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Sparse Methods for Model Estimation with Applications to Radar Imaging

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Sparse Methods for Model Estimation with Applications to Radar Imaging Sparse Methods for Model Estimation with Applications to Radar Imaging Dissertation Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By Christian D. Austin, B.E., B.S., M.S. Graduate Program in Electrical and Computer Engineering The Ohio State University 2012 Dissertation Committee: Dr. Randolph L. Moses, Advisor Dr. Lee C. Potter Dr. Philip Schniter c Copyright by Christian D. Austin 2012 Abstract In additive component model estimation problems, the number of additive com- ponents (model order) and values of the model parameters in each of the additive components are estimated. Traditional methods typically estimate parameters for a set of models with fixed order; parameter estimation is performed over a continuous space when parameters are not discrete. The model order is estimated as the min- imizer, over the set of fixed model orders, of a cost function compromising between signal fit to measurements and model complexity. This dissertation explores dictionary-based estimation methods for joint model order and parameter estimation. In dictionary estimation, the continuous parameter space is discretized, forming a dictionary. Each column of the dictionary is a model component at a sampled parameter value, and a linear combination of a subset of columns is used to represent the model. It is assumed that the model consists of a small number of components, and a sparse reconstruction algorithm is used to select a sparse superposition of columns to represent the signal. The number of columns selected is the estimated model order, and the parameters of each column are the parameter estimates. We examine both static and dynamic dictionary-based estimation methods. In static estimation, the dictionary is fixed, while in dynamic estimation, dictionary pa- rameters adapt to the data. We propose two new dynamic dictionary-based estimation ii algorithms and examine the performance of both static and dynamic algorithms in terms of model order probability and parameter estimation error when dictionaries are highly correlated. Highly correlated dictionaries arise from using closely spaced parameter samples in dictionary formation; we propose a method for selecting algo- rithm settings based on an information criterion. We show the following results: 1) dictionary-based estimation methods are capable of performance comparable to the Cram´er Rao lower bound and to traditional benchmark estimation algorithms over a wide range of signal-to-noise ratios; 2) in the complex exponential model, dictionary- based estimation can superresolve closely spaced frequencies, and 3) dynamic dictio- nary methods overcome parameter estimation bias caused by quantization error in static dictionary-based estimation. We apply dictionary-based estimation to the problem of 3D synthetic aperture radar (SAR) imaging. Traditional 3D SAR image formation requires collection of data over a large contiguous sector of azimuth-elevation aspect angles; this collection is difficult or impossible to obtain in practice. We show that dictionary-based estima- tion can be used to produce well-resolved, wide-angle 3D SAR images from sparse, irregular flight paths. iii In memory my grandfathers, David Austin, and Walter Sobol iv Acknowledgments I would like to thank my family for their continual support, love, and encourage- ment. My parents have always emphasized the importance of education and stood beside me in all of my decisions; I would not be where I am today without them. When in need of someone to talk to in tough times, my mother has always been there for me, bringing the current situation into perspective. I’ve often drawn upon my father’s realist views and life-experiences when in need of motivation or focus. My sister, Marielle, and I left home at the same time and experienced college concurrently, and I feel that we intellectually “grew-up” together. I value the experiences that we had together during this time of our lives. To the rest of my family who inquired into my progress, offered advice, and never questioned my many years of graduate school, I thank you for showing interest in my work and always believing in me. My academic advisor and mentor, Professor Randolph Moses, taught me how to conduct research, from formulating a problem to publishing the results. I thank him not only for teaching me the skills necessary to be a researcher, but for always being very professional and making my graduate school experience a very pleasant one. Having good officemates is an important part of graduate school, given that you share many hours of your graduate life together. I thank both Dr. Josh Ash and Dr. Julie Jackson for being great officemates. We’ve had the opportunity to discuss a multitude of ideas, and many of our conversations have taught me something v new; hopefully, I have reciprocated. One day I hope to implement at least a small fraction of the projects that Josh and I have discussed over the years. Members of the Compressive Sensing reading group also deserve my gratitude, especially Professor Lee Potter, and Professor Phil Schniter, for the valuable conversations that we had about compressive sensing and research in general. I thank my friend, and fellow graduate student, Anthony D’Orazio, for listening to my problems, and at times, just dealing with me during the ups and downs of graduate school. Being able to discuss everyday problems with someone who is in a similar situation and can relate was a great stress-relief. Ed Zelnio of the Air Force Research Laboratory (AFRL) has been supportive of my research and has provided valuable input; I am thankful for his involvement. I also owe my gratitude to Dr. Greg Arnold, who volunteered to be our AFRL collaborator during Ohio Space Grant Consortium funding. Lastly, my graduate research would not have been possible without financial support from the AFRL, Ohio Space Grant Consortium, and NSF IUCRC; I am greatly appreciative of their support. vi Vita November 11, 1980 .........................Born - West Islip, New York 2003 ........................................B.E. Computer Engineering, B.S. Mathematics, State University of New York at Stony Brook 2006 ........................................M.S. Electrical Engineering, The Ohio State University 2003-2004, 2006-2009 .......................Graduate Fellow, The Ohio State University 2004-2006, 2009-present .................... Graduate Research Associate, The Ohio State University Publications C. D. Austin, E. Ertin, and R.L. Moses, “Sparse Signal Methods for 3D Radar Imag- ing,” IEEE Journal of Selected Topics in Signal Processing, vol. 5, no. 3, pp. 408-423, June 2011. C. D. Austin, J. N. Ash and R. L. Moses, “Parameter Estimation Using Sparse Reconstruction With Dynamic Dictionaries,” Proc. IEEE Int. Conf. on Acoustics, Speech, and Signal Processing (ICASSP), Prague, Czech Republic, May 22 - 27, 2011. C. D. Austin, J. N. Ash and R. L. Moses, “Performance Analysis of Sparse 3D SAR Imaging,” Algorithms for Synthetic Aperture Radar Imagery XVIII, SPIE Defense and Security Symposium, Orlando, FL., April 25 - 29, 2011 C. D. Austin, E. Ertin, J. N. Ash, and R. L. Moses, “On the Relation Between Sparse Reconstruction and Parameter Estimation with Model Order Selection,” IEEE Journal of Selected Topics in Signal Processing, vol. 4, no. 3, pp. 560 - 570, June 2010. vii K. E. Dungan, C. D. Austin, J. Nehrbass, and L. C. Potter, “Civilian Vehicle Radar Data Domes,” Algorithms for Synthetic Aperture Radar Imagery XVII, SPIE Defense and Security Symposium, Orlando, FL., April 5 - 9, 2010. C. D. Austin, E. Ertin, and R. L. Moses, “Sparse Multipass 3D SAR Imaging: Appli- cations to the GOTCHA Data Set,” Algorithms for Synthetic Aperture Radar Imagery XVI, SPIE Defense and Security Symposium, Orlando, FL., April 13 - 17, 2009. M. Ferrara, J. A. Jackson, and C. Austin, “Enhancement of Multi-Pass 3D Circu- lar SAR Images using Sparse Reconstruction Techniques,” Algorithms for Synthetic Aperture Radar Imagery XVI, SPIE Defense and Security Symposium, Orlando, FL., April 13 - 17, 2009. C. D. Austin, E. Ertin, J. N. Ash, and R. L. Moses, “On the Relation Between Sparse Sampling and Parametric Estimation,” IEEE 13th DSP workshop and 5th Sig. Proc. Workshop 2009 (DSP/SPE 2009), Jan. 4 - 7, 2009. C. D. Austin and R. L. Moses, “Wide-angle Sparse 3D Synthetic Aperture Radar Imaging for Nonlinear Flight Paths,” IEEE National Aerospace and Electronics Con- ference (NAECON) 2008, July 16 - 18, 2008. E. Ertin, C. D. Austin, S. Sharma, R. L. Moses, and L. C. Potter,“GOTCHA Experi- ence Report: Three-Dimensional SAR Imaging with Complete Circular Apertures,” Algorithms for Synthetic Aperture Radar Imagery XIV, SPIE Defense and Security Symposium, Orlando, FL., April 9 - 13, 2007. C. D. Austin, “Interferometric Synthetic Aperture Radar Height Estimation with Multiple Scattering Centers in a Resolution Cell,” Master’s Thesis, The Ohio State University, 2006. C. D. Austin and R. L. Moses, “Interferometric Synthetic Aperture Radar Detection and Estimation Based 3D Image Reconstruction,” Algorithms for Synthetic Aperture Radar Imagery XIII, SPIE Defense and Security Symposium, Orlando, FL, Apr. 17 - 21, 2006. C. D. Austin and R. L. Moses, “IFSAR Processing for 3D Target Reconstruction,” Algorithms for Synthetic Aperture Radar Imagery XII, SPIE Defense and Security Symposium, Orlando, FL, Mar. 28 - Apr. 1, 2005. viii R. L. Moses, L. C. Potter, E. Ertin, and C. D. Austin, “Synthetic Aperture Radar Visualization,”
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