68,353 research outputs found
An Efficient Algorithm by Kurtosis Maximization in Reference-Based Framework
This paper deals with the optimization of kurtosis for complex-valued signals in the independent component analysis (ICA) framework, where source signals are linearly and instantaneously mixed. Inspired by the recently proposed reference-based contrast schemes, a similar contrast function is put forward, based on which a new fast fixed-point (FastICA) algorithm is proposed. The new optimization method is similar in spirit to the former classical kurtosis-based FastICA algorithm but differs in the fact that it is much more efficient than the latter in terms of computational speed, which is significantly striking with large number of samples. The performance of this new algorithm is confirmed through computer simulations
A Novel FastICA Method for the Reference-based Contrast Functions
This paper deals with the efficient optimization problem of Cumulant-based contrast criteria in the Blind Source Separation (BSS) framework, in which sources are retrieved by maximizing the Kurtosis contrast function. Combined with the recently proposed reference-based contrast schemes, a new fast fixed-point (FastICA) algorithm is proposed for the case of linear and instantaneous mixture. Due to its quadratic dependence on the number of searched parameters, the main advantage of this new method consists in the significant decrement of computational speed, which is particularly striking with large number of samples. The method is essentially similar to the classical algorithm based on the Kurtosis contrast function, but differs in the fact that the reference-based idea is utilized. The validity of this new method was demonstrated by simulations
Spectral analysis of stationary random bivariate signals
A novel approach towards the spectral analysis of stationary random bivariate
signals is proposed. Using the Quaternion Fourier Transform, we introduce a
quaternion-valued spectral representation of random bivariate signals seen as
complex-valued sequences. This makes possible the definition of a scalar
quaternion-valued spectral density for bivariate signals. This spectral density
can be meaningfully interpreted in terms of frequency-dependent polarization
attributes. A natural decomposition of any random bivariate signal in terms of
unpolarized and polarized components is introduced. Nonparametric spectral
density estimation is investigated, and we introduce the polarization
periodogram of a random bivariate signal. Numerical experiments support our
theoretical analysis, illustrating the relevance of the approach on synthetic
data.Comment: 11 pages, 3 figure
Simultaneous diagonalisation of the covariance and complementary covariance matrices in quaternion widely linear signal processing
Recent developments in quaternion-valued widely linear processing have
established that the exploitation of complete second-order statistics requires
consideration of both the standard covariance and the three complementary
covariance matrices. Although such matrices have a tremendous amount of
structure and their decomposition is a powerful tool in a variety of
applications, the non-commutative nature of the quaternion product has been
prohibitive to the development of quaternion uncorrelating transforms. To this
end, we introduce novel techniques for a simultaneous decomposition of the
covariance and complementary covariance matrices in the quaternion domain,
whereby the quaternion version of the Takagi factorisation is explored to
diagonalise symmetric quaternion-valued matrices. This gives new insights into
the quaternion uncorrelating transform (QUT) and forms a basis for the proposed
quaternion approximate uncorrelating transform (QAUT) which simultaneously
diagonalises all four covariance matrices associated with improper quaternion
signals. The effectiveness of the proposed uncorrelating transforms is
validated by simulations on both synthetic and real-world quaternion-valued
signals.Comment: 41 pages, single column, 10 figure
Complex Independent Component Analysis of Frequency-Domain Electroencephalographic Data
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 spatio-temporal 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 frequency-domain, convolutive
mixing is equivalent to multiplicative mixing of complex signal sources within
distinct spectral bands. We decompose the recorded spectral-domain signals into
independent components by a complex infomax ICA algorithm. First results from a
visual attention EEG experiment exhibit (1) sources of spatio-temporal 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.Comment: 21 pages, 11 figures. Added final journal reference, fixed minor
typo
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