Fast, Iterative Subsampled Spiral Reconstruction via Circulant Majorizers
Matthew J. Muckley1,2, Douglas C. Noll1, and Jeffrey A. Fessler1,2
1Biomedical Engineering, University of Michigan, Ann Arbor, MI, United States, 2Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, MI, United States
Majorize-minimize algorithms are a powerful tool for solving image
reconstruction problems with sparsity-promoting regularization; however,
when non-Cartesian trajectories are used it becomes challenging to design a suitable majorizer for these methods due to the high density of
samples near the center of k-space. We derive a new circulant majorizer
that is related to the density compensation function of the
k-space trajectory. We then use the frequency localization
properties of wavelets
and the circulant majorizer to design an algorithm
that converges faster than conventional FISTA for reconstructing images from undersampled,
non-Cartesian k-space data.
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