3D pyramid interpolation |
The pyramid domain was introduced by Ronen (Hung et al., 2005), and is a resampled representation of an ordinary - domain. Although it has frequency and space axes, the spatial sampling is different for different frequencies. This is attractive because we can use sparser sampling to adequately sample the data at lower frequencies, which makes uniform sampling for all frequencies unnecessary. Therefore in the pyramid domain, coarser grid spacing is used for lower frequencies, while finer spacing is used for higher frequencies. This makes it possible to capture the character of all frequency components of stationary events with only one PEF. So the information in the low frequency data can be better used to interpolate higher frequency data.
In this paper, I present a 3D version of data interpolation in the pyramid domain based on PEF estimation, which is based on Shen (2008). The paper is organized as follows: I first show the 3D pyramid transform and corresponding missing-data interpolation and PEF estimation. I then show synthetic data examples. Finally, I conclude with the advantages and disadvantages of this interpolation method.
3D pyramid interpolation |