Skip to main content

Incorporating the Sparsity of Edges into the Fourier Reconstruction of Piecewise Smooth Functions


Abstract In applications such as Magnetic Resonance Imaging (MRI), data are acquired as Fourier samples. Since the underlying images are only piecewise smooth, standard recon- struction techniques will yield the Gibbs phenomenon, which can lead to misdiagnosis. Although filtering will reduce the oscillations at jump locations, it can often have the adverse effect of blurring at these critical junctures, which can also lead to misdiagno- sis. Incorporating prior information into reconstruction methods can help reconstruct a sharper solution. For example, compressed sensing (CS) algorithms exploit the expected sparsity of some features of the image. In this thesis, we develop a method to exploit the sparsity in the edges of the underlying image. We de... (more)
Created Date 2014-05
Contributor Wasserman, Gabriel Kanter (Author) / Gelb, Anne (Thesis Director) / Cochran, Doug (Committee Member) / Archibald, Rick (Committee Member) / Barrett, The Honors College / School of Mathematical and Statistical Sciences
Subject Sparsity / MRI / Fourier Reconstruction / Compressed Sensing
Series Academic Year 2013-2014
Type Text
Extent 16 pages
Language English
Copyright
Reuse Permissions All Rights Reserved
Collaborating Institutions Barrett, the Honors College
Additional Formats MODS / OAI Dublin Core / RIS


  ThesisCopt.pdf
835.5 KB application/pdf
  • Download restricted to ASU - Sign In
Download Count: 18