Properties and Computational Implications of Zero-Sheets

Abstract

The spectrum (i.e. Fourier transform) of a K-dimensional compact (i.e. of finite amplitude and size) image is characterised (up to an arbitrary complex constant) by its zero-sheet, which is the (2K-2)-dimensional surface whereon the spectrum vanishes in 2K-dimensional complex Fourier space (constructed by generalising each real Fourier coordinate to a complex variable) [1].