It is well known that for 1D signals, a dispersion relation or Hilbert transform can be written between the magnitude and phase of a bandlimited function, provided it satisfies the so-called minimum phase condition. This condition requires that the complex zeros of the bandlimited function lie in only one half of the complex plane. When this is not the case the Hilbert transform generates the incorrect phase. Extending this concept for two and higher dimensional signals is of great practical interest but has been limited by the fundamental differences that exist between the properties of one and higher dimensional entire functions. We examine these difference and identify some classes of properties that 2D functions should satisfy, in order to possess minimum phase properties.© (2003) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.