Humans perceive the world in three dimensions, but many sensing capabilities only display two-dimensional information to users by way of images. In this work we develop two novel reconstruction techniques utilizing synthetic aperture radar (SAR) data in three dimensions given sparse amounts of available data. We additionally leverage a hybrid joint-sparsity and sparsity approach to remove a-priori influences on the environment and instead explore general imaging properties in our reconstructions. We evaluate the required sampling rates for our techniques and a thorough analysis of the accuracy of our methods. The results presented in this thesis suggest a solution to sparse three-dimensional object reconstruction that effectively uses a substantially less amount of phase history data (PHD) while still extracting critical features off an object of interest.

Inverse Synthetic Aperture Radar (ISAR) provides full-range detection and classification of sea-based and air-based targets through two-dimensional range-Doppler imaging. The Naval Postgraduate School (NPS) has developed a custom integrated circuit that can simulate false ISAR images in order to fool enemy ISAR platforms. To validate specific hardware choices within this design, this thesis explores the effect on image quality of an overflow occurring within the final 16-bit summation adder of this circuit, Three solutions to the problem of overflows are presented and analyzed. The logical extension of ISAR development, that of three-dimensional target imaging, is next presented through the discussion of 3D monopulse radar, 3D interferometer ISAR, and a 3D, three- receiver ISAR. The relative strengths of each approach are compared, along with both MATLAB and Extensible 3D (X3D) Graphics software models created for one specific 3D ISAR implementation. Through the superposition of 2D ISAR images it is shown how 3D ISAR images may be created. Moreover, emphasis is placed on using this knowledge to both enhance current 2D ISAR techniques and to modify the false-target chip design to handle 3D ISAR return signals. The thesis concludes with a study of Non-Uniform Rational 13-Splines, through which the X3D software model was created.

Describing a field that has been transformed by the recent availability of data from a new generation of space and airborne systems, the authors offer a synthetic geometrical approach to the description of synthetic aperture radar, one that addresses physicists, radar specialists, as well as experts in image processing.

Conventional synthetic aperture radar (SAR) offers high-resolution imaging of a target region in the range and cross-range dimensions along the ground plane. Little or no data are available in the range-altitude dimension, however, and target functions and models are limited to two-dimensional images. This thesis first investigates some existing methods for the computation of target reflectivity data in the deficient elevation domain, and a new method is then proposed for three-dimensional (3-D) SAR target feature extraction. Simulations are implemented to test the decoupled least-squares technique for high-resolution spectral estimation of target reflectivity, and the accuracy of the technique is assessed. The technique is shown to be sufficiently accurate at resolving targets in the third axis, but is limited in practicality due to restrictive requirements on the input data. An attempt is then made to overcome some of the practical limitations inherent in the current 3-D SAR methods by proposing a new technique based on the direct extraction of 3-D target features from arbitrary SAR image inputs. The radar shadow present in SAR images of MSTAR vehicle targets is extracted and used in conjunction with the radar beam depression angle to compute physical target heights along the range axis. Multiple inputs of elevation data are then merged to forge rough 3-D target models.