78,369 research outputs found
MISEP - Linear and Nonlinear ICA Based on Mutual Information
MISEP is a method for linear and nonlinear ICA, that is able to handle a large variety of situations. It is an extension of the well known INFOMAX method, in two directions: (1) handling of nonlinear mixtures, and (2) learning the nonlinearities to be used at the outputs. The method can therefore separate linear and nonlinear mixtures of components with a wide range of statistical distributions.
This paper presents the basis of the MISEP method, as well as experimental results obtained with it. The results illustrate the applicability of the method to various situations, and show that, although the nonlinear blind separation problem is ill-posed, use of regularization allows the problem to be solved when the nonlinear mixture is relatively smooth
Sparsity and adaptivity for the blind separation of partially correlated sources
Blind source separation (BSS) is a very popular technique to analyze
multichannel data. In this context, the data are modeled as the linear
combination of sources to be retrieved. For that purpose, standard BSS methods
all rely on some discrimination principle, whether it is statistical
independence or morphological diversity, to distinguish between the sources.
However, dealing with real-world data reveals that such assumptions are rarely
valid in practice: the signals of interest are more likely partially
correlated, which generally hampers the performances of standard BSS methods.
In this article, we introduce a novel sparsity-enforcing BSS method coined
Adaptive Morphological Component Analysis (AMCA), which is designed to retrieve
sparse and partially correlated sources. More precisely, it makes profit of an
adaptive re-weighting scheme to favor/penalize samples based on their level of
correlation. Extensive numerical experiments have been carried out which show
that the proposed method is robust to the partial correlation of sources while
standard BSS techniques fail. The AMCA algorithm is evaluated in the field of
astrophysics for the separation of physical components from microwave data.Comment: submitted to IEEE Transactions on signal processin
Tensor Decompositions for Signal Processing Applications From Two-way to Multiway Component Analysis
The widespread use of multi-sensor technology and the emergence of big
datasets has highlighted the limitations of standard flat-view matrix models
and the necessity to move towards more versatile data analysis tools. We show
that higher-order tensors (i.e., multiway arrays) enable such a fundamental
paradigm shift towards models that are essentially polynomial and whose
uniqueness, unlike the matrix methods, is guaranteed under verymild and natural
conditions. Benefiting fromthe power ofmultilinear algebra as theirmathematical
backbone, data analysis techniques using tensor decompositions are shown to
have great flexibility in the choice of constraints that match data properties,
and to find more general latent components in the data than matrix-based
methods. A comprehensive introduction to tensor decompositions is provided from
a signal processing perspective, starting from the algebraic foundations, via
basic Canonical Polyadic and Tucker models, through to advanced cause-effect
and multi-view data analysis schemes. We show that tensor decompositions enable
natural generalizations of some commonly used signal processing paradigms, such
as canonical correlation and subspace techniques, signal separation, linear
regression, feature extraction and classification. We also cover computational
aspects, and point out how ideas from compressed sensing and scientific
computing may be used for addressing the otherwise unmanageable storage and
manipulation problems associated with big datasets. The concepts are supported
by illustrative real world case studies illuminating the benefits of the tensor
framework, as efficient and promising tools for modern signal processing, data
analysis and machine learning applications; these benefits also extend to
vector/matrix data through tensorization. Keywords: ICA, NMF, CPD, Tucker
decomposition, HOSVD, tensor networks, Tensor Train
Separating a Real-Life Nonlinear Image Mixture
When acquiring an image of a paper document, the image printed on the back page sometimes shows through. The mixture of the front- and back-page images thus obtained is markedly nonlinear, and thus constitutes a good real-life test case for nonlinear blind source separation.
This paper addresses a difficult version of this problem, corresponding to the use of "onion skin" paper, which results in a relatively strong nonlinearity of the mixture, which becomes close to singular in the lighter regions of the images. The separation is achieved through the MISEP technique, which is an extension of the well known INFOMAX method. The separation results are assessed with objective quality measures. They show an improvement over the results obtained with linear separation, but have room for further improvement
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