On the Reconstruction of Regular Grids from Incomplete, Filtered or Unevenly Sampled Band-Limited Data

Abstract

This paper discusses some extensions and generalizations of Shannon’s sampling theorem and points out possible applications in geodesy. More specifically, it shows that, for band-limited signals, missing data can be recovered from the remaining data on incomplete, filtered, rotated, scaled and/or transposed grids without the need of employing extra interpolation functions. In geodesy, such signals can be terrain-corrected gravity anomalies, geoid undulations from satellite altimetry, airborne gravity measurements, etc. These techniques are also applicable when irregularly distributed data are used directly to produce results on regular grids. Besides the recovery of the missing values, general schemes can be developed for interpolating at arbitrary locations employing only the remaining values, i.e., without the need to recover the missing data first. The sensitivity of these procedures to errors due to truncation, data noise, and jitter is also discussed briefly.