Signal processing issues in synthetic aperture radar and computer tomography

This dissertation addresses issues in the area of synthetic aperture radar (SAR) and computer tomography. SAR imaging is based on the synthesis of very long aperture using the relative motion between the radar and target. One of the recently developed algorithms is the {dollar}omega-k{dollar} algorithm, which was introduced using the concepts in geophysics. The signal processing involved in the original derivation of the algorithm was difficult to understand for the people in the signal processing community.; This difficulty led to our detailed investigation of the {dollar}omega-k{dollar} algorithm in a signal processing perspective. A derivation of the algorithm by finding the key Fourier relations and approximations was explored. It was shown both by analysis and numerical simulation that the algorithm may be inaccurate when the radar squint angle approaches 90 degrees.; Another study, motivated by the problem of imaging moving targets, involved the formulation of the displaced phase center antenna (DPCA) processing theory. When multiple antennas are used to make an image of a scene with moving targets, it was shown that the motion of the moving targets can be estimated and this information can be used to compensate for the effect of target motion in SAR images.; The inversion of acquired Fourier data in SAR and computer tomography is an important problem for accurate image formation. The possibility of using the direct Fourier inversion algorithms was investigated in SAR and tomography. It was shown that there is a possibility of better tomographic inversion algorithms than the popular convolution-backprojection method, and the difficulties in the implementation of the optimal algorithm was discussed.; Other work dealt with bandlimited signal interpolation. These studies involved designing a new interpolation algorithm, which is minimax optimal for the interpolation of bandlimited signals. Assuming a class of computationally efficient interpolators, a suboptimal interpolation algorithm was developed and it was shown that the new algorithm outperforms many other interpolators often used in practice. Then, the interpolation problem is formulated as a problem of statistical estimation. This study answers many questions regarding the choice of interpolator and regularization of the algorithm when the original data are noisy.