The computation of two-dimensional cepstra

Abstract

In this paper we shall explore two methods of computing the complex cepstrum of a two-dimensional (2-D) signal. The two principal methods for computing 1-D cepstra, using discrete Fourier transforms (DFT's) and the complex logarithm function or using a recursion relation for minimum-phase signals, may be extended to two dimensions. These two algorithms are developed and simple examples of their use are given. As a matter of course, we shall also be drawn into considering the definitions of 2-D causality and 2-D minimum-phase signals. In addition, we shall explore the relationship among the nonzero regions of a signal, its inverse, and its cepstrum.