Accurate, fast and stable denoising source separation algorithms

8

a: gamma update

b: denoising function

Fig. 2. Speedup tests. a) Effects of spectral shift and step-size adaptation on conver-
gence speed. The leftmost bar not fully shown. b) Average SNRs for different denoising
functions: variance whitening and tanh with and without smoothing.

5 Experiments

In this section, we show that the developed algorithms are fast, stable, accurate
and produce meaningful results. First, in Sec. 5.1, we demonstrate the different
spectral shifts and step-size adaptation. Then the accuracy of different denoising
algorithms is tested with artificial data (Sec. 5.2). Finally, we demonstrate the
separation capability and convergence speed of the variance-based-denoising in
real MEG data (Sec. 5.3).

5.1 Speedup comparison

In Sec. 3, we reviewed two spectral shifts that can accelerate convergence in
DSS algorithms. Later in the section, we proposed two additional methods to
adapt these spectral shifts to increase stability. In this section, we compare these
adaptive-spectral-shift methods together with the stability improvements in de-
flatory separation. The data consists of M = 50 channels and T = 8192 time
samples of rhythmic magnetoencephalograms (MEG) [6, 1]. The data was pre-
processed as in [1] to enhance weak phenomena. Simple f(s) = s - tanh s was
used as the denoising function. DSS was run to extract 30 components from this
data and average number of iterations was calculated. To be fair for all the meth-
ods, each of them was run until convergence, where the angle between old and
new projection vectors (w and w_new) was less than 0.0001^o. We then measured
the number of iterations that had taken w within 0.1^o of the final solution.

The results are shown in Fig. 2a. Both types of spectral shift and γ adap-
tation always accelerated convergence. Convergence without any speedups took
on average more than 1500 iterations. Without γ adaptation, the FastICA-type
scheme (8) converged faster on average than the fixed-shift scheme (7), but γ
adaptation reversed the situation. Standard FastICA used about 50% more it-
erations than the best method.

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