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Title:
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Inverting Monotonic Nonlinearities by Entropy Maximization
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Author:
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Solé-Casals, Jordi; Lopez-de-Ipiña, Karmele; Caiafa, Cesar F.
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Other authors:
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Universitat de Vic - Universitat Central de Catalunya. Grup de Recerca en Tractament de Dades i senyals |
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Notes:
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This paper proposes a new method for blind inversion of a monotonic nonlinear map
applied to a sum of random variables. Such kinds of mixtures of random variables are
found in source separation and Wiener system inversion problems, for example. The importance
of our proposed method is based on the fact that it permits to decouple the estimation
of the nonlinear part (nonlinear compensation) from the estimation of the linear one (source
separation matrix or deconvolution filter), which can be solved by applying any convenient
linear algorithm. Our new nonlinear compensation algorithm, the MaxEnt algorithm, generalizes
the idea of Gaussianization of the observation by maximizing its entropy instead. We
developed two versions of our algorithm based either in a polynomial or a neural network
parameterization of the nonlinear function. We provide a sufficient condition on the nonlinear
function and the probability distribution that gives a guarantee for the MaxEnt method to
succeed compensating the distortion. Through an extensive set of simulations, MaxEnt is
compared with existing algorithms for blind approximation of nonlinear maps. Experiments
show that MaxEnt is able to successfully compensate monotonic distortions outperforming
other methods in terms of the obtained Signal to Noise Ratio in many important cases, for
example when the number of variables in a mixture is small. Besides its ability for compensating
nonlinearities, MaxEnt is very robust, i.e. showing small variability in the results.
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Subject(s):
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-Tractament del senyal |
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Rights:
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Aquest document està subjecte a aquesta llicència Creative Commons
http://creativecommons.org/licenses/by/4.0/
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Document type:
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Article
info:eu-repo/publishedVersion |
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Published by:
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Plos One
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