Pattern recognition

As shown in Guitton (2003b), the estimated signal is given by:  

$${\bf \hat{s}} = ({\bf N'KN+}\epsilon^2{\bf S'KS})^{-1}{\bf N'KNd},$$ (3)

where ${\bf N}$ and ${\bf S}$ are the noise and signal prediction error filters (PEFs), respectively, ${\epsilon}$ a trade-off parameter and ${\bf K}$ a masking operator. The noise PEFs are estimated from the noise model. The signal PEFs are estimated with the Spitz approximation Guitton (2004). As we shall see later, the Spitz approximation works very well when the noise and signal are uncorrelated. 3D filters are estimated since they lead to the best multiple attenuation results Guitton (2003a, 2004).

For the following results, the filters size is 15 $\times$ 3 $\times$ 3 (the last number corresponds to the shot axis) and the patch size is 16 $\times$ 8 $\times$ 5. These numbers are identical for both noise and signal filters. With 3D filters, because of memory limitations, we cannot estimate the signal for a complete 2D line on one computer only. Therefore, we segment the 2D line into macro-patches of 50 successive shots. There is an overlap of 5 shots between adjacent macro-patches. Each macro-patch is processed on one node before being merged into the final file.