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  • Nonuniform sampling problems in computed tomography

    Creator:
    Gratton, Larry A.
    Abstract:
    Two problems involving high-resolution reconstruction from nonuniformly sampled data in x-ray computed tomography are addressed. A technique based on the theorem for sampling on unions of shifted lattices is introduced which exploits the symmetry property in two-dimensional fan beam computed tomography and permits the reconstruction of images with twice the...
    Resource Type:
    Dissertation
    Full Text:
    : _______________________ _ Adel Faridani Two problems involving high-resolution reconstruction from nonuniformly

  • π-line reconstruction formulas in computed tomography

    Creator:
    Hass, Ryan Andrew
    Abstract:
    X-ray computed tomography is a noninvasive imaging modality capable of reconstructing exact density values of 3D objects. Computed tomography machines are deployed across the world to provide doctors with an image that reveals more detail than a standard x-ray image. We investigate algorithms based on exact computed tomography reconstruction formulas...
    Resource Type:
    Dissertation
    Full Text:
    -Line Reconstruction Formulas in Computed Tomography Abstract approved: Adel Faridani X-ray computed

  • Nonuniform Sampling Of Band-limited Functions

    Creator:
    Al-Hammali, Hussain Y.
    Abstract:
    In this thesis, we will study certain generalizations of the classical Shannon Sampling Theorem, which allows for the reconstruction of a pi-band-limited, square-integrable function from its samples on the integers. J. R. Higgins provided a generalization where the integers can be perturbed by less than 1/4, which includes nonuniform and...
    Resource Type:
    Dissertation
    Full Text:
    . Title: Nonuniform Sampling Of Band-limited Functions Abstract approved: Adel Faridani In this thesis

  • Nonperiodic sampling theorems and filter banks

    Creator:
    Behmard, Hamid R.
    Abstract:
    Sampling theorems provide exact interpolation formulas for bandlimited functions. They play a fundamental role in signal processing. A function is called bandlimited if its Fourier transform vanishes outside a compact set. A generalized sampling theorem in the framework of locally compact Abelian groups is presented. Sampling sets are finite unions...
    Resource Type:
    Dissertation

  • Regions of Backprojection and Comet Tail Artifacts for π-Line Reconstruction Formulas in Tomography

    Creator:
    Hass, Ryan and Faridani, Adel
    Abstract:
    We explore two characteristic features of x-ray computed tomography inversion formulas in two and three dimensions that are dependent on π-lines. In such formulas the data from a given source position contribute only to the reconstruction of ƒ(x) for x in a certain region, called the region of backprojection. The...
    Resource Type:
    Article
    Full Text:
    Backprojection and Comet Tail Artifacts for π-Line Reconstruction Formulas in Tomography∗ Ryan Hass† and Adel

  • A Partial Proof of Bertrand's Theorem

    Creator:
    Musgrove, John F.
    Abstract:
    In this paper, we provide a thorough proof of most of Bertrand's Theorem. Using Arnold's book "Mathematical methods of classical mechanics" as a backbone and calculus methods demonstrated by Jovanović in his article "A note on the proof of Bertrand's theorem," we show that for masses in a central field...
    Resource Type:
    Honors College Thesis
    Full Text:
    , representing Mathematics Adel Faridani, Committee Member, representing Mathematics Enrique Thomann, Committee

  • Enhancing Facial Recognition: A Comparative Analysis of Image Preprocessing Techniques in PCA, KL Expansion and SVD

    Creator:
    Tuffour, Prince A.
    Abstract:
    Facial recognition has become increasingly important in recent years, due to the wide range of applications it has in fields such as security, surveillance, and human-computer interaction. Three popular methods for facial recognition are the Principal Component Analysis (PCA), Karhunen-Loeve Expansions, which is fundamentally a continuous form of PCA but...
    Resource Type:
    Capstone Project

  • Mathematical and Computational Considerations of a Model of Microbiologically Induced Calcite Precipitation

    Creator:
    Barry, Zachary T.
    Abstract:
    In this paper, we discuss two possible modifications to a numerical solution method for a model of microbiologically induced calcite precipitation (MICP). MICP provides a means to seal cracks in the surfaces of geological structures. From a mathematical and computational point of view MICP has very interesting features which make...
    Resource Type:
    Capstone Project

  • Kaczmarz and randomized Kaczmarz method

    Creator:
    Abubakari, Nurideen
    Resource Type:
    Capstone Project
    Full Text:
    like to thank all other committee members, Professor Adel Faridani, Professor Mary De Raeve Beisiegel

  • Determination of the Filippov solutions of the nonlinear oscillator with dry friction

    Creator:
    Moreland, Heather L.
    Abstract:
    In previous papers by Awrejcewicz in 1986 and Narayanan and Jayaraman in 1991, it was claimed that the nonlinear oscillator with dry friction exhibited chaos for several forcing frequencies. The chaos determination was achieved using the characteristic exponent of Lyapunov which requires the right-hand side of the differential equation to...
    Resource Type:
    Masters Thesis
    Full Text:
    shared. Many thanks to the members of my committee, Professors Jeff Barnes, Adel Faridani, and John Lee