Solutions with non-zero initial estimates

When solving for the signal with equation () using an initial estimate of the signal being the data, the common event now appears in the calculated signal, as is seen in Figure . When solving for the noise with equation () using an initial estimate of the noise being the data, the common event now appears in the calculated noise, as seen in Figure .

 

separ7san Figure 5 The calculated signal and noise using an initial solution of the data for the signal.

 

separ7nas Figure 6 The calculated signal and noise using an initial solution of the data for the noise.

The initial estimates for the signal and noise are not limited to zero and the data. If there is no reason to believe that the data in the null space of the operators $\st S$ or $\st N$ should belong to either the noise or the data, a more symmetrical approach would be to use one-half the data as the initial estimates of both the signal and noise.

In real data, the separation between the signal operator $\st S$ and the noise operator $\st N$ is likely to be less clear than it is in these examples. True null spaces, where an event is completely zeroed, are less likely in the presence of noise. The separation of events that are suppressed by both filters, but not in the null space, is considered next.