Nonstationary pattern-based signal-noise separation using adaptive prediction-error filter

Discussion

We considered that the APEF can characterize the properties of data and treated the corresponding APEF as the pattern operator. Data pattern operator $\mathbf{D}$ and noise pattern operator $\mathbf{N}$ can be obtained by solving the corresponding APEF. Since APEF uses the shaping regularization constraint, there are two main parameters that affect the filter: one is the filter size, and the other is the smoothing radius (Liu et al., 2011). These two parameters are empirical, and they are related to the characteristics of the events, including spatial distribution, local slope, etc. We applied the pattern operators to the corresponding dataset and adjusted the parameters of the APEF by observing whether the corresponding data components were absorbed or not. For example, the noise component can be absorbed by using pattern operator $\mathbf{N}$ in the noise model ( $\mathbf{0} \approx \mathbf{Nn}$ ).