Phase recovery for 3D SAR range focusing

Abstract

The problem of calibrating Synthetic Aperture Radar (SAR) data for 3D image formation will be investigated here. A source of errors in modern radar systems is inaccurate range estimations, during the data collection. This is caused by two ambiguities in the platform location and the scene topography map. Such range estimation errors induce some asynchronization in the dechirping process, i.e. a shift in the range direction. When such an error is small, the final image will be blurred and possibly compensated using conventional autofocus techniques. In multipass SAR image formation, this error between the passes is large and we need a different machinery to correct it. We formulate the problem of SAR pulse compression with the range estimation error, in a general setting. The range estimation error appears as some structured phase error in the phase history. We then introduce a new phase recovery technique for compensating the phase error. Some simulation results show the capabilities of the introduced method. The main principle of SAR systems is to generate a synthetic aperture, using a moving platform and collect the pulse information from different spacial locations. The accurate knowledge of location of the platform and the scene topography is the necessary part of a high resolution SAR image formation. However, none of these two information are precisely known for various reasons, including an inaccuracy of the navigation systems and the imaging of an unknown area. The conventional approach to calibrate the location information is to use some reference targets with the ground truth information about their locations. While such techniques are generally successful, such reference targets may not exist in the real experiments or the precise location is unknown. As a result, many digital focusing techniques, i.e. called the autofocus techniques, have been proposed, including Phase Gradient Algorithm (PGA) [1], map drift [2], [3] and sparsity based autofocus [4], [5] techniques. In these techniques, we often assume a small aperture, a far-field setting and/or small errors [6]. As a result, such techniques have limitations in the wide-angle, with a large error and possibly digitally chipped SAR image [7]. Particularly, any autofocus techniques, based on the single phase error per pulse model, i.e. the most frequent approach for single pass SAR autofocus, cannot correctly compensate the range error, when it is larger than A/16, where A is the wavelenght [6], [8]. 3D-SAR imaging needs a new set of autofocus techniques which incorporates the multipass nature of the trials [9], to compensate relatively larger range errors [7]. The most intuitive approach is to extend the prominent point autofocus techniques to a three-dimensional setting [10]. This approach needs to have a single dominant bright target in the scene to aligned the pulses with respect to the range compressed peaks. An extension of such a technique is to use multiple Quad-Trihedral (QT) corner reflectors to correct the location of the platform [11]. Another approach is to use a parametric frequency domain linear filter and adaptively find the parameters [8], [12]. In this work, we reformulate the effect of the range estimation error, and show that such an error appears as a structured phase error in the phase history. We then tackle this problem by formulating it as a phase retrieval problem. Inspired by the Gerchberg-Saxton phase recovery algorithm, we introduce an easy range estimation error correction technique for multipass SAR imaging. We also discuss about the necessary and preferred settings which allow us to successfully recover the range estimation errors, in terms of phase errors. Some simulation results will be presented to demonstrate the success of the algorithm in a (controlled) synthetic and a real data experiment.