A Wavelet Packet Model of Evoked Potentials

Raz, Jonathan; Dickerson, Linda W.; Turetsky, Bruce I.

doi:10.1006/brln.1998.2025

Cited by 32 publications

(14 citation statements)

References 34 publications

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“…The problem of estimating regression model parameters in the presence of contaminating errors with strong correlation between observations far apart from each other is now widespread in many diverse fields, simply because natural signals very commonly exhibit long-range dependence (see examples in physics, Cassandro and Jona-Lasinio, 1978), geophysics (FoufoulaGeorgiou and Kumar, 1994;Torrence and Compo, 1998;, electronics (Voss, 1979;Ziel, 1986), econometrics Jensen, 1994), electrophysiology (Goldberger et al, 1990;Raz et al, 1999), and imaging (Mallat, 1989;Lundahl et al, 1986;Krueger et al, 1996). In particular, there is some evidence to suggest that the error structure of functional magnetic resonance imaging (fMRI) time series may be complicated by long-range dependencies or, to put it another way, may be characterized by a 1/f-like power spectrum (Zarahn et al, 1997).…”

Section: Introductionmentioning

confidence: 99%

Wavelet-Generalized Least Squares: A New BLU Estimator of Linear Regression Models with 1/f Errors

Fadili

Bullmore

2002

NeuroImage

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Long-memory noise is common to many areas of signal processing and can seriously confound estimation of linear regression model parameters and their standard errors. Classical autoregressive moving average (ARMA) methods can adequately address the problem of linear time invariant, short-memory errors but may be inefficient and/or insufficient to secure type 1 error control in the context of fractal or scale invariant noise with a more slowly decaying autocorrelation function. Here we introduce a novel method, called wavelet-generalized least squares (WLS), which is (to a good approximation) the best linear unbiased (BLU) estimator of regression model parameters in the context of long-memory errors. The method also provides maximum likelihood (ML) estimates of the Hurst exponent (which can be readily translated to the fractal dimension or spectral exponent) characterizing the correlational structure of the errors, and the error variance. The algorithm exploits the whitening or Karhunen-Loé ve-type property of the discrete wavelet transform to diagonalize the covariance matrix of the errors generated by an iterative fitting procedure after both data and design matrix have been transformed to the wavelet domain. Properties of this estimator, including its Cramè r-Rao bounds, are derived theoretically and compared to its empirical performance on a range of simulated data. Compared to ordinary least squares and ARMA-based estimators, WLS is shown to be more efficient and to give excellent type 1 error control. The method is also applied to some real (neurophysiological) data acquired by functional magnetic resonance imaging (fMRI) of the human brain. We conclude that wavelet-generalized least squares may be a generally useful estimator of regression models in data complicated by long-memory or fractal noise. © 2002 Elsevier Science

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Section: Introductionmentioning

confidence: 99%

Wavelet-Generalized Least Squares: A New BLU Estimator of Linear Regression Models with 1/f Errors

Fadili

Bullmore

2002

NeuroImage

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“…These levels were considered sufficient to cover the dominant spectral content of the ABR waveform in dogs, previously shown by Kawasaki and Inada (1993) to be between 0 and 1500 Hz with peaks at approximately 200, 490, 850, and 1170 Hz. Further frequency band analyses using wavelet packet models such as that offered by (Raz et al, 1999) were not considered.…”

Section: Signal Processingmentioning

confidence: 99%

On the dual structure of the auditory brainstem response in dogs

Wilson

Bailey

Balke

et al. 2006

Clinical Neurophysiology

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Objective: To use the over-complete discrete wavelet transform (OCDWT) to further examine the dual structure of auditory brainstem response (ABR) in the dog. Methods: ABR waveforms recorded from 20 adult dogs at supra-threshold (90 and 70 dBnHL) and threshold (0-15 dBSL) levels were decomposed using a six level OCDWT and reconstructed at individual scales (frequency ranges) A6 (0-391 Hz), D6 (391-781 Hz), and D5 (781-1563 Hz). Results: At supra-threshold stimulus levels, the A6 scale (0-391 Hz) showed a large amplitude waveform with its prominent wave corresponding in latency with ABR waves II/III; the D6 scale (391-781 Hz) showed a small amplitude waveform with its first four waves corresponding in latency to ABR waves I, II/III, V, and VI; and the D5 scale (781-1563 Hz) showed a large amplitude, multiple peaked waveform with its first six waves corresponding in latency to ABR waves I, II, III, IV, V, and VI. At threshold stimulus levels (0-15 dBSL), the A6 scale (0-391 Hz) continued to show a relatively large amplitude waveform, but both the D6 and D5 scales (391-781 and 781-1563 Hz, respectively) now showed relatively small amplitude waveforms. Conclusions: A dual structure exists within the ABR of the dog, but its relative structure changes with stimulus level. Significance: The ABR in the dog differs from that in the human both in the relative contributions made by its different frequency components, and the way these components change with stimulus level.

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“…Among the most popular methods for EP decomposition, one will find Principal Component Analysis (PCA) [2], Independent Component Analysis (ICA) [3], [4] or wavelet-based analysis [5]. In general, a common way to represent real-valued EPs can be based upon a linear superposition of some basis functions (i.e.…”

Section: Introductionmentioning

confidence: 99%

“…components). Bases such as wavelets can provide a very useful representation of some signals, however, they have serious limitations in terms of the number as well as the characteristics of the basis functions they employ [5], [6].…”

Section: Introductionmentioning

confidence: 99%

Evolutionary Algorithms and Rough Sets-Based Hybrid Approach to Classificatory Decomposition of Cortical Evoked Potentials

Smolinski

Boratyn

Milanova

et al. 2002

Rough Sets and Current Trends in Computing

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Abstract. This paper presents a novel approach to decomposition and classification of rat's cortical evoked potentials (EPs). The decomposition is based on learning of a sparse set of basis functions using Evolutionary Algorithms (EAs). The basis functions are generated in a potentially overcomplete dictionary of the EP components according to a probabilistic model of the data. Compared to the traditional, statistical signal decomposition techniques, this allows for a number of basis functions greater than the dimensionality of the input signals, which can be of a great advantage. However, there arises an issue of selecting the most significant components from the possibly overcomplete collection. This is especially important in classification problems performed on the decomposed representation of the data, where only those components that provide a substantial discernibility between EPs of different groups are relevant. In this paper, we propose an approach based on the Rough Set theory's (RS) feature selection mechanisms to deal with this problem. We design an EA and RS-based hybrid system capable of signal decomposition and, based on a reduced component set, signal classification.

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A Wavelet Packet Model of Evoked Potentials

Cited by 32 publications

References 34 publications

Wavelet-Generalized Least Squares: A New BLU Estimator of Linear Regression Models with 1/f Errors

Wavelet-Generalized Least Squares: A New BLU Estimator of Linear Regression Models with 1/f Errors

On the dual structure of the auditory brainstem response in dogs

Evolutionary Algorithms and Rough Sets-Based Hybrid Approach to Classificatory Decomposition of Cortical Evoked Potentials

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