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108
A Fast FixedPoint Algorithm for Independent Component Analysis of Complex Valued Signals
, 2000
"... Separation of complex valued signals is a frequently arising problem in signal processing. For example, separation of convolutively mixed source signals involves computations on complex valued signals. In this article it is assumed that the original, complex valued source signals are mutually statis ..."
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Cited by 133 (1 self)
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Separation of complex valued signals is a frequently arising problem in signal processing. For example, separation of convolutively mixed source signals involves computations on complex valued signals. In this article it is assumed that the original, complex valued source signals are mutually statistically independent, and the problem is solved by the independent component analysis (ICA) model. ICA is a statistical method for transforming an observed multidimensional random vector into components that are mutually as independent as possible. In this article, a fast xedpoint type algorithm that is capable of separating complex valued, linearly mixed source signals is presented and its computational efficiency is shown by simulations. Also, the local consistency of the estimator given by the algorithm is proved.
Complex independent component analysis of frequencydomain electroencephalographic data
, 2003
"... Independent component analysis (ICA) has proven useful for modeling brain and electroencephalographic (EEG) data. Here, we present a new, generalized method to better capture the dynamics of brain signals than previous ICA algorithms. We regard EEG sources as eliciting spatiotemporal activity patte ..."
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Cited by 67 (7 self)
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Independent component analysis (ICA) has proven useful for modeling brain and electroencephalographic (EEG) data. Here, we present a new, generalized method to better capture the dynamics of brain signals than previous ICA algorithms. We regard EEG sources as eliciting spatiotemporal activity patterns, corresponding to, e.g. trajectories of activation propagating across cortex. This leads to a model of convolutive signal superposition, in contrast with the commonly used instantaneous mixing model. In the frequencydomain, convolutive mixing is equivalent to multiplicative mixing of complex signal sources within distinct spectral bands. We decompose the recorded spectraldomain signals into independent components by a complex infomax ICA algorithm. First results from a visual attention EEG experiment exhibit: (1) sources of spatiotemporal dynamics in the data, (2) links to subject behavior, (3) sources with a limited spectral extent, and (4) a higher degree of independence compared to sources derived by standard ICA.
Dimensionality reduction in higherorder signal processing and rank(R_1,R__2,...,R_N) reduction in multilinear algebra
, 2004
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BiQuadratic Optimization over Unit Spheres and Semidefinite Programming Relaxations
, 2008
"... Abstract. This paper studies the socalled biquadratic optimization over unit spheres min x∈R n,y∈R m bijklxiyjxkyl ..."
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Cited by 32 (15 self)
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Abstract. This paper studies the socalled biquadratic optimization over unit spheres min x∈R n,y∈R m bijklxiyjxkyl
Blind Inversion of Wiener Systems
 IEEE Trans. on Signal Processing
, 1999
"... A system in which a linear dynamic part is followed by a nonlinear memoryless distortion, a Wiener system, is blindly inverted. This kind of systems can be modelised as a postnonlinear mixture, and using some results about these mixtures, an efficient algorithm is proposed. Results in a hard situati ..."
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Cited by 29 (9 self)
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A system in which a linear dynamic part is followed by a nonlinear memoryless distortion, a Wiener system, is blindly inverted. This kind of systems can be modelised as a postnonlinear mixture, and using some results about these mixtures, an efficient algorithm is proposed. Results in a hard situation are presented, and illustrate the efficiency of this algorithm. 1
2002. Variational Bayes for generalized autoregressive models
 IEEE Trans. Signal Processing
"... Abstract—We describe a variational Bayes (VB) learning algorithm for generalized autoregressive (GAR) models. The noise is modeled as a mixture of Gaussians rather than the usual single Gaussian. This allows different data points to be associated with different noise levels and effectively provides ..."
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Cited by 24 (0 self)
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Abstract—We describe a variational Bayes (VB) learning algorithm for generalized autoregressive (GAR) models. The noise is modeled as a mixture of Gaussians rather than the usual single Gaussian. This allows different data points to be associated with different noise levels and effectively provides robust estimation of AR coefficients. The VB framework is used to prevent overfitting and provides modelorder selection criteria both for AR order and noise model order. We show that for the special case of Gaussian noise and uninformative priors on the noise and weight precisions, the VB framework reduces to the Bayesian evidence framework. The algorithm is applied to synthetic and real data with encouraging results. Index Terms—Bayesian inference, generalized autoregressive models, model order selection, robust estimation. I.
Adaptive blind deconvolution of linear channels using Renyi entropy with Parzen windowing estimation
 IEEE Transactions on Signal Processing
, 2004
"... Abstract. Blind deconvolution of linear channels is a fundamental signal processing problem that has immediate extensions to multiplechannel applications. In this paper, we investigate the suitability of a class of Parzenwindowbased entropy estimates, namely Renyi’s entropy, as a criterion for bl ..."
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Cited by 16 (3 self)
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Abstract. Blind deconvolution of linear channels is a fundamental signal processing problem that has immediate extensions to multiplechannel applications. In this paper, we investigate the suitability of a class of Parzenwindowbased entropy estimates, namely Renyi’s entropy, as a criterion for blind deconvolution of linear channels. Comparisons between maximum and minimum entropy approaches, as well as the effect of entropy order, equalizer length, sample size, and measurement noise on performance, will be investigated through Monte Carlo simulations. The results indicate that this nonparametric entropy estimation approach outperforms the standard BellSejnowski and normalized kurtosis algorithms in blind deconvolution. In addition, the solutions using Shannon’s entropy were not optimal either for super or subGaussian source densities. I.
Variational bayes for generalised autoregressive models
 IEEE Trans. Signal Process
, 2002
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Higher Order Spectra Based Deconvolution of Utrasound Images
, 1995
"... We address the problem of improving the spatial resolution of ultrasound images through blind deconvolution. The ultrasound image formation process in the RF domaim can be expressed as a spatiotemporal convolution between the tissue response and the ultrasonic system response, plus additive noise. ..."
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Cited by 15 (2 self)
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We address the problem of improving the spatial resolution of ultrasound images through blind deconvolution. The ultrasound image formation process in the RF domaim can be expressed as a spatiotemporal convolution between the tissue response and the ultrasonic system response, plus additive noise. Convolutional components of the dispersive attenuation and aberrations introduced by propagating through the object being imaged are also incorporated in the ultrasonic system response. Our goal is to identify and remove the convolutional distortion in order to reconstruct the tissue response, thus enhancing the diagnostic quality of the ultrasonic image. Under the assumption of an independent, identically distributed, zeromean, nonGaussian tissue response, we were able to estimate djstortion kernels using bicepstrum operations on RF data. Separate 1D distortion kernels were estimated corresponding to axial and lateral image lines and used in the deconvolution pracess. The estimated axial kernels showed similarities to the experimentally measured pulseecho wavelet of the imaging system. Deconvolution results from Bscan images obtained with clinical imaging equipment showed a 2.55.2 times gain in lateral resolution, where the definition of the resolution has been based on the width of the autocovariance function of the image. The gain in axial resolution was found to be between 1.5 and 1.9.
Elsherbeni, “Detection and localization of rf radar pulses in noise environments using wavelet packet transform and higher order statistics
 Progress In Electromagnetics Research, PIER
, 2006
"... Abstract—Weak signal detection and localization are basic and important problems in radar systems. Radar performance can be improved by increasing the receiver output signaltonoise ratio (SNR). Localizing the received signal is an important task in the detection of signal in noise. Distorting the ..."
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Cited by 13 (0 self)
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Abstract—Weak signal detection and localization are basic and important problems in radar systems. Radar performance can be improved by increasing the receiver output signaltonoise ratio (SNR). Localizing the received signal is an important task in the detection of signal in noise. Distorting the localization of the received signal can leads to incorrect target range measurements. In this paper an algorithm is described for extracting and localizing an RF radar pulse from a noisy background. The algorithm combines two powerful tools: the wavelet packet analysis and higherorderstatistics (HOS). The use of the proposed technique makes detection and localization of RF radar pulses possible in very low signaltonoise ratio conditions, which leads to a reduction of the required microwave power or alternatively extending the detection range of radar systems. 1.