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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
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Breast cancer affects about 12% of women in the US. Arguably, it is one of the most advertised cancers. Mammography became a popular tool of breast cancer screening in the 1970s, and patient-geared guidelines came from the American Cancer Society (ACS) and the US Preventative Task Force (USPSTF). This research

Breast cancer affects about 12% of women in the US. Arguably, it is one of the most advertised cancers. Mammography became a popular tool of breast cancer screening in the 1970s, and patient-geared guidelines came from the American Cancer Society (ACS) and the US Preventative Task Force (USPSTF). This research focuses on ACS guidelines, as they were the earliest as well as the most changed guidelines. Mammography guidelines changed over time due to multiple factors. This research has tracked possible causes of those changes. Research began with an extensive literature search of clinical trials, the New York Times and the Washington Post archives, systematic reviews, ACS and USPSTF archives.

Created2021-02-16
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Science fiction works can reflect the relationship between science and society by telling stories that are set in the future of ethical implications or social consequences of scientific advancements. This thesis investigates how the concept of reproduction is depicted in popular science fiction works.

Created2021-02-10
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By questioning methods of sex selection since their early development, and often discovering that they are unreliable, scientists have increased the creative and technological capacity of the field of reproductive health. The presentation of these methods to the public, via published books on timing methods and company websites for sperm

By questioning methods of sex selection since their early development, and often discovering that they are unreliable, scientists have increased the creative and technological capacity of the field of reproductive health. The presentation of these methods to the public, via published books on timing methods and company websites for sperm sorting, increased interest in, and influence of, sex selection within the global society. The purpose of explaining the history, interest, development, and impact of various sex selection methods in the mid-twentieth century based on the information that is available on them today is to show couples which methods have failed and provide them with the knowledge necessary to make an informed decision on how they choose to go about utilizing methods of sex selection.

Created2021-02-26
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By demonstrating the struggle for sound standard of care for non-medical reproductive health care providers during the nineteenth and early twentieth century, this project emphasizes what the standards of reproductive health care for abortion and contraception might be like if the organizations that made them so readily available, like Planned

By demonstrating the struggle for sound standard of care for non-medical reproductive health care providers during the nineteenth and early twentieth century, this project emphasizes what the standards of reproductive health care for abortion and contraception might be like if the organizations that made them so readily available, like Planned Parenthood, were defunded or criminalized in our modern setting.

Created2021-02-23