Arnab K. Shaw, Ph.D. (Advisor); Brian D. Rigling, Ph.D. (Committee Member); Michael A. Saville, Ph.D. (Committee Member); Partha P. Banerjee, Ph.D. (Committee Member); Matthew P. Dierking, Ph.D. (Committee Member)
Doctor of Philosophy (PhD)
Synthetic aperture ladar (SAL) is an emerging remote sensing technology capable of providing high-resolution, interpretable, and timely imagery. SAL and synthetic aperture radar (SAR) are similar in that they provide high-resolution imagery suitable for a wide-variety of applications beyond the diffraction limit of the real aperture. Several advantages of SAL are; realistic imagery resulting from diffuse scattering of optically-rough objects, fine directionality of laser beam making the technology inherently low probability-of-detect, and shorter synthetic aperture collection times, all of which result from operating at optical as opposed to RF wavelengths. With the dramatic decrease in wavelength, SAL systems become more susceptible to phase errors induced by platform motion, vibration, and atmospheric turbulence. In this research effort, we focus on mitigating the detrimental effects of atmospheric turbulence on SAL image quality. We show that traditional autofocusing algorithms; Phase Gradient Autofocus (PGA), Sharpness-based Autofocus, and Sparsity Driven Autofocus (SDA), are unable to mitigate atmospheric phase errors due to their spatially-variant nature. We overcome the challenge imposed by spatially-variant atmospheric phase errors through the use of a model-based image reconstruction framework. Utilizing this framework we implement three different spatially-variant model error correction algorithms; Moving Target Autofocus (MTA), Spatially-variant Phase Correction (SVPC), and Model-based Atmospheric Phase Correction (MBAPC) algorithms. The MTA algorithm is a spatially-variant phase error estimation algorithm originally designed for focusing moving targets in SAR. We develop an image-quality metric (IQM) based parameter tuning algorithm that enables the success of the MTA algorithm for the unique challenges presented by atmospheric phase errors. Both SVPC and MBAPC are spatially-variant model error correction algorithms developed to handle atmospheric phase errors corrupting SAL data. In SVPC we estimate the atmospheric phase error for all targets in the scene, under the assumption that the scene is inherently sparse. In MBAPC we decompose the atmospheric phase errors onto well-established spatial basis sets, Zernike polynomials and Fourier series. The spatial basis sets are used to parametrically represent the spatial variations of the atmospheric phase error throughout the scene. We implement the model error correction algorithms with a sparse image reconstruction (SIR) algorithm and quantify their performance using multiple simulations. We design an atmospheric ray trace simulation to test the efficacy of the three model error correction algorithms for wide-range of turbulence strengths. The atmospheric phase perturbations are simulated by tracing diverging rays through multiple Kolmogorov-distributed atmospheric phase screens. Utilizing the developed IQM-based parameter tuning algorithm we optimize each algorithm, in the sense that image sharpness is maximized across all turbulence strengths. Lastly, we quantify algorithm performance using reconstruction performance metrics averaged over numerous independent atmospheric realization. In this analysis, we show that each of the proposed model error correction algorithms are capable of mitigating the atmospheric phase errors over a wide range of atmospheric turbulence strengths. Lastly, we derive the Cramer-Rao Lower Bound (CRLB) for the unknown coefficient parameter used to model the atmospheric phase errors in the MBAPC algorithm and validate the theory using a Monte Carlo simulation. We show that the MBAPC algorithm is the maximum likelihood estimator (MLE) for the unknown coefficient parameter under of additive, complex white Gaussian noise (CWGN).
Department or Program
Department of Electrical Engineering
Year Degree Awarded
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