Signal Representation and the Nonlinear Property of Phase Images

This letter proposes a representation of pixel value in a phase image as a complex number, which implies that the phase image is a nonlinear field. Consequently, conventional linear filtering will not properly work. Local statistics filters (LSFs) are chosen as a special case of the signal-processing algorithm to show the significance of signal representation to filtering performance. First, relationships among various LSFs, namely, ordinary LSF, speckle LSF, and phasor LSF, are discussed. We found that they are related to each other, whose general form is a complex-valued LSF (CV-LSF). It is also realized that directional windowing for the CV-LSF is actually not required, which indicates that the complex-valued formulation (representation and algorithm) is the most suitable one for phase image filtering. We demonstrate that the linear filtering to a simulated complex-valued image and an actual interferometric synthetic aperture radar image will start to fail when the window size is subsequently enlarged due to the nonlinear nature of the phase image.