Series of first-order phase shifts correct lattice reduction of fractional K-space indices

Vesselin Z Miloushev; Kofi Deh; Kayvan R Keshari

doi:10.1016/j.jmr.2023.107407

Series of first-order phase shifts correct lattice reduction of fractional K-space indices

J Magn Reson. 2023 Apr:349:107407. doi: 10.1016/j.jmr.2023.107407. Epub 2023 Feb 17.

Authors

Vesselin Z Miloushev¹, Kofi Deh², Kayvan R Keshari²

Affiliations

¹ Department of Radiology, Memorial Sloan Kettering Cancer Center, New York, NY, USA. Electronic address: miloushv@mskcc.org.
² Department of Radiology, Memorial Sloan Kettering Cancer Center, New York, NY, USA; Molecular Pharmacology Program, Memorial Sloan Kettering Cancer Center, New York, NY, USA.

Abstract

Lattice reduction of K-space acquisition at fractional indices refers to reducing the indices to the smallest nearby integer, thereby generating a Cartesian grid, allowing subsequent inverse Fourier Transformation. For band-limited signals, we show that the error in lattice reduction is equivalent to first order phase shifts, which in the infinite limit approaches W^∞=φ(cotφ-i), where φ is a first-order phase shift vector. In general, the inverse corrections can be specified from the binary representation of the fractional part of the K-space indices. For non-uniform sparsity, we show how to incorporate the inverse corrections into compressed sensing reconstructions.

Keywords: Compressed sensing; Gridding; MRI.

Abstract

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