Table 1
Level of aliasing for different gridding methods and kernel sizes.
β | Classical | Image domain gridding | |||||
---|---|---|---|---|---|---|---|
PSWF | L = 8 | L = 16 | L = 24 | L = 32 | L = 48 | L = 64 | |
3.0 | 3.33e–02 | 4.63e–02 | 2.87e–02 | 2.25e–02 | 1.92e–02 | 1.54e–02 | 1.32e–02 |
5.0 | 1.68e–03 | 4.60e–03 | 2.59e–03 | 1.94e–03 | 1.60e–03 | 1.25e–03 | 1.06e–03 |
7.0 | 7.96e–05 | 2.99e–04 | 1.67e–04 | 1.25e–04 | 1.03e–04 | 7.89e–05 | 6.62e–05 |
9.0 | 3.68e–06 | 9.08e–06 | 6.96e–06 | 5.78e–06 | 4.45e–06 | 3.71e–06 | |
11.0 | 1.68e–07 | 4.82e–07 | 3.55e–07 | 2.98e–07 | 2.33e–07 | 1.95e–07 | |
13.0 | 7.58e–09 | 2.70e–08 | 1.79e–08 | 1.47e–08 | 1.16e–08 | 9.83e–09 | |
15.0 | 3.40e–10 | 1.45e–09 | 9.15e–10 | 7.25e–10 | 5.61e–10 | 4.78e–10 |
Notes. Level of aliasing for classical gridding with the PSWF and for image domain gridding with the optimal window for different subgrid sizes L, and different kernel sizes β. Numbers in bold indicate where image domain gridding has lower aliasing than classical gridding. The numbers in this table were generated with code using mpmath (1), a Python library for arbitrary-precision floating-point arithmetic.
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