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Edge Informed Fourier Reconstruction from Non-Uniform Spectral Data


Abstract The reconstruction of piecewise smooth functions from non-uniform Fourier data arises in sensing applications such as magnetic resonance imaging (MRI). This thesis presents a new polynomial based resampling method (PRM) for 1-dimensional problems which uses edge information to recover the Fourier transform at its integer coefficients, thereby enabling the use of the inverse fast Fourier transform algorithm. By minimizing the error of the PRM approximation at the sampled Fourier modes, the PRM can also be used to improve on initial edge location estimates. Numerical examples show that using the PRM to improve on initial edge location estimates and then taking of the PRM approximation of the integer frequency Fourier coefficients is a viable ... (more)
Created Date 2013-05
Contributor Gutierrez, Alexander Jay (Author) / Platte, Rodrigo (Thesis Director) / Gelb, Anne (Committee Member) / Viswanathan, Adityavikram (Committee Member) / Barrett, The Honors College / School of International Letters and Cultures / School of Mathematical and Statistical Sciences
Subject Gridding / MRI / Approximation Theory / Fourier Data
Series Academic Year 2012-2013
Type Text
Extent 47 pages
Language English
Copyright
Reuse Permissions All Rights Reserved
Collaborating Institutions Barrett, the Honors College
Additional Formats MODS / OAI Dublin Core / RIS


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