ETDs

This collection includes most of the ASU Theses and Dissertations from 2011 to present. ASU Theses and Dissertations are available in downloadable PDF format; however, a small percentage of items are under embargo. Information about the dissertations/theses includes degree information, committee members, an abstract, supporting data or media.

In addition to the electronic theses found in the ASU Digital Repository, ASU Theses and Dissertations can be found in the ASU Library Catalog.

Dissertations and Theses granted by Arizona State University are archived and made available through a joint effort of the ASU Graduate College and the ASU Libraries. For more information or questions about this collection contact or visit the Digital Repository ETD Library Guide or contact the ASU Graduate College at gradformat@asu.edu.

Displaying 1 - 3 of 3
Filtering by

Clear all filters

149953-Thumbnail Image.png

A sparsity enforcing framework with TVL1 regularization and its application in MR imaging and source localization

Description
The theme for this work is the development of fast numerical algorithms for sparse optimization as well as their applications in medical imaging and source localization using sensor array processing. Due to the recently proposed theory of Compressive Sensing (CS), the $\ell_1$ minimization problem attracts more attention for its ability…

The theme for this work is the development of fast numerical algorithms for sparse optimization as well as their applications in medical imaging and source localization using sensor array processing. Due to the recently proposed theory of Compressive Sensing (CS), the $\ell_1$ minimization problem attracts more attention for its ability to exploit sparsity. Traditional interior point methods encounter difficulties in computation for solving the CS applications. In the first part of this work, a fast algorithm based on the augmented Lagrangian method for solving the large-scale TV-$\ell_1$ regularized inverse problem is proposed. Specifically, by taking advantage of the separable structure, the original problem can be approximated via the sum of a series of simple functions with closed form solutions. A preconditioner for solving the block Toeplitz with Toeplitz block (BTTB) linear system is proposed to accelerate the computation. An in-depth discussion on the rate of convergence and the optimal parameter selection criteria is given. Numerical experiments are used to test the performance and the robustness of the proposed algorithm to a wide range of parameter values. Applications of the algorithm in magnetic resonance (MR) imaging and a comparison with other existing methods are included. The second part of this work is the application of the TV-$\ell_1$ model in source localization using sensor arrays. The array output is reformulated into a sparse waveform via an over-complete basis and study the $\ell_p$-norm properties in detecting the sparsity. An algorithm is proposed for minimizing a non-convex problem. According to the results of numerical experiments, the proposed algorithm with the aid of the $\ell_p$-norm can resolve closely distributed sources with higher accuracy than other existing methods.
ContributorsShen, Wei (Author) / Mittlemann, Hans D (Thesis advisor) / Renaut, Rosemary A. (Committee member) / Jackiewicz, Zdzislaw (Committee member) / Gelb, Anne (Committee member) / Ringhofer, Christian (Committee member) / Arizona State University (Publisher)
Created2011
158258-Thumbnail Image.png

Computational Methods for Kinetic Reaction Systems

Description
This work is concerned with the study and numerical solution of large reaction diffusion systems with applications to the simulation of degradation effects in solar cells. A discussion of the basics of solar cells including the function of solar cells, the degradation of energy efficiency that happens over time, defects…

This work is concerned with the study and numerical solution of large reaction diffusion systems with applications to the simulation of degradation effects in solar cells. A discussion of the basics of solar cells including the function of solar cells, the degradation of energy efficiency that happens over time, defects that affect solar cell efficiency and specific defects that can be modeled with a reaction diffusion system are included. Also included is a simple model equation of a solar cell. The basics of stoichiometry theory, how it applies to kinetic reaction systems, and some conservation properties are introduced. A model that considers the migration of defects in addition to the reaction processes is considered. A discussion of asymptotics and how it relates to the numerical simulation of the lifetime of solar cells is included. A reduced solution is considered and a presentation of a numerical comparison of the reduced solution with the full solution on a simple test problem is included. Operator splitting techniques are introduced and discussed. Asymptotically preserving schemes combine asymptotics and operator splitting to use reasonable time steps. A presentation of a realistic example of this study applied to solar cells follows.
ContributorsShapiro, Bruce G. (Author) / Ringhofer, Christian (Thesis advisor) / Gardner, Carl L (Committee member) / Jackiewicz, Zdzislaw (Committee member) / Platte, Rodrigo B (Committee member) / Vasileska, Dragica (Committee member) / Arizona State University (Publisher)
Created2020
151397-Thumbnail Image.png

Dynamic Hopf bifurcation in spatially extended excitable systems from neuroscience

Description
One explanation for membrane accommodation in response to a slowly rising current, and the phenomenon underlying the dynamics of elliptic bursting in nerves, is the mathematical problem of dynamic Hopf bifurcation. This problem has been studied extensively for linear (deterministic and stochastic) current ramps, nonlinear ramps, and elliptic bursting. These…

One explanation for membrane accommodation in response to a slowly rising current, and the phenomenon underlying the dynamics of elliptic bursting in nerves, is the mathematical problem of dynamic Hopf bifurcation. This problem has been studied extensively for linear (deterministic and stochastic) current ramps, nonlinear ramps, and elliptic bursting. These studies primarily investigated dynamic Hopf bifurcation in space-clamped excitable cells. In this study we introduce a new phenomenon associated with dynamic Hopf bifurcation. We show that for excitable spiny cables injected at one end with a slow current ramp, the generation of oscillations may occur an order one distance away from the current injection site. The phenomenon is significant since in the model the geometric and electrical parameters, as well as the ion channels, are uniformly distributed. In addition to demonstrating the phenomenon computationally, we analyze the problem using a singular perturbation method that provides a way to predict when and where the onset will occur in response to the input stimulus. We do not see this phenomenon for excitable cables in which the ion channels are embedded in the cable membrane itself, suggesting that it is essential for the channels to be isolated in the spines.
ContributorsBilinsky, Lydia M (Author) / Baer, Steven M. (Thesis advisor) / Crook, Sharon M (Committee member) / Jackiewicz, Zdzislaw (Committee member) / Gardner, Carl L (Committee member) / Jung, Ranu (Committee member) / Arizona State University (Publisher)
Created2012