Series of first-order phase shifts correct lattice reduction of fractional K-space indices Journal Article
| Authors: | Miloushev, V. Z.; Deh, K.; Keshari, K. R. |
| Article Title: | Series of first-order phase shifts correct lattice reduction of fractional K-space indices |
| 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. © 2023 Elsevier Inc. |
| Keywords: | mri; fourier transforms; compressed sensing; compressed-sensing; lattice reduction; k-space; band-limited signal; cartesian grid; first order; fourier transformations; gridding; ordering phase; space acquisition |
| Journal Title: | Journal of Magnetic Resonance |
| Volume: | 349 |
| ISSN: | 1090-7807 |
| Publisher: | Academic Press Inc., Elsevier Science |
| Date Published: | 2023-04-01 |
| Start Page: | 107407 |
| Language: | English |
| DOI: | 10.1016/j.jmr.2023.107407 |
| PROVIDER: | scopus |
| PUBMED: | 36848687 |
| PMCID: | PMC10135416 |
| DOI/URL: | |
| Notes: | Article -- MSK Cancer Center Support Grant (P30 CA008748) acknowledged in PDF -- MSK corresponding author is Vesselin Miloushev -- Source: Scopus |
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