Theory and practice of interpolation in the pyramid domain

Parameter estimation

One of the most important parameters in our algorithm is the sampling in the pyramid domain. We find that for interpolating irregularly-spaced data, half of the value of $\delta u$ given in equation 11 is usually enough. For interpolating aliased data, however, the sampling becomes more difficult to establish. In this case, the sampling becomes smaller as the maximum non-aliased frequency becomes smaller. In practice, we tend to find the right sampling by trial and error, starting from the value we would use for the irregularly-spaced data case. This approach is unsatisfying and we feel that more work should be done to automate this important parameter selection.