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| Nonstationarity: patching | |
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signoi
Figure 12. The input signal is on the left. Next is that signal with noise added. Next, for my favorite value of epsilon=1., is the estimated signal and the estimated noise. |
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Before I discovered helix preconditioning,
Ray Abma found that different results were obtained when the
fitting goal was cast in terms of 
instead of 
.
Theoretically it should not make any difference.
Now I believe that with preconditioning, or even without it,
if there are enough iterations,
the solution should be independent
of whether the fitting goal is cast with either
or
.
Figure 13 shows the result of experimenting with
the choice of 
.
As expected, increasing
weakens
and increases
.
When
is too small,
the noise is small and
the signal is almost the original data.
When
is too large,
the signal is small and
coherent events are pushed into the noise.
(Figure 13
rescales both signal and noise images for the clearest display.)
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signeps
Figure 13. Left is an estimated signal-noise pair where epsilon=4 has improved the appearance of the estimated signal but some coherent events have been pushed into the noise. Right is a signal-noise pair where epsilon=.25, has improved the appearance of the estimated noise but the estimated signal looks no better than original data. |
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Notice that the leveling operators
and 
were both estimated
from the original signal and noise mixture
shown in Figure 12.
Presumably we could do even better if we were to reestimate
and
from the estimates
and
in Figure 13.
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| Nonstationarity: patching | |
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