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An l1 Regularization Algorithm for Reconstructing Piecewise Smooth Functions from Fourier Data Using Wavelet Projection


Abstract Imaging technologies such as Magnetic Resonance Imaging (MRI) and Synthetic Aperture Radar (SAR) collect Fourier data and then process the data to form images. Because images are piecewise smooth, the Fourier partial sum (i.e. direct inversion of the Fourier data) yields a poor approximation, with spurious oscillations forming at the interior edges of the image and reduced accuracy overall. This is the well known Gibbs phenomenon and many attempts have been made to rectify its effects. Previous algorithms exploited the sparsity of edges in the underlying image as a constraint with which to optimize for a solution with reduced spurious oscillations. While the sparsity enforcing algorithms are fairly effective, they are sensitive to several i... (more)
Created Date 2015-12
Contributor Fan, Jingjing (Co-Author) / Mead, Ryan (Co-Author) / Gelb, Anne (Thesis Director) / Platte, Rodrigo (Committee Member) / Archibald, Richard (Committee Member) / School of Music / School of Mathematical and Statistical Sciences / Barrett, The Honors College
Subject Computational Mathematics / Image Processing / L1 Regularization
Series Academic Year 2015-2016
Type Text
Extent 30 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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