Phase-Scale Analysis of Complex-Valued SAR Images

The extraction of different parts of the spectrum from complex-valued synthetic aperture radar (SAR) images is equivalent to selecting a same number of low-resolution images, each of which is acquired using a sub-antenna. This subantenna can be viewed as a part of azimuth squint angle and a part of the range chirp bandwidth in the full synthetic aperture. Due to this process, which is also called sub-aperture extraction, it is not possible to apply traditional band-pass filters to complex-valued SAR images using modulated window-based multi-scale approaches (such as wavelet decomposition). Thus, in this paper we proposes the use of a chirplet-derived transform, that is, the fractional Fourier transform (FrFT), as an alternative scaling approach, where the scaling is carried out in phase. We also underline the physical significance of classical wavelet decomposition for complex-valued SAR images, demonstrating that this is equivalent to a modulated sub-aperture extraction or aspect angle filtering rather than shape filtering.