Adaptive subtraction results

Figure a shows the estimated primaries when the $\ell^2$ norm is used to compute the shaping filters. Figure b displays the estimated internal multiples. As expected, because of the local amplitude differences between the signal (primaries) and the noise (multiples), the adaptive subtraction fails and we retrieve the behavior explained in the preceding section with the 1-D example. Now, in Figure , we see the beneficial effects of the $\ell^1$ norm. Figure a shows the estimated primaries and Figure b the estimated multiples. The noise subtracted matches very well the internal multiple model in Figure b, as anticipated. Note that with this dataset, $\alpha$ had to be changed to $\alpha=max\vert{\bf d}\vert/1000$.

 

comp-diffL1L2
Figure 9 (a) The difference between the exact multiples (Figure b) and the subtracted multiples with the $\ell^2$ norm. (b) The difference between the exact multiples (Figure b) and the subtracted multiples with the $\ell^1$ norm.

As a final comparison, Figure displays the difference between the internal-multiple model (Figure b) and the subtracted multiples with the two norms. The $\ell^1$ norm (Figure b) matches the multiple model much better than the $\ell^2$ norm (Figure a).