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 - 2 of 2
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
155789-Thumbnail Image.png

Optimum Experimental Design Issues in Functional Neuroimaging Studies

Description
Functional magnetic resonance imaging (fMRI) is one of the popular tools to study human brain functions. High-quality experimental designs are crucial to the success of fMRI experiments as they allow the collection of informative data for making precise and valid inference with minimum cost. The primary goal of this study…

Functional magnetic resonance imaging (fMRI) is one of the popular tools to study human brain functions. High-quality experimental designs are crucial to the success of fMRI experiments as they allow the collection of informative data for making precise and valid inference with minimum cost. The primary goal of this study is on identifying the best sequence of mental stimuli (i.e. fMRI design) with respect to some statistically meaningful optimality criteria. This work focuses on two related topics in this research field. The first topic is on finding optimal designs for fMRI when the design matrix is uncertain. This challenging design issue occurs in many modern fMRI experiments, in which the design matrix of the statistical model depends on both the selected design and the experimental subject's uncertain behavior during the experiment. As a result, the design matrix cannot be fully determined at the design stage that makes it difficult to select a good design. For the commonly used linear model with autoregressive errors, this study proposes a very efficient approach for obtaining high-quality fMRI designs for such experiments. The proposed approach is built upon an analytical result, and an efficient computer algorithm. It is shown through case studies that our proposed approach can outperform the existing method in terms of computing time, and the quality of the obtained designs. The second topic of the research is to find optimal designs for fMRI when a wavelet-based technique is considered in the fMRI data analysis. An efficient computer algorithm to search for optimal fMRI designs for such cases is developed. This algorithm is inspired by simulated annealing and a recently proposed algorithm by Saleh et al. (2017). As demonstrated in the case studies, the proposed approach makes it possible to efficiently obtain high-quality designs for fMRI studies, and is practically useful.
ContributorsZhou, Lin (Author) / Kao, Ming-Hung (Thesis advisor) / Welfert, Bruno (Thesis advisor) / Jackiewicz, Zdzislaw (Committee member) / Reiser, Mark R. (Committee member) / Stufken, John (Committee member) / Taylor, Jesse Earl (Committee member) / Arizona State University (Publisher)
Created2017