14,326 research outputs found
New Negentropy Optimization Schemes for Blind Signal Extraction of Complex Valued Sources
Blind signal extraction, a hot issue in the field of communication signal processing, aims to retrieve the sources through the optimization of contrast functions. Many contrasts based on higher-order statistics such as kurtosis, usually behave sensitive to outliers. Thus, to achieve robust results, nonlinear functions are utilized as contrasts to approximate the negentropy criterion, which is also a classical metric for non-Gaussianity. However, existing methods generally have a high computational cost, hence leading us to address the problem of efficient optimization of contrast function. More precisely, we design a novel “reference-based” contrast function based on negentropy approximations, and then propose a new family of algorithms (Alg.1 and Alg.2) to maximize it. Simulations confirm the convergence of our method to a separating solution, which is also analyzed in theory. We also validate the theoretic complexity analysis that Alg.2 has a much lower computational cost than Alg.1 and existing optimization methods based on negentropy criterion. Finally, experiments for the separation of single sideband signals illustrate that our method has good prospects in real-world applications
A general framework for online audio source separation
We consider the problem of online audio source separation. Existing
algorithms adopt either a sliding block approach or a stochastic gradient
approach, which is faster but less accurate. Also, they rely either on spatial
cues or on spectral cues and cannot separate certain mixtures. In this paper,
we design a general online audio source separation framework that combines both
approaches and both types of cues. The model parameters are estimated in the
Maximum Likelihood (ML) sense using a Generalised Expectation Maximisation
(GEM) algorithm with multiplicative updates. The separation performance is
evaluated as a function of the block size and the step size and compared to
that of an offline algorithm.Comment: International conference on Latente Variable Analysis and Signal
Separation (2012
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
Overlearning in marginal distribution-based ICA: analysis and solutions
The present paper is written as a word of caution, with users of
independent component analysis (ICA) in mind, to overlearning
phenomena that are often observed.\\
We consider two types of overlearning, typical to high-order
statistics based ICA. These algorithms can be seen to maximise the
negentropy of the source estimates. The first kind of overlearning
results in the generation of spike-like signals, if there are not
enough samples in the data or there is a considerable amount of
noise present. It is argued that, if the data has power spectrum
characterised by curve, we face a more severe problem, which
cannot be solved inside the strict ICA model. This overlearning is
better characterised by bumps instead of spikes. Both overlearning
types are demonstrated in the case of artificial signals as well as
magnetoencephalograms (MEG). Several methods are suggested to
circumvent both types, either by making the estimation of the ICA
model more robust or by including further modelling of the data
A Primal-Dual Proximal Algorithm for Sparse Template-Based Adaptive Filtering: Application to Seismic Multiple Removal
Unveiling meaningful geophysical information from seismic data requires to
deal with both random and structured "noises". As their amplitude may be
greater than signals of interest (primaries), additional prior information is
especially important in performing efficient signal separation. We address here
the problem of multiple reflections, caused by wave-field bouncing between
layers. Since only approximate models of these phenomena are available, we
propose a flexible framework for time-varying adaptive filtering of seismic
signals, using sparse representations, based on inaccurate templates. We recast
the joint estimation of adaptive filters and primaries in a new convex
variational formulation. This approach allows us to incorporate plausible
knowledge about noise statistics, data sparsity and slow filter variation in
parsimony-promoting wavelet frames. The designed primal-dual algorithm solves a
constrained minimization problem that alleviates standard regularization issues
in finding hyperparameters. The approach demonstrates significantly good
performance in low signal-to-noise ratio conditions, both for simulated and
real field seismic data
Flexible methods for blind separation of complex signals
One of the main matter in Blind Source Separation (BSS) performed with a neural network approach is the choice of the nonlinear activation function (AF). In fact if the shape of the activation function is chosen as the cumulative density function (c.d.f.) of the original source the problem is solved.
For this scope in this thesis a flexible approach is introduced and the shape of the
activation functions is changed during the learning process using the so-called “spline functions”.
The problem is complicated in the case of separation of complex sources where there is the problem of the dichotomy between analyticity and boundedness of the complex activation functions. The problem is solved introducing the “splitting function” model as activation function. The “splitting function” is a couple of “spline function” which wind off the real and the imaginary part of the complex activation function, each of one depending from the real and imaginary variable.
A more realistic model is the “generalized splitting function”, which is formed by a couple of two bi-dimensional functions (surfaces), one for the real and one for
the imaginary part of the complex function, each depending by both the real and imaginary part of the complex variable.
Unfortunately the linear environment is unrealistic in many practical applications.
In this way there is the need of extending BSS problem in the nonlinear environment: in this case both the activation function than the nonlinear distorting function are realized by the “splitting function” made of “spline function”.
The complex and instantaneous separation in linear and nonlinear environment allow us to perform a complex-valued extension of the well-known INFOMAX algorithm in several practical situations, such as convolutive mixtures, fMRI signal analysis and bandpass signal transmission.
In addition advanced characteristics on the proposed approach are introduced and deeply described. First of all it is shows as splines are universal nonlinear functions for BSS problem: they are able to perform separation in anyway. Then it is analyzed as the “splitting solution” allows the algorithm to obtain a phase recovery:
usually there is a phase ambiguity. Finally a Cramér-Rao lower bound for ICA is discussed.
Several experimental results, tested by different objective indexes, show the
effectiveness of the proposed approaches
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