197 research outputs found
Blind Source Separation of Overdetermined Linear-Quadratic Mixtures
ISBN 978-3-642-15994-7, SoftcoverInternational audienceThis work deals with the problem of source separation in overdetermined linear-quadratic (LQ) models. Although the mixing model in this situation can be inverted by linear structures, we show that some simple independent component analysis (ICA) strategies that are often employed in the linear case cannot be used with the studied model. Motivated by this fact, we consider the more complex yet more robust ICA framework based on the minimization of the mutual information. Special attention is given to the development of a solution that be as robust as possible to suboptimal convergences. This is achieved by defining a method composed of a global optimization step followed by a local search procedure. Simulations confirm the effectiveness of the proposal
Differential fast fixed-point algorithms for underdetermined instantaneous and convolutive partial blind source separation
This paper concerns underdetermined linear instantaneous and convolutive
blind source separation (BSS), i.e., the case when the number of observed mixed
signals is lower than the number of sources.We propose partial BSS methods,
which separate supposedly nonstationary sources of interest (while keeping
residual components for the other, supposedly stationary, "noise" sources).
These methods are based on the general differential BSS concept that we
introduced before. In the instantaneous case, the approach proposed in this
paper consists of a differential extension of the FastICA method (which does
not apply to underdetermined mixtures). In the convolutive case, we extend our
recent time-domain fast fixed-point C-FICA algorithm to underdetermined
mixtures. Both proposed approaches thus keep the attractive features of the
FastICA and C-FICA methods. Our approaches are based on differential sphering
processes, followed by the optimization of the differential nonnormalized
kurtosis that we introduce in this paper. Experimental tests show that these
differential algorithms are much more robust to noise sources than the standard
FastICA and C-FICA algorithms.Comment: this paper describes our differential FastICA-like algorithms for
linear instantaneous and convolutive underdetermined mixture
A Blind Source Separation Method for Chemical Sensor Arrays based on a Second-order mixing model
International audienceIn this paper we propose a blind source separation method to process the data acquired by an array of ion-selective electrodes in order to measure the ionic activity of different ions in an aqueous solution. While this problem has already been studied in the past, the method presented differs from the ones previously analyzed by approximating the mixing function by a second-degree polynomial, and using a method based on the differential of the mutual information to adjust the parameter values. Experimental results, both with synthetic and real data, suggest that the algorithm proposed is more accurate than the other models in the literature
Theoretical Studies and Algorithms Regarding the Solution of Non-invertible Nonlinear Source Separation
International audienceIn this paper, we analyse and solve a source separation problem based on a mixing model that is nonlinear and non-invertible at the space of mixtures. The model is relevant considering it may represent the data obtained from ion-selective electrode arrays. We apply a new approach for solving the problems of local stability of the recurrent network previously used in the literature, which allows for a wider range of source concentration. In order to achieve this, we utilize a second-order recurrent network which can be shown to be locally stable for all solutions. Using this new network and the priors that chemical sources are continuous and smooth, our proposal performs better than the previous approach
Overdetermined independent vector analysis
We address the convolutive blind source separation problem for the
(over-)determined case where (i) the number of nonstationary target-sources
is less than that of microphones , and (ii) there are up to
stationary Gaussian noises that need not to be extracted. Independent vector
analysis (IVA) can solve the problem by separating into sources and
selecting the top highly nonstationary signals among them, but this
approach suffers from a waste of computation especially when . Channel
reductions in preprocessing of IVA by, e.g., principle component analysis have
the risk of removing the target signals. We here extend IVA to resolve these
issues. One such extension has been attained by assuming the orthogonality
constraint (OC) that the sample correlation between the target and noise
signals is to be zero. The proposed IVA, on the other hand, does not rely on OC
and exploits only the independence between sources and the stationarity of the
noises. This enables us to develop several efficient algorithms based on block
coordinate descent methods with a problem specific acceleration. We clarify
that one such algorithm exactly coincides with the conventional IVA with OC,
and also explain that the other newly developed algorithms are faster than it.
Experimental results show the improved computational load of the new algorithms
compared to the conventional methods. In particular, a new algorithm
specialized for outperforms the others.Comment: To appear at the 45th International Conference on Acoustics, Speech,
and Signal Processing (ICASSP 2020
Sparse and Non-Negative BSS for Noisy Data
Non-negative blind source separation (BSS) has raised interest in various
fields of research, as testified by the wide literature on the topic of
non-negative matrix factorization (NMF). In this context, it is fundamental
that the sources to be estimated present some diversity in order to be
efficiently retrieved. Sparsity is known to enhance such contrast between the
sources while producing very robust approaches, especially to noise. In this
paper we introduce a new algorithm in order to tackle the blind separation of
non-negative sparse sources from noisy measurements. We first show that
sparsity and non-negativity constraints have to be carefully applied on the
sought-after solution. In fact, improperly constrained solutions are unlikely
to be stable and are therefore sub-optimal. The proposed algorithm, named nGMCA
(non-negative Generalized Morphological Component Analysis), makes use of
proximal calculus techniques to provide properly constrained solutions. The
performance of nGMCA compared to other state-of-the-art algorithms is
demonstrated by numerical experiments encompassing a wide variety of settings,
with negligible parameter tuning. In particular, nGMCA is shown to provide
robustness to noise and performs well on synthetic mixtures of real NMR
spectra.Comment: 13 pages, 18 figures, to be published in IEEE Transactions on Signal
Processin
Exploitation of source nonstationarity in underdetermined blind source separation with advanced clustering techniques
The problem of blind source separation (BSS) is
investigated. Following the assumption that the time-frequency
(TF) distributions of the input sources do not overlap, quadratic
TF representation is used to exploit the sparsity of the statistically
nonstationary sources. However, separation performance is shown
to be limited by the selection of a certain threshold in classifying
the eigenvectors of the TF matrices drawn from the observation
mixtures. Two methods are, therefore, proposed based on recently
introduced advanced clustering techniques, namely Gap statistics
and self-splitting competitive learning (SSCL), to mitigate the
problem of eigenvector classification. The novel integration of
these two approaches successfully overcomes the problem of artificial
sources induced by insufficient knowledge of the threshold and
enables automatic determination of the number of active sources
over the observation. The separation performance is thereby
greatly improved. Practical consequences of violating the TF orthogonality
assumption in the current approach are also studied,
which motivates the proposal of a new solution robust to violation
of orthogonality. In this new method, the TF plane is partitioned
into appropriate blocks and source separation is thereby carried
out in a block-by-block manner. Numerical experiments with
linear chirp signals and Gaussian minimum shift keying (GMSK)
signals are included which support the improved performance of
the proposed approaches
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