Quadtree BackProjection (QBP) is a fast space-time domain SAR imaging algorithm that performs an iterative fractional imaging process derived from a divide and conquer strategy. Although the original derivation was based on the intuitive idea of approximating standard backprojection, the algorithm did not have an analytical justification. Furthermore, the QBP has a complicated internal structure, so the actual implementation usually has significant processing overhead. This thesis provides a mathematical analysis of the quadtree backprojection algorithm and also provides several variations of the QBP algorithm that improve its implementation. A Fourier transform analysis has been performed on the SAR data spectrum that is associated with QBP, in order to show that quadtree backprojection is equivalent to an iterative subband decomposition of the SAR data spectrum. Finally, several variations of QBP have been studied: multiresolution imaging, sensor array linearization, multiradix decompositions, and the fast QBP. Each of these has been developed to provide less complicated and more flexible implementations or to provide other imaging capabilities. Finally, the QBP algorithm has been extended to two related application areas: medical tomographic backprojection and delay-sum beamforming.
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