Date of Award
Open Access Thesis
College of Arts and Sciences
In its two-dimensional form, the Radon transform of an image (function) is a collection of projections of the image which are parameterized by a set of angles (from the positive x-axis) and distances from the origin. Computational methods of the Radon transform are important in many image processing and computer vision problems, such as pattern recognition and the reconstruction of medical images. However, computability requires the construction of a discrete analog to the Radon transform, along with discrete alternatives for its inversion. In this paper, we present discrete analogs using classical methods of Chebyshev polynomial reconstruction, along with a new computational method which makes use of sub-exponentially localized frames comprised of Chebyshev polynomials. This new method leads directly to a potential new algorithm for image reconstruction using Radon inversion.
Szi, J. C.(2016). Chebyshev Inversion of the Radon Transform. (Master's thesis). Retrieved from https://scholarcommons.sc.edu/etd/3758