Convolution Backprojection for SAR Image Formation

Convolution Back Projection (CBP) is an imaging algorithm, which can be applied to data gathered by a Synthetic Aperture Radar (SAR) system to produce high resolution images. The Mathematics of CBP was first studied in the context of tomographic image reconstruction for medical applications. CBP image processing has also been applied to a variety of other fields, such as seismic imaging, sonar, and radio astronomy. In terms of SAR image processing algorithms, CBP is far less efficient than direct Fourier Inversion Algorithms. The purpose of this thesis is to study the CBP algorithm as it is applied to SAR image formation. Specifically, thesis will provide the formulation of the CBP algorithm for a circular SAR geometry. The starting point for the development of this algorithm is a common radar wave model, which can be derived from Maxwells Equation’s

Point Spread Function Characterization of a Radially Displaced Scatterer Using Circular Synthetic Aperture Radar

This research effort investigated characterizing the point spread function (PSF) behavior of radially displaced point scatterers using circular synthetic aperture radar (CSAR). Thus far, research has been conducted to understand PSF of a scatterer located at the imaging scene center. An analytic closed-form solution has been derived assuming the scatterer is located at the origin of the CSAR imaging geometry. However, it is difficult to derive an analytic PSF solution for a scatterer that is radially displaced from the imaging scene center. Using the back projection image formation algorithm, PSF responses are generated at various point target locations. Consistent with previous studies, the three dimensional PSF for a point target located at the image center is cone shaped and serves as the basis for comparing and characterizing the PSFs of radially displaced scatterers. Simulated results show the impulse response of a radially displaced point scatterer is asymmetric and tends to exhibit increased ellipticity as it moves further from the scene center

Comparison of Image Processing Techniques Using Random Noise Radar

Radar imaging is a tool used by our military to provide information to enhance situational awareness for both war fighters on the front lines and military leaders planning and forming strategies from afar. Noise radar technology is especially exciting as it has properties of covertness as well as the ability to see through walls, foliage, and other types of cover. In this thesis, AFIT\u27s NoNet was used to generate images utilizing a random noise radar waveform as the transmission signal. The NoNet was arranged in four configurations: arc, line, cluster, and surround. Images were formed using three algorithms: multilateration and the SAR imaging techniques, convolution backprojection, and polar format algorithm. Each configuration was assessed based on image quality, in terms of its resolution, and computational complexity, in terms of its execution time. Experiments revealed tradeoffs between computational complexity and achieving fine resolutions. Depending on image size, the multilateration algorithm was approximately 6 to 35 faster than polar format and 16 to 26 times faster than convolution backprojection. Backprojection yielded images with resolutions up to approximately 11 times finer in range and 18 times finer in cross-range for the surround configuration, over multilateration images. Pixel size in polar format images made comparisons of resolution unusable. This thesis provides information on the performance of imaging algorithms given a configuration of nodes. The information will provide groundwork for future use of the AFIT NoNet as a covertly operating imaging radar in dynamic applications

Radar Image Processing and Its Applications Based on Convolution Back Projection

A general synthetic aperture radar (SAR) signal model is derived from the Maxwell’s equations, and a SAR image processing algorithm called Convolution Back Projection (CBP) will be introduced in this thesis, which can be applied to data gathered by a Synthetic Aperture Radar (SAR) system to produce high resolution images. The purpose of this thesis is starting from Maxwell’s equations to study the CBP algorithm as it is applied to SAR image processing. Two different image simulation results will be provided by this method

Frequency Diversity for Improving Synthetic Aperture Radar Imaging

In this work, a novel theoretical framework is presented for using recent advances in frequency diversity arrays (FDAs). Unlike a conventional array, the FDA simultaneously transmits a unique frequency from each element in the array. As a result, special time and space properties of the radiation pattern are exploited to improve cross-range resolution. The idealized FDA radiation pattern is compared with and validated against a full-wave electromagnetic solver, and it is shown that the conventional array is a special case of the FDA. A new signal model, based on the FDA, is used to simulate SAR imagery of ideal point mass targets and the new model is used to derive the impulse response function of the SAR system, which is rarely achievable with other analytic methods. This work also presents an innovative solution for using the convolution back-projection algorithm, the gold standard in SAR image processing, and is a significant advantage of the proposed FDA model. The new FDA model and novel SAR system concept of operation are shown to reduce collection time by 33 percent while achieving a 4.5 dB improvement in cross-range resolution as compared to traditional imaging systems

Implementation and Performance of Factorized Backprojection on Low-cost Commercial-Off-The-Shelf Hardware

Traditional Synthetic Aperture Radar (SAR) systems are large, complex, and expensive platforms that require significant resources to operate. The size and cost of the platforms limits the potential uses of SAR to strategic level intelligence gathering or large budget research efforts. The purpose of this thesis is to implement the factorized backprojection SAR image processing algorithm in the C++ programming language and test the code\u27s performance on a low cost, low size, weight, and power (SWAP) computer: a Raspberry Pi Model B. For a comparison of performance, a baseline implementation of filtered backprojection is adapted to C++ from pre-existing MATLAB® code. The factorized backprojection algorithm shows a computational improvement factor of 2-3 compared to filtered backprojection. Execution on a single Raspberry Pi is too slow for real-time imaging. However, factorized backprojection is easily parallelized, and we include a discussion of parallel implementation across multiple Pis

A comparison of spotlight synthetic aperture radar image formation techniques

Spotlight synthetic aperture radar images can be formed from the complex phase history data using two main techniques: (1) polar-to-cartesian interpolation followed by two-dimensional inverse Fourier transform (2DFFT), and (2) convolution backprojection (CBP). CBP has been widely used to reconstruct medical images in computer aided tomography, and only recently has been applied to form synthetic aperture radar imagery. It is alleged that CBP yields higher quality images because (1) all the Fourier data are used and (2) the polar formatted data is used directly to form a 2D Cartesian image and therefore 2D interpolation is not required. This report compares the quality of images formed by CBP and several modified versions of the 2DFFT method. We show from an image quality point of view that CBP is equivalent to first windowing the phase history data and then interpolating to an exscribed rectangle. From a mathematical perspective, we should expect this conclusion since the same Fourier data are used to form the SAR image. We next address the issue of parallel implementation of each algorithm. We dispute previous claims that CBP is more readily parallelizable than the 2DFFT method. Our conclusions are supported by comparing execution times between massively parallel implementations of both algorithms, showing that both experience similar decreases in computation time, but that CBP takes significantly longer to form an image

Display and Analysis of Tomographic Reconstructions of Multiple Synthetic Aperture LADAR (SAL) images

Synthetic aperture ladar (SAL) is similar to synthetic aperture radar (SAR) in that it can create range/cross-range slant plane images of the illuminated scatters; however, SAL has wavelengths 10,000x smaller than SAR enabling a relatively narrow real aperture, diffraction limited beam widths. The relatively narrow real aperture resolutions allow for multiple slant planes to be created for a single target with reasonable range/aperture combinations. These multiple slant planes can be projected into a single slant plane projections (as in SAR). It can also be displayed as a 3-D image with asymmetric resolutions, diffraction limited in the dimension orthogonal to the SAL baseline. Multiple images with diversity in angle orthogonal to SAL baselines can be used to synthesize resolution with tomographic techniques and enhance the diffraction limited resolution. The goal of this research is to explore methods to enhance the diffraction limited resolutions with multiple observations and/or multiple slant plane imaging with SAL systems. Specifically, metrics associated with the information content of the tomographic based 3 dimensional reconstructions of SAL intensity imagery will be investigated to see how it changes as a function of number of slant planes in the SAL images and number of elevation observations are varied

Factorized Geometrical Autofocus for Synthetic Aperture Radar Processing

Synthetic Aperture Radar (SAR) imagery is a very useful resource for the civilian remote sensing community and for the military. This however presumes that images are focused. There are several possible sources for defocusing effects. For airborne SAR, motion measurement errors is the main cause. A defocused image may be compensated by way of autofocus, estimating and correcting erroneous phase components. Standard autofocus strategies are implemented as a separate stage after the image formation (stand-alone autofocus), neglecting the geometrical aspect. In addition, phase errors are usually assumed to be space invariant and confined to one dimension. The call for relaxed requirements on inertial measurement systems contradicts these criteria, as it may introduce space variant phase errors in two dimensions, i.e. residual space variant Range Cell Migration (RCM). This has motivated the development of a new autofocus approach. The technique, termed the Factorized Geometrical Autofocus (FGA) algorithm, is in principle a Fast Factorized Back-Projection (FFBP) realization with a number of adjustable (geometry) parameters for each factorization step. By altering the aperture in the time domain, it is possible to correct an arbitrary, inaccurate geometry. This in turn indicates that the FGA algorithm has the capacity to compensate for residual space variant RCM. In appended papers the performance of the algorithm is demonstrated for geometrically constrained autofocus problems. Results for simulated and real (Coherent All RAdio BAnd System II (CARABAS II)) Ultra WideBand (UWB) data sets are presented. Resolution and Peak to SideLobe Ratio (PSLR) values for (point/point-like) targets in FGA and reference images are similar within a few percents and tenths of a dB. As an example: the resolution of a trihedral reflector in a reference image and in an FGA image respectively, was measured to approximately 3.36 m/3.44 m in azimuth, and to 2.38 m/2.40 m in slant range; the PSLR was in addition measured to about 6.8 dB/6.6 dB. The advantage of a geometrical autofocus approach is clarified further by comparing the FGA algorithm to a standard strategy, in this case the Phase Gradient Algorithm (PGA)