Random lines in a plane

INTERPOLATION

We'll need to know a wavelet in the time and space domain whose amplitude spectrum is $\sqrt{k_r}$ (so its power spectrum is $k_r$). Do not mistake this for the the helix derivative (Claerbout, 1998) whose power spectrum is $k_r^2$. What we need to use here is the square root of the helix derivative. Let the (unknown) wavelet with amplitude spectrum $\sqrt{k_r}$ be known as $G$.

1. Apply $G$ to the data. The prior spectrum of the modified data is now white.
2. Estimate the PEF of the modified data.
3. The interpolation filter for the original data is now $G$ times the PEF of the modified data.

Why is this more efficient? The important point is that the PEF should estimate the minimal practical number of freely adjustable parameters. If $G$ is a function that is lengthy in time or space, then the PEF does not need to be.

How important is this extra statistical efficiency? I don't know.

Random lines in a plane