Multi-resolution analysis of polarimetric SAR data using wavelets

An analysis technique is presented for quantifying statistically and under a unified framework non-stationarity in polarimetric SAR imagery. The unified framework is provided by a multi-resolution analysis (MRA) based on a particular wavelet frame that works like a differential operator. The wavelet MRA provides local estimates of a statistics called structure function, that in turn can characterize two types of non-stationary behavior: smoothed singularities (e.g. edges, point targets); self-similar processes with stationary increments (e.g. fractional Brownian motion). In the polarimetric case we are interested in the combined dependencies on scale and polarization state. To the purpose an extension of the wavelet MRA is introduced for deriving wavelet representations of an intensity image synthesized at any polarization state (pol-MRA). A novel formalism called the polarimetric structure signature condenses in graphical form the properties of points of discontinuity with respect to scale and polarization transformations. A test case illustrates the application of the pol-MRA technique to the analysis of weak but polarimetrically diverse linear features embedded in clutter.