Complex signal representation, Mandel's theorem, and spiral phase quadrature transform

摘要

Complex (or analytic) signal representation as introduced by Gabor plays an important role in optical signal processing and in coherence theory of optical fields. Several definitions for extending the notion of complex signal representation to two dimensions have appeared in the literature. These definitions differ in their choice of the quadrature transform for a two-dimensional signal. We study the problem of determining the complex representation for two-dimensional real signals (or images) using a least-square minimization framework first used by Mandel [J. Opt. Soc. Am. 57, 613 (1967)]. In particular, we seek a suitable quadrature transform such that the resultant complex image has the least fluctuating envelope in an ensemble-averaged sense. It is observed that the spiral phase quadrature transform for two-dimensional signals is a solution of this analysis.