Study On Fast Back-Projection Algorithms For Airborne SAR Imaging

Synthetic aperture radar (SAR) is a powerful and well-established remote sensing technique. It is capable of working day and night under all-weather conditions, with the properties of long range, high resolution and wide illumination area, which improves the capability of radar in information acquisition. Currently, SAR has been widely used in civil applications, such as resource mapping, land or sea ice monitoring, oceans observation, persistent surveillance on shifting landforms, and also in military applications, such as battlefield reconnaissance and monitoring of military motion. With the development of SAR technology, more flexible beam steering, higher resolution and wider swath become more and more important for accurate SAR observation.Depending on flexible and accurate beam steering, SAR has been equipped with different operation modes, inculding stripmap SAR, spotlight SAR, sliding spotlight SAR, and Terrain Observation by Progressive Scans (TOPS) SAR, etc. Meantime, each operation mode can work in broadside-looking or squinted-looking configuration. Actually, different operation modes and configurations would produce radar echoes with different characteristics. As such, different imaging algorithms need to be developed. To solve the key problems in multi-mode imaging and motion compensation for airborne SAR, we manage to improve the applicability and efficiency of fast time-domain algorithms in this dissertation. The relevant work is supported by the National Science Foundation of China, the Doctoral Foundation and the "973" Program. The main content of this dissertation is summarized as follows.Chapter 2 involves basic imaging theory and reviews several typical SAR imaging algorithms. For each algorithm, its basic principles, key operations, advantages as well as disadvantages are discussed. Two different interpolation methods, namely Line-Of-Sight Polar Interpolation (LOSPI) and Stabilized Scene Polar Interpolation (SSPI), are introduced for resampling polar-formatted spectrum of squinted spotlight SAR. The mathematical expressions of resampled spectrum are derived. It is worth noting that, PFA shows a great vitality in high-resolution spotlight SAR, circular SAR and video SAR. Both LOSPI and azimuth focusing achieved in the Doppler domain serve as a foundation for PGA processing in the FFBP. Besides PFA, three BP-kind algorithms are introduced. The influence of APC position and topography on the quality of backprojected images are discussed. The operations count for each algorithm is then analyzed.Combined with the information recorded by GPS/INS, bulk of motion errors can be corrected in most practical applications. In high-resolution imaging occasions, however, even the most sophisticated motion measurement system may not be sufficient to ensure diffraction-limited SAR images and residual errors of the order several centimeters may still degrade image quality significantly. Therefore, image-based autofocus techniques are required for fast time-domain algorithms. To achieve this goal, Chapter 3 proposes some necessary modifications to the original FFBP. The main contributions of Chapter 3 are two-fold. Firstly, a line of sight (LOS) pseudo-polar coordinate system is employed as the imaging plane, which not only ensures the spread of azimuth impulse response function along the horizontal dimension, but also could provide an approximate Fourier transform relationship, which paves the way for the use of PGA. Secondly, overlapped-subaperture frame (OSF) in FFBP is built according to its multi-aperture characteristics. OSF is a bridge connecting original subaperture phase errors and a full-aperture phase error. Each desired subaperture phase error can be updated with its linear component according to the full-aperture phase error function. As phase correction is recursively performed, phase estimation tends to converge and the degraded image becomes refocused.Interpolation-based image fusion is recursively performed in the FFBP flow. However, interpolation operations inevitably induce approximate errors, leading to a poor image quality and low efficiency. To solve this problem, Chapter 4 presents an expediting back-projection (EBP) for high-resolution spotlight SAR. In EBP, a unified polar coordinate system is used to represent subimages, so that all the subimage spectra are located in the same wavenumber space. Instead of interpolation-based recursive fusion, a full aperture wavenumber spectrum is obtained by recombining subimage spectra. Since there is no interpolation but only fast Fourier transform (FFT) and circular shift, EBP could reduce the loss of image quality with a great improvement of the efficiency. The experimental results prove the superiority of EBP over FFBP on both precision and efficiency FFBP has shown great success in the spotlight SAR filed. However, its extension to stripmap SAR processing is not straightforward. Enlighted by Chapter 4, Chapter 5 revaluates the principle of FFBP from the wavenumber-spectrum perspective, and points out the limitations. The first one is integration aperture, and the second one is great computational burden generated by angular upsampling. To investigate the applicability of FFBP to stripmap SAR, Chapter 5 describes a reasonable implementation of overlapped-image method. Without angular upsampling, this method retains high efficiency of the original FFBP. Moreover, this method can be extended to sliding spotlight SAR and TOPS SAR imaging. In the end of Chapter 5, both the simulated SAR data and the real measured SAR data are utilized to demonstrate the performance of this method. Unitl now, signal processing of all different operation modes in linear aperture can be implemented by fast time-domain algorithms.In the previous chapters, we have succeeded in applying fast time-domain algorithms to the linear aperture cases. In Chapter 6, we perform imaging processing for circular SAR (CSAR), and present a circular EBP algorithm, namely CEBP. To avoid an extortionate angular sample rate, we divide the full synthetic aperture into 8 processed apertures. For each processed apertures, subaperture factorization, subimage formation and spectrum fusion need to be performed. Followed by a two-dimensional Fourier transform, the final CSAR image is obtained by coherently accumulating all processed-aperture images together. Without time-consuming interpolation operation, CEBP is capable of decreasing the loss of spectrum while improving the computational efficiency significantly. CEBP has the potential to provide resolution of approximately λ/4 when the information of a single pass is coherently added over 360°.