Adaptive subtraction results

Figure 8a shows the estimated primaries when the $\ell^2$-norm is used to compute the shaping filters. Figure 8b displays the estimated internal multiples. As expected, because of the 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 1D example. Now, in Figure 9, we see the beneficial effects of the $\ell^1$-norm. Figure 9a shows the estimated primaries and Figure 9b the estimated multiples. The noise subtracted almost perfectly matches the internal multiple model in Figure 6b, as anticipated.

 

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Figure 8 (a) The estimated primaries with the $\ell^2$-norm. (b) The estimated internal multiples with the $\ell^2$-norm. Ideally, (b) should look like Figure 6b, but it does not.

 

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Figure 9 (a) The estimated primaries with the $\ell^1$-norm. (b) The estimated internal multiples with the $\ell^1$-norm. Beside some edge-effects, (b) resembles closely Figure 6b. The adaptive subtraction worked very well.