Theses and dissertations

This collection includes both ASU Theses and Dissertations, submitted by graduate students, and the Barrett, Honors College theses submitted by undergraduate students. 

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Recursive Bayesian Estimation on Projective Spaces: Theoretical Foundations and Practical Algorithms

Description
This thesis develops geometrically and statistically rigorous foundations for multivariate analysis and bayesian inference posed on grassmannian manifolds. Requisite to the development of key elements of statistical theory in a geometric realm are closed-form, analytic expressions for many differential geometric objects, e.g., tangent vectors, metrics, geodesics, volume forms. The first…

This thesis develops geometrically and statistically rigorous foundations for multivariate analysis and bayesian inference posed on grassmannian manifolds. Requisite to the development of key elements of statistical theory in a geometric realm are closed-form, analytic expressions for many differential geometric objects, e.g., tangent vectors, metrics, geodesics, volume forms. The first part of this thesis is devoted to a mathematical exposition of these. In particular, it leverages the classical work of Alan James to derive the exterior calculus of differential forms on special grassmannians for invariant measures with respect to which integration is permissible. Motivated by various multi-­sensor remote sensing applications, the second part of this thesis describes the problem of recursively estimating the state of a dynamical system propagating on the Grassmann manifold. Fundamental to the bayesian treatment of this problem is the choice of a suitable probability distribution to a priori model the state. Using the Method of Maximum Entropy, a derivation of maximum-­entropy probability distributions on the state space that uses the developed geometric theory is characterized. Statistical analyses of these distributions, including parameter estimation, are also presented. These probability distributions and the statistical analysis thereof are original contributions. Using the bayesian framework, two recursive estimation algorithms, both of which rely on noisy measurements on (special cases of) the Grassmann manifold, are the devised and implemented numerically. The first is applied to an idealized scenario, the second to a more practically motivated scenario. The novelty of both of these algorithms lies in the use of thederived maximum­entropy probability measures as models for the priors. Numerical simulations demonstrate that, under mild assumptions, both estimation algorithms produce accurate and statistically meaningful outputs. This thesis aims to chart the interface between differential geometry and statistical signal processing. It is my deepest hope that the geometric-statistical approach underlying this work facilitates and encourages the development of new theories and new computational methods in geometry. Application of these, in turn, will bring new insights and bettersolutions to a number of extant and emerging problems in signal processing.
ContributorsCrider, Lauren N (Author) / Cochran, Douglas (Thesis advisor) / Kotschwar, Brett (Committee member) / Scharf, Louis (Committee member) / Taylor, Thomas (Committee member) / Turaga, Pavan (Committee member) / Arizona State University (Publisher)
Created2021
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Augnosis: Self-Diagnosis in Augmented Reality

Description
Oftentimes, patients struggle to accurately describe their symptoms to medical professionals, which produces erroneous diagnoses, delaying and preventing treatment. My app, Augnosis, will streamline constructive communication between patient and doctor, and allow for more accurate diagnoses. The goal of this project was to create an app capable of gathering data…

Oftentimes, patients struggle to accurately describe their symptoms to medical professionals, which produces erroneous diagnoses, delaying and preventing treatment. My app, Augnosis, will streamline constructive communication between patient and doctor, and allow for more accurate diagnoses. The goal of this project was to create an app capable of gathering data on visual symptoms of facial acne and categorizing it to differentiate between diagnoses using image recognition and identification. “Augnosis”, is a combination of the words “Augmented Reality” and “Self-Diagnosis”, the former being the medium in which it is immersed and the latter detailing its functionality.
ContributorsGoyal, Nandika (Author) / Johnson, Mina (Thesis director) / Bryan, Chris (Committee member) / Turaga, Pavan (Committee member) / Barrett, The Honors College (Contributor) / Computer Science and Engineering Program (Contributor)
Created2022-05