<p>The Fast Factorized Back Pro jection (FFBP) algorithm is a computationally efficient </p><p>algorithm for image formation in a Very High Frequency Synthetic Aperture Radar (VHF </p><p>SAR) system. In this report an investigation of the feasibility of using an FPGA with a </p><p>hard CPU core to calculate the FFBP in real-time has been done. Two System on a Chip </p><p>designs for this task have been proposed for calculating the FFBP. A simplified version of </p><p>the FFBP has also been implemented in Matlab and used during this pro ject. The result </p><p>is that the computationally intensive parts, such as index generating and interpolation </p><p>calculations, should be implemented in the logic part of the FPGA and the CPU should </p><p>handle scheduling. This kind of modular system is easy to maintain and upgrade.</p>

The Fast Factorized Back Pro jection (FFBP) algorithm is a computationally efficient algorithm for image formation in a Very High Frequency Synthetic Aperture Radar (VHF SAR) system. In this report an investigation of the feasibility of using an FPGA with a hard CPU core to calculate the FFBP in real-time has been done. Two System on a Chip designs for this task have been proposed for calculating the FFBP. A simplified version of the FFBP has also been implemented in Matlab and used during this pro ject. The result is that the computationally intensive parts, such as index generating and interpolation calculations, should be implemented in the logic part of the FPGA and the CPU should handle scheduling. This kind of modular system is easy to maintain and upgrade.

Opportunities to use synthetic aperture radar (SAR) in scientific studies and military operations are expanding with the development of small SAR systems that can be operated on small unmanned air vehicles (UAV)s. While the nimble nature of small UAVs make them an attractive platform for many reasons, small UAVs are also more prone to deviate from a linear course due autopilot errors and external forces such as turbulence and wind. Thus, motion compensation and improved processing algorithms are required to properly focus the SAR images. The work of this dissertation overcomes some of the challenges and addresses some of the opportunities of operating SAR on small UAVs. Several contributions to SAR backprojection processing for UAV SARs are developed including: 1. The derivation of a novel SAR backprojection algorithm that accounts for motion during the pulse that is appropriate for narrow or ultra-wide-band SAR. 2. A compensation method for SAR backprojection to enable radiometrically accurate image processing. 3. The design and implementation of a real-time backprojection processor on a commercially available GPU that takes advantage of the GPU texture cache. 4. A new autofocus method that improves the image focus by estimating motion measurement errors in three dimensions, correcting for both amplitude and phase errors caused by inaccurate motion parameters. 5. A generalization of factorized backprojection, which we call the Dually Factorized Backprojection method, that factorizes the correlation integral in both slow-time and fast-time in order to efficiently account for general motion during the transmit of an LFM-CW pulse. Much of this work was conducted in support of the Characterization of Arctic Sea Ice Experiment (CASIE), and the appendices provide substantial contributions for this project as well, including: 1. My work in designing and implementing the digital receiver and controller board for the microASAR which was used for CASIE. 2. A description of how the GPU backprojection was used to improved the CASIE imagery. 3. A description of a sample SAR data set from CASIE provided to the public to promote further SAR research.

Factorized backprojection is a processing algorithm for reconstructing images from data collected by synthetic aperture radar (SAR) systems. Factorized backprojection requires less computation than conventional time-domain backprojection with little loss in accuracy for straight-line motion. However, its implementation is not as straightforward as direct backprojection. Further, implementing an azimuth window has been difficult in previous versions of factorized backprojection. This thesis provides a new, easily parallelizable formulation of factorized backprojection designed for both pulsed and linearly frequency modulated continuous wave (LFM-CW) stripmap SAR data. A method of easily implementing an azimuth window as part of the factorized backprojection algorithm is introduced. The approximations made in factorized backprojection are investigated and a detailed analysis of the corresponding errors is provided. We compare the performance of windowed factorized backprojection to direct backprojection for simulated and actual SAR data.

One of the main topics in the modern String Theory are the conjectured string/gauge (AdS/CFT) dualities. Proving such conjectures is extremely difficult since the gauge and string theory perturbative regimes do not overlap. In this perspective, the discovery of infinitely many conserved charges, i.e. the integrability, in the planar AdS/CFT has allowed us to reach immense progresses in understanding and confirming the duality.The first part of this thesis is focused on the gravity side of the AdS5/CFT4 duality: we investigate the quantum integrability of the type IIB superstring on AdS5 x S5. In the pure spinor formulation we analyze the operator algebra by computing the operator product expansion of the Maurer-Cartan currents at the leading order in perturbation theory. With the same approach at one loop order, we show the path-independence of the monodromy matrix which implies the charge conservation law, strongly supporting the quantum integrability of the string sigma-model. We also verify that the Lax pair field strength remains well-defined at one-loop order being free from UV divergences. The same string sigma-model is analyzed in the Green-Schwarz formalism in the near-flat-space (NFS) limit. Such a limit remarkably simplifies the string world-sheet action but still leaving interesting physics. We use the NFS truncation to show the factorization of the world-sheet S-matrix at one-loop order. This property defines a two-dimensional field theory as integrable: it is the manifestation of the higher conserved charges. Hence, we have explicitly checked their presence at quantum level. The second part is dedicated to the AdS4/CFT3 duality: in particular the type IIA superstring on AdS4 x CP3. We compute the leading quantum corrections to the string energies for string configurations with a large but yet finite angular momentum on CP3 and show that they match the conjectured all-loop Bethe Ansatz equations.

For sequences of related linear systems, the computation of a preconditioner for every system can be expensive. Often a fixed preconditioner is used, but this may not be effective as the matrix changes. This research examines the benefits of both reusing and recycling preconditioners, with special focus on ILUTP and factorized sparse approximate inverses and proposes an update that we refer to as a sparse approximate map or SAM update. Analysis of the residual and eigenvalues of the map will be provided. Applications include the Quantum Monte Carlo method, model reduction, oscillatory hydraulic tomography, diffuse optical tomography, and Helmholtz-type problems. / Master of Science

<p>Synthetic antenna aperture (SAR) is a pulses focusing airborne radar which can achieve high resolution radar image. A number of image process algorithms have been developed for this kind of radar, but the calculation burden is still heavy. So the image processing of SAR is normally performed “off-line”.</p><p>The Fast Factorized Back Projection (FFBP) algorithm is considered as a computationally efficient algorithm for image formation in SAR, and several applications have been implemented which try to make the process “on-line”.</p><p>CELL Broadband Engine is one of the newest multi-core-processor jointly developed by Sony, Toshiba and IBM. CELL is good at parallel computation and floating point numbers, which all fit the demands of SAR image formation.</p><p>This thesis is going to implement FFBP algorithm on CELL Broadband Engine, and compare the results with pre-projects. In this project, we try to make it possible to perform SAR image formation in real-time.</p>

Synthetic antenna aperture (SAR) is a pulses focusing airborne radar which can achieve high resolution radar image. A number of image process algorithms have been developed for this kind of radar, but the calculation burden is still heavy. So the image processing of SAR is normally performed “off-line”. The Fast Factorized Back Projection (FFBP) algorithm is considered as a computationally efficient algorithm for image formation in SAR, and several applications have been implemented which try to make the process “on-line”. CELL Broadband Engine is one of the newest multi-core-processor jointly developed by Sony, Toshiba and IBM. CELL is good at parallel computation and floating point numbers, which all fit the demands of SAR image formation. This thesis is going to implement FFBP algorithm on CELL Broadband Engine, and compare the results with pre-projects. In this project, we try to make it possible to perform SAR image formation in real-time.