Blind Separation of Nonlinear Mixing Signals Using … IJVIPNS-IJENS.pdfestimating an orthonormal bases, 2) mapping the data into the subspace using this orthonormal bases, 3) applying
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International Journal of Video& Image Processing and Network Security IJVIPNS-IJENS Vol:09 No:10 27
Fig. 5. the original data are the first two signals on the top, the mixing data
are in the middle and the recovering data are in the last two rows
(a) (b) ( c)
Fig. 6. (a) scatter plot of the original data. (b) Scatter plot of the mixed data. (c) scatter plot of the estimated data
Experiment 4: In this experiment two speech signals with
length 30000 samples T
21 (T)]S (t)[SS(t) are used, the
nonlinear mixed is done using Equation (17). Fig. (7) shows
the original, the mixing and the estimating sources. Moreover,
the scattering plot of the original signals, the mixed signals
and the estimating signals are shown in Fig. (8).
))]()((sin[)(
)]()(tanh[)(
122
121
tStStX
tStStX
(17)
In this experiment a polynomial kernel equation (23) is used
as a kernel function but with degree 7, and 19 point
(v1,….,v19) is selected, so the dimension of ψx will be 19 ×
30000. When linear BSS is applied on ψx 19 different vectors
will be generated. The slow feature analysis is used to get 2 ×
30000 vectors from 19 × 20000 different vectors.
Fig. 7. the original data are the first two signals on the top, the mixing data
are in the middle and the recovering data are in the last two rows
(a) (b) ( c)
Fig. 8. (a) scatter plot of the original data. (b) Scatter plot of the mixed data. (c) scatter plot of the estimated data
VII. CONCLUDING REMARKS
In this paper, a novel hybrid scheme to solve the problem of
blind source separation in nonlinear mixing model (NL-BSS)
is proposed. The proposed hybrid scheme combines simply
the kernel-feature Spaces separation technique (KTDSEP) and
the principle of the slow feature analysis (SFA). The proposed
algorithm overcomes the drawback of the kernel base
nonlinear blind source separation algorithm (KTDSEP). The
slow feature analysis principle is used in selecting the n
separated signals from d output signals. Moreover, new
approach to construct the orthonormal bases by selecting the
bases points from the lowest frequency band in the wavelet
transformed is introduced. The advantage in performance of
HBSSA lays in the complexity reduction in the orthonormal
bases estimation process and the fast selection of the desired
signals from the output signals of the KTDSEP algorithm.
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