Abstract
On-line adaptive learning algorithms for cancellation of additive, convolutive noise from linear mixtures of sources with a simultaneous blind source separation are developed. Associated neural network architectures are proposed. A simple convolutive noise model is assumed, i.e. the unknown additive noise in each channel is a (FIR) filtering version of environmental noise, where some convolutive reference noise is measurable. Two approaches are considered: in the first, the noise is cancelled from the linear mixture of source signals as pre-processing, after that the source signals are separated; in the second, both source separation and additive noise cancellation are performed simultaneously. Both steps consist of adaptive learning processes. By computer simulation experiments, it was found that the first approach is applicable for a large amount of noise, whereas in the second approach, a considerable increase of the convergence speed of the separation process can be achieved. Performance and validity of the proposed approaches are demonstrated by extensive computer simulations.
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Abbreviations
- Symbol :
-
Meaning
- κ 4 :
-
normalised kurtosis of a signal
- η(t),\(\tilde \eta \) t :
-
learning rates
- m :
-
number of sources
- n :
-
number of sensors
- N,M :
-
order of the FIR filters
- s(t) :
-
m-dimensional vector of (unknown) source signals
- x(t) :
-
n-dimensional vector of mixed signals (sensors)
- y(t) :
-
n-dimensional vector of separated output signals (estimated sources)
- v R(t):
-
(unknown) primary environment noise signal
- n R(t):
-
secondary reference noise signal
- n(t) :
-
n-dimensional vector of additive noise signals
- f(·),g(·) :
-
activation functions in separation rule
- f R(·):
-
activation function in noise cancellation rule
- A=[a ij]m×n :
-
(unknown) mixing matrix
- B=[b ij]n×N :
-
additive noise generation matrix
- H(t)=[h ij]n×M :
-
noise cancellation matrix
- W(t)=[w ij]n×n :
-
global de-mixing matrix
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Kasprzak, W., Cichocki, A. & Amari, S. Blind source separation with convolutive noise cancellation. Neural Comput & Applic 6, 127–141 (1997). https://doi.org/10.1007/BF01413824
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DOI: https://doi.org/10.1007/BF01413824