Abstract #0521

Fast, Iterative Subsampled Spiral Reconstruction via Circulant Majorizers

Matthew J. Muckley^1,2, Douglas C. Noll¹, and Jeffrey A. Fessler^1,2

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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