources, we can isolate each source from different mixtures of sources without any a priori information, except for assuming statistical independence of the different sources. Jutten and Herault (1991) proposed a neuromimetic solution to the problem. In our work, we use this solution to separate convolutive mixtures of simulated complex underwater signals in a shallow water environment. To allow multipath identification a whitening step has to be introduced. We propose a local whitening procedure that does not impact the separated signal output and preserves the signal characteristics. This promising technique can be improved using non causal whitening filters more adapted to the target environment View full abstract»

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  • Covariance of finite-sample cumulants in array-processing

    Page(s): 306 - 310
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    In this paper we provide explicit formulas for the covariances of second-third-, and fourth-order sample cumulants as used in narrowband array processing. These covariances provide a basis for analysing the performance of cumulant based algorithms for finite-sample length, which is in contrast to usual asymptotic performance analyses. The use of these formulas, which consist of several thousand terms, will be demonstrated, and a rough idea of their applicability to a performance analysis for finite numbers of samples will be given View full abstract»

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  • TDE, DOA and related parameter estimation problems in impulsive noise

    Page(s): 273 - 277
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    We address the problem of time-delay estimation (TDE) and direction-of-arrival (DOA) estimation in the presence of symmetric alpha-stable noise. We show that these problems can be handled by conventional correlation or cumulant based techniques, provided that the noisy signals are first passed through a generic zero-memory non-linearity. This pre-processing is also useful in the detection context. We also address the problem of blind linear system identification, where the input is an iid alpha-stable process; we show that consistent estimates of the possibly non-minimum phase ARMA parameters can be obtained by using self-normalized correlations and cumulants. Theoretical arguments are supported by simulations View full abstract»

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  • Near-field localization using inverse filter criteria-based blind separation and cumulant matching

    Page(s): 300 - 304
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    This paper is concerned with the problem of near-field source localization. The problem is tackled using the method of blind separation of independent signals (sources) from their linear instantaneous (memoryless) mixtures. The various signals are assumed to be zero-mean non-Gaussian but not necessarily linear or i.i.d. Approaches using higher-order cumulants are developed using the fourth-order normalized cumulants of the “beamformed” data. The instantaneous mixture matrix is obtained by cross-correlating the extracted inputs with the observed outputs. The first approach is source-extractive, i.e., the sources are extracted and cancelled one-by-one. The other approach is based upon cumulant matching of the estimated and model-based cumulants parametrized by the source parameters (range, bearing and cumulant). Illustrative simulation examples are provided View full abstract»

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  • Exploring lag diversity in the high-order ambiguity function for polynomial phase signals

    Page(s): 103 - 106
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    High-order ambiguity function (HAF) is an effective tool for retrieving coefficients of polynomial phase signals (PPS). The lag choice is dictated by conflicting requirements: a large lag improves estimation accuracy but drastically limits the range of the parameters that can be estimated. By using two (large) co-prime lags and solving linear Diophantine equations using the Euclidean algorithm, we are able to recover the PPS coefficients from aliased peak positions without-compromising the dynamic range and the estimation accuracy. Separating components of a multi-component PPS whose phase polynomials have very similar leading coefficients has been a challenging task, but can now be tackled easily with the two-lag approach. Numerical examples are presented to illustrate the effectiveness of our method View full abstract»

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  • Sampling jitter detection using higher-order statistics

    Page(s): 448 - 452
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    The spectrum of a signal subjected, to sampling jitter can be significantly different from the spectrum of the same signal sampled without jitter. The first part of the paper shows that the spectrum of a continuous Gaussian signal can be reconstructed from a combined use of the sampled (with jitter) signal second and fourth-order statistics. This spectral reconstruction is then used to detect the presence or absence of jitter in a sampled signal. A likelihood ratio detector based on the spectral corrective term is studied. It gives a reference to which suboptimal detectors can be compared View full abstract»

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  • Blind channel identification based on higher-order cumulant fitting using genetic algorithms

    Page(s): 184 - 188
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    A family of blind equalisation algorithms identifies a channel model based on a higher-order cumulant (HOC) fitting approach. Since HOC cost functions are multimodal, gradient search techniques require a good initial estimate to avoid converging to local minima. We present a blind identification scheme which uses genetic algorithms (GAs) to optimise a HOC cost function. Because GAs are efficient global optimal search strategies, the proposed method guarantees to find a global optimal channel estimate. A micro-GA implementation is adopted to further enhance computational efficiency. As is demonstrated in computer simulation, this GA based scheme is robust and accurate, and has a fast convergence performance View full abstract»

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  • Combination of HOS based blind equalization algorithms for use in mobile communications

    Page(s): 219 - 223
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    Mobile communication links require adaptive equalization with a fast rate of convergence while keeping computational effort at reasonable levels. In this paper we propose to combine known algorithms for blind equalization in order to exploit their desirable properties to reach this goal. A switching criterion is proposed which is based on the change in the equalizer impulse response between iterations of the adaption algorithm and may be used to detect changes of the channel impulse response. Algorithms under consideration include Godard's algorithm, stop-and-go algorithm, and tricepstrum equalization algorithm (TEA) View full abstract»

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