Part I: Various image reconstruction algorithms used for subsurface targets are reviewed. It is shown how some approximate wavefield inversion techniques: Stripmap Synthetic Aperture Radar (SAR), Kirchhoff Migration (KM) and Frequency-Wavenumber (FK) migration are developed from various models for wavefield scattering. The similarities of these techniques are delineated both from a theoretical and practical perspective and it is shown that Stripmap SAR is, computationally, almost identical to FK migration. A plane wave interpretation of both Stripmap SAR and FK migration is used to show why they are so similar. The electromagnetic assumptions made in the image reconstruction algorithms are highlighted. In addition, it is shown that, theoretically, FK and KM are identical. Image reconstruction results for KM, Stripmap SAR and FK are shown for both synthetic and experimental Ground Penetrating Radar (GPR) data. Subjectively the reconstructed images show little difference, but computationally, Stripmap SAR (and therefore, FK migration) are much more efficient. Part II: A preliminary investigation into the use of the Singularity Expansion Method (SEM) for use in identifying landmines is completed using a Finite-Difference Time-Domain code to simulate a simplified GPR system. The Total Least Squares Matrix Pencil Method (TLS-MPM) is used to determine the complex poles from an arbitrary late-time signal. Both dielectric and metallic targets buried in lossless and lossy half-spaces are considered. Complex poles (resonances) of targets change significantly when the objects are buried in an external medium, and perturbation formulae for Perfect Electric Conductor (PEC) and dielectric targets are highlighted and used. These perturbation formulae are developed for homogenous surrounding media, and their utilization for the half-space (layered medium) GPR problem causes inaccuracies in their predictions. The results show that the decay rate (real part) of the complex poles is not suitable for identification in this problem, but that with further research, the resonant frequency (imaginary part) of the complex poles shows promise as an identification feature. / February 2005

Part I: Various image reconstruction algorithms used for subsurface targets are reviewed. It is shown how some approximate wavefield inversion techniques: Stripmap Synthetic Aperture Radar (SAR), Kirchhoff Migration (KM) and Frequency-Wavenumber (FK) migration are developed from various models for wavefield scattering. The similarities of these techniques are delineated both from a theoretical and practical perspective and it is shown that Stripmap SAR is, computationally, almost identical to FK migration. A plane wave interpretation of both Stripmap SAR and FK migration is used to show why they are so similar. The electromagnetic assumptions made in the image reconstruction algorithms are highlighted. In addition, it is shown that, theoretically, FK and KM are identical. Image reconstruction results for KM, Stripmap SAR and FK are shown for both synthetic and experimental Ground Penetrating Radar (GPR) data. Subjectively the reconstructed images show little difference, but computationally, Stripmap SAR (and therefore, FK migration) are much more efficient. Part II: A preliminary investigation into the use of the Singularity Expansion Method (SEM) for use in identifying landmines is completed using a Finite-Difference Time-Domain code to simulate a simplified GPR system. The Total Least Squares Matrix Pencil Method (TLS-MPM) is used to determine the complex poles from an arbitrary late-time signal. Both dielectric and metallic targets buried in lossless and lossy half-spaces are considered. Complex poles (resonances) of targets change significantly when the objects are buried in an external medium, and perturbation formulae for Perfect Electric Conductor (PEC) and dielectric targets are highlighted and used. These perturbation formulae are developed for homogenous surrounding media, and their utilization for the half-space (layered medium) GPR problem causes inaccuracies in their predictions. The results show that the decay rate (real part) of the complex poles is not suitable for identification in this problem, but that with further research, the resonant frequency (imaginary part) of the complex poles shows promise as an identification feature.

Part I: Various image reconstruction algorithms used for subsurface targets are reviewed. It is shown how some approximate wavefield inversion techniques: Stripmap Synthetic Aperture Radar (SAR), Kirchhoff Migration (KM) and Frequency-Wavenumber (FK) migration are developed from various models for wavefield scattering. The similarities of these techniques are delineated both from a theoretical and practical perspective and it is shown that Stripmap SAR is, computationally, almost identical to FK migration. A plane wave interpretation of both Stripmap SAR and FK migration is used to show why they are so similar. The electromagnetic assumptions made in the image reconstruction algorithms are highlighted. In addition, it is shown that, theoretically, FK and KM are identical. Image reconstruction results for KM, Stripmap SAR and FK are shown for both synthetic and experimental Ground Penetrating Radar (GPR) data. Subjectively the reconstructed images show little difference, but computationally, Stripmap SAR (and therefore, FK migration) are much more efficient. Part II: A preliminary investigation into the use of the Singularity Expansion Method (SEM) for use in identifying landmines is completed using a Finite-Difference Time-Domain code to simulate a simplified GPR system. The Total Least Squares Matrix Pencil Method (TLS-MPM) is used to determine the complex poles from an arbitrary late-time signal. Both dielectric and metallic targets buried in lossless and lossy half-spaces are considered. Complex poles (resonances) of targets change significantly when the objects are buried in an external medium, and perturbation formulae for Perfect Electric Conductor (PEC) and dielectric targets are highlighted and used. These perturbation formulae are developed for homogenous surrounding media, and their utilization for the half-space (layered medium) GPR problem causes inaccuracies in their predictions. The results show that the decay rate (real part) of the complex poles is not suitable for identification in this problem, but that with further research, the resonant frequency (imaginary part) of the complex poles shows promise as an identification feature.

Synthetic aperture radar (SAR) is a type of remote sensor that provides its own illumination and is capable of forming high resolution images of the reflectivity of a scene. The reflectivity of the scene that is measured is dependent on the choice of carrier frequency; different carrier frequencies will yield different images of the same scene. There are different modes for SAR sensors; two common modes are spotlight mode and stripmap mode. Furthermore, SAR sensors can either be continuously transmitting a signal, or they can transmit a pulse at some pulse repetition frequency (PRF). The work in this dissertation is for pulsed stripmap SAR sensors. The resolvable limit of closely spaced reflectors in range is determined by the bandwidth of the transmitted signal and the resolvable limit in azimuth is determined by the bandwidth of the induced azimuth signal, which is strongly dependent on the length of the physical antenna on the SAR sensor. The point-spread function (PSF) of a SAR system is determined by these resolvable limits and is limited by the physical attributes of the SAR sensor. The PSF of a SAR system can be defined in different ways. For example, it can be defined in terms of the SAR system including the image processing algorithm. By using this definition, the PSF is an algorithm-specific sinc-like function and produces the bright, star-like artifacts that are noticeable around strong reflectors in the focused image. The PSF can also be defined in terms of just the SAR system before any image processing algorithm is applied. This second definition of the PSF will be used in this dissertation. Using this definition, the bright, algorithm-specific, star-like artifacts will be denoted as the inter-pixel interference (IPI) of the algorithm. To be specific, the combined effect of the second definition of PSF and the algorithm-dependent IPI is a decomposition of the first definition of PSF. A new comprehensive forward model for stripmap SAR is derived in this dissertation. New image formation methods are derived in this dissertation that invert this forward model and it is shown that the IPI that corrupts traditionally processed stripmap SAR images can be removed. The removal of the IPI can increase the resolvability to the resolution limit, thus making image analysis much easier. SAR data is inherently corrupted by uncompensated phase errors. These phase errors lower the contrast of the image and corrupt the azimuth processing which inhibits proper focusing (to the point of the reconstructed image being unusable). If these phase errors are not compensated for, the images formed by system inversion are useless, as well. A model-based autofocus method is also derived in this dissertation that complements the forward model and corrects these phase errors before system inversion.

The Phase Gradient Autofocus (PGA) algorithm is widely used in spotlight mode SAR for motion compensation. The Maximum Likelihood PGA (ML PGA) algorithm has been shown to be a superior autofocus method. The PGA is restricted to high altitude aircraft. Since lower altitude SARs have significant range dependencies that cannot be ignored, the PGA could not be used. This thesis eliminates the high altitude restriction and extends the PGA for use with all spotlight SARs. The new algorithm is tested with three images. Each image has a unique quality. A desert image provides a low signal to clutter ratio with no distinct targets and the mountain image has areas with high signal-to-clutter and areas with low signal-to-clutter. Each image was corrupted with a low frequency and high frequency motion induced low altitude phase error. The new Phase Weighted Estimation (PWE) low altitude autofocus method converged to a lower standard deviation than the ML PGA, but required more iterations. Another limitation of the PGA is that it will only work for spotlight SAR. In this thesis, the spotlight PGA is extended to stripmap by using a conversion similar to spotlight mode. With the space frequency relationship an altered PGA is used to extend the PGA to stripmap mode SAR. The stripmap SAR, range dependant PGA allows for focusing of low altitude low cost stripmap SARs. The phase weighted estimation method is extended to range dependent stripmap. The stripmap mode estimator is most successful with high signal-to-noise images.