Convergence Analysis of Local Algorithms for Blind Deconvolution

            Scott Douglas and Andrzej Cichocki
            University of Utah, Dept. EE, USA,
     FRP Riken, Information Processing in the Brain, JAPAN

                          Abstract

In this paper, we analyze and extend a class of adaptive
networks for second-order blind decorrelation of instantaneous 
signal mixtures.  Firstly, we compare the performance of the 
decorrelation neural network employing global knowledge of
the adaptive coefficients in with a similar structure whose 
coefficients are adaptive via local output connections in
Through statistical analyses, the convergence behaviors and
stability bounds for the algorithms' step sizes are studied
and derived.  Secondly, we analyze the behaviors of 
locally-adaptive multilayer decorrelation networks 
and quantify their performances for poorly-conditioned signal
mixtures. Thirdly, we derive a robust locally-adaptive network 
structure based on  a posteriori output signals that
remains stable for any step size value.  Finally, we present
an extension of the locally-adaptive network for linear-phase
temporal and spatial whitening of multichannel signals.
Simulations verify the analyses and indicate the usefulness of the 
locally-adaptive networks for decorrelating signals in space and time.