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Notes:
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Although sources in general nonlinear mixturm arc not separable iising only statistical
independence, a special and realistic case of nonlinear mixtnres, the post nonlinear
(PNL) mixture is separable choosing a suited separating system. Then, a natural approach is
based on the estimation of tho separating Bystem parameters by minimizing an indcpendence
criterion, like estimated mwce mutual information. This class of methods requires higher
(than 2) order statistics, and cannot separate Gaarsian sources. However, use of [weak) prior,
like source temporal correlation or nonstationarity, leads to other source separation Jgw
rithms, which are able to separate Gaussian sourra, and can even, for a few of them, works
with second-order statistics. Recently, modeling time correlated s011rces by Markov models,
we propose vcry efficient algorithms hmed on minimization of the conditional mutual information.
Currently, using the prior of temporally correlated sources, we investigate the fesihility
of inverting PNL mixtures with non-bijectiw non-liacarities, like quadratic functions. In this
paper, we review the main ICA and BSS results for riunlinear mixtures, present PNL models
and algorithms, and finish with advanced resutts using temporally correlated snu~sm |
