CONCLUSION AND FUTURE WORK

Pyramid transform is a new sampling scheme. It is based on Shannon's sampling theorem. Theoretically pyramid transform will not introduce error to the dataset. After the pyramid transform, we get a frequency-dependent grid. This new grid has a feature that $f\Delta x = const$. This feature makes the spatial prediction filter estimated in the pyramid domain frequency-independent. We apply this new sampling scheme to signal/noise separation. Our result shows that subsampling will not make the data more unpredictable. The subsampled data is even more predictable than the oversampled one. Pyramid scheme can eliminate low frequency noise, but it also hurts the signal as well. We will continue this project and try to get better results.