Wigner distributions and ambiguity functions in image analysis

Abstract

The Wigner distribution of a two-dimensional image function has the form of a four-dimensional Fourier transform of a correlation product r(x1,x2,χ1,χ2) with respect to the spatial-shift variables χ1 and χ2. The corresponding ambiguity function has the form of the inverse Fourier transform of r(x1,x2,χ1,χ2) with respect to spatial variables x1 and x2. There exist dual definitions in the frequency domain (f1,f2,μ1,μ2), where μ 1, μ 2 are frequency-shift variables. The paper presents the properties of these distributions and describes applications for image analysis.