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    Solutions to Space-Time Inverse Problems

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    Author
    Alfowzan, Mohammed Fowzan
    Issue Date
    2016
    Keywords
    Medical Imaging
    OAM
    Optical communications
    SPECT
    Electrical & Computer Engineering
    Inverse Problems
    Advisor
    Rodriguez, Jeffrey J.
    
    Metadata
    Show full item record
    Publisher
    The University of Arizona.
    Rights
    Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
    Abstract
    Two inverse problems are investigated in this dissertation, taking into account both the spatial and temporal aspects. The first problem addresses the under determined image reconstruction problem for dynamic SPECT. The quality of the reconstructed image is often limited due to having fewer observations than the number of voxels. The proposed algorithms make use of the generalized α-divergence function to improve the estimation performance. The first algorithm is based on an alternating minimization framework to minimize a regularized α-divergence objective function. We demonstrate that selecting an adaptive α policy depending on the time evolution of the voxels gives better performance than a fixed α assignment. The second algorithm is based on Newton's method. A regularized approach has been taken to avoid stability issues. Newton's method is generally computationally demanding due to the complexity associated with inverting the Hessian matrix. A fast Newton-based method is proposed using majorization-minimization techniques that diagonalize the Hessian matrix. In dynamically evolving systems, the prediction matrix plays an important role in the estimation process. An estimation technique is proposed to estimate the prediction matrix using the α-divergence function. The simulation results show that our algorithms provide better performance than the techniques based on the Kullback-Leibler distance. The second problem is the recovery of data transmitted over free-space optical communication channels using orbital angular momentum (OAM). In the presence of atmospheric turbulence, crosstalk occurs among OAM optical modes resulting in an error floor at a relatively high bit error rate. The modulation format considered for the underlying problem is Q-ary pulse position modulation (PPM). We propose and evaluate three joint detection strategies to overcome the OAM crosstalk problem: i) maximum likelihood sequence estimation (MLSE). ii) Q-PPM factor graph detection. iii) branch-and-bound detection. We compare the complexity and the bit-error-rate performance of these strategies in realistic scenarios.
    Type
    text
    Electronic Dissertation
    Degree Name
    Ph.D.
    Degree Level
    doctoral
    Degree Program
    Graduate College
    Electrical & Computer Engineering
    Degree Grantor
    University of Arizona
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