Topics in CT and SAR imaging: Fast back-projection algorithms and optimal antenna spacings

This dissertation addresses topics in the areas of synthetic aperture radar (SAR) and tomography. There are two different topics in the dissertation: fast back-projection algorithms for 2-D SAR imaging and for tomography, and optimal antenna spacings in interferometric SAR.; The study of the fast algorithms for SAR imaging is motivated by the recently proposed fast algorithm developed for computer tomography. We propose novel, fast algorithms of complexity O(N 2 log N) for both the far-field and the near-field SAR scenarios based on that. The performance of our new algorithms is demonstrated through simulation and is compared to other SAR image formation algorithms such as the FFT-based algorithm and the ω − k algorithm.; Furthermore, we extend the fast algorithm for parallel-beam to direct fan-beam tomographic reconstruction. The quality of the image generated by the O(N2 log N) fast fan-beam algorithm is comparable to that of the fast parallel-beam back-projection after rebinning. We also develop a fast Feldkamp algorithm for cone-beam 3-D reconstruction based on the fast fan-beam algorithm. It reduces the computational cost from O(N4) to O(N3 log N) and shows more promise in practice than do other fast Feldkamp algorithms.; Another study is motivated by the investigation of the phase unwrapping problem in 3-D SAR imaging. In this thesis, we study the optimal antenna spacings for pointwise terrain height estimation. In particular, we start from the maximum likelihood estimates of the terrain height. The ambiguous terrain height derived from any pair of antennas is modeled by a periodic waveform with each period having a Gaussian shape. For multiple pairs of antennas, the corresponding waveforms have different periods, which helps resolve the ambiguity. For the three-antenna case, a closed-form formula approximating the mean squared error (MSE) of the estimated terrain height is derived as a function of antenna spacing. By minimizing the MSE, we determine the optimal antenna spacing. The algorithm is tested with simulated data.