LORAKS: Low-Rank Modeling of Local k -Space Neighborhoods
Justin P. Haldar 1
Signal and Image Processing Institute,
University of Southern California, Los Angeles, CA,
This work presents a novel framework for constrained
image reconstruction based on Low-Rank Modeling of Local
Neighborhoods (LORAKS). We first demonstrate that
data for low-dimensional images can be mapped into
high-dimensional matrices, such that the resulting
matrices possess low-rank structure when the original
images have limited support and/or slowly-varying phase.
Subsequently, we propose a flexible approach to
exploiting this low-rank structure that enables image
reconstruction from undersampled data. The approach is
analogous to a single-channel calibrationless
generalization of GRAPPA, and is demonstrated to
outperform sparsity-guided reconstructions of
undersampled data in certain contexts.
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