Edwin A. Marengo
Anthony Devaney, Jose A. Martinez
Date of Award
Doctor of Philosophy
Department or Academic Unit
College of Engineering, Department of Electrical and Computer Engineering
engineering, electrical engineering, communication, information science, compressive, fisher information, information, scattering, sensing
Electrical and Computer Engineering
This Ph.D. dissertation project addresses two related topics in wave-based signal processing: 1) Cramer-Rao bound (CRB) analysis of scattering systems formed by pointlike scatterers in one-dimensional (1D) and three-dimensional (3D) spaces. 2) Compressive optical coherent imaging, based on the incorporation of sparsity priors in the reconstructions. The first topic addresses for wave scattering systems in 1D and 3D spaces the information content about scattering parameters, in particular, the targets' positions and strengths, and derived quantities, that is contained in scattering data corresponding to reflective, transmissive, and more general sensing modalities. This part of the dissertation derives the Cramer-Rao bound (CRB) for the estimation of parameters of scalar wave scattering systems formed by point scatterers. The results shed light on the fundamental difference between the approximate Born approximation model for weak scatterers and the more general multiple scattering model, and facilitate the identification of regions in parameter space where multiple scattering facilitates or obstructs the estimation of parameters from scattering data, as well as of sensing configurations giving maximal or minimal information about the parameters. The derived results are illustrated with numerical examples, with particular emphasis on the imaging resolution which we quantify via a relative resolution index borrowed from a previous paper. Additionally, this work investigates fundamental limits of estimation performance for the localization of the targets and the inverse scattering problem. The second topic of the effort describes a novel compressive-sensing-based technique for optical imaging with a coherent single-detector system. This hybrid opto-micro-electromechanical, coherent single-detector imaging system applies the latest developments in the nascent field of compressive sensing to the problem of computational imaging of wavefield intensity from a small number of projective measurements of the field. The projective measurements are implemented using spatial light modulators of the digital micromirror device (DMD) family, followed by a geometrical-optics-based image casting system to capture the data using a single photodetector. The reconstruction process is based on the new field of compressive sensing which allows, thanks to the exploitation of statistical priors such as sparsity, the imaging of the main features of the objects under illumination with much less data than a typical CCD camera. The present system expands the scope of single-detector imaging systems based on compressive sensing from the incoherent light regime, which has been the past focus, to the coherent light regime which is key in many biomedical and Homeland security applications (THz imaging).
Maytee Zambrano Núñez
Zambrano Núñez, Maytee, "Statistical signal processing methods in scattering" (2012). Electrical Engineering Dissertations. Paper 43. http://hdl.handle.net/2047/d20002419
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