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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- Creators: Turaga, Pavan
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 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
Description
Antibiotic resistance is a very important issue that threatens mankind. As bacteria
are becoming resistant to multiple antibiotics, many common antibiotics will soon
become ineective. The ineciency of current methods for diagnostics is an important
cause of antibiotic resistance, since due to their relative slowness, treatment plans
are often based on physician's experience rather than on test results, having a high
chance of being inaccurate or not optimal. This leads to a need of faster, pointof-
care (POC) methods, which can provide results in a few hours. Motivated by
recent advances on computer vision methods, three projects have been developed
for bacteria identication and antibiotic susceptibility tests (AST), with the goal of
speeding up the diagnostics process. The rst two projects focus on obtaining features
from optical microscopy such as bacteria shape and motion patterns to distinguish
active and inactive cells. The results show their potential as novel methods for AST,
being able to obtain results within a window of 30 min to 3 hours, a much faster
time frame than the gold standard approach based on cell culture, which takes at
least half a day to be completed. The last project focus on the identication task,
combining large volume light scattering microscopy (LVM) and deep learning to
distinguish bacteria from urine particles. The developed setup is suitable for pointof-
care applications, as a large volume can be viewed at a time, avoiding the need
for cell culturing or enrichment. This is a signicant gain compared to cell culturing
methods. The accuracy performance of the deep learning system is higher than chance
and outperforms a traditional machine learning system by up to 20%.
are becoming resistant to multiple antibiotics, many common antibiotics will soon
become ineective. The ineciency of current methods for diagnostics is an important
cause of antibiotic resistance, since due to their relative slowness, treatment plans
are often based on physician's experience rather than on test results, having a high
chance of being inaccurate or not optimal. This leads to a need of faster, pointof-
care (POC) methods, which can provide results in a few hours. Motivated by
recent advances on computer vision methods, three projects have been developed
for bacteria identication and antibiotic susceptibility tests (AST), with the goal of
speeding up the diagnostics process. The rst two projects focus on obtaining features
from optical microscopy such as bacteria shape and motion patterns to distinguish
active and inactive cells. The results show their potential as novel methods for AST,
being able to obtain results within a window of 30 min to 3 hours, a much faster
time frame than the gold standard approach based on cell culture, which takes at
least half a day to be completed. The last project focus on the identication task,
combining large volume light scattering microscopy (LVM) and deep learning to
distinguish bacteria from urine particles. The developed setup is suitable for pointof-
care applications, as a large volume can be viewed at a time, avoiding the need
for cell culturing or enrichment. This is a signicant gain compared to cell culturing
methods. The accuracy performance of the deep learning system is higher than chance
and outperforms a traditional machine learning system by up to 20%.
ContributorsIriya, Rafael (Author) / Turaga, Pavan (Thesis advisor) / Wang, Shaopeng (Committee member) / Grys, Thomas (Committee member) / Zhang, Yanchao (Committee member) / Arizona State University (Publisher)
Created2020