Computational Complexity. Nx and Ny are the pixel size of the image in height and width, respectively, FOV is the field of view, Wrange and |$W_{\rm range\_fit}$| are the values of w-range before and after the w-plane fitting, respectively. Nvis is the amount of visibility data. Nfac is the number of facets. B is the BDA compression factor. The computational cost for FFTs and gridding is shown separately.
| Method . | FFT cost . | Gridding cost . |
|---|---|---|
| W-Snapshot(snapshot imaging) | |$\mathcal {O}(N_{x}N_{y}\log ({N_{x}N_{y}}))$| | |$\mathcal {O}(N_{\rm vis}$|) |
| W-Stacking | |$\mathcal {O}(W_{\rm range} \times FOV \times N_{x}N_{y}\log ({N_{x}N_{y}})$|) | |$\mathcal {O}(N_{\rm vis})$| |
| WS-Snapshot(snapshot imaging) | |$\mathcal {O}(W_{\rm range\_fit} \times FOV \times N_{x}N_{y}\log ({N_{x}N_{y}}) + N_{x}N_{y}$|) | |$\mathcal {O}(N_{\rm vis}$|) |
| DDFacet | |$\mathcal {O}(N_{x}N_{y}\log ({N_{x}N_{y}/N_{\rm fac}) + N_{x}N_{y}}$|) | |$\mathcal {O}(N_{\rm vis}N_{\rm fac}/B)$| |
| Method . | FFT cost . | Gridding cost . |
|---|---|---|
| W-Snapshot(snapshot imaging) | |$\mathcal {O}(N_{x}N_{y}\log ({N_{x}N_{y}}))$| | |$\mathcal {O}(N_{\rm vis}$|) |
| W-Stacking | |$\mathcal {O}(W_{\rm range} \times FOV \times N_{x}N_{y}\log ({N_{x}N_{y}})$|) | |$\mathcal {O}(N_{\rm vis})$| |
| WS-Snapshot(snapshot imaging) | |$\mathcal {O}(W_{\rm range\_fit} \times FOV \times N_{x}N_{y}\log ({N_{x}N_{y}}) + N_{x}N_{y}$|) | |$\mathcal {O}(N_{\rm vis}$|) |
| DDFacet | |$\mathcal {O}(N_{x}N_{y}\log ({N_{x}N_{y}/N_{\rm fac}) + N_{x}N_{y}}$|) | |$\mathcal {O}(N_{\rm vis}N_{\rm fac}/B)$| |
Computational Complexity. Nx and Ny are the pixel size of the image in height and width, respectively, FOV is the field of view, Wrange and |$W_{\rm range\_fit}$| are the values of w-range before and after the w-plane fitting, respectively. Nvis is the amount of visibility data. Nfac is the number of facets. B is the BDA compression factor. The computational cost for FFTs and gridding is shown separately.
| Method . | FFT cost . | Gridding cost . |
|---|---|---|
| W-Snapshot(snapshot imaging) | |$\mathcal {O}(N_{x}N_{y}\log ({N_{x}N_{y}}))$| | |$\mathcal {O}(N_{\rm vis}$|) |
| W-Stacking | |$\mathcal {O}(W_{\rm range} \times FOV \times N_{x}N_{y}\log ({N_{x}N_{y}})$|) | |$\mathcal {O}(N_{\rm vis})$| |
| WS-Snapshot(snapshot imaging) | |$\mathcal {O}(W_{\rm range\_fit} \times FOV \times N_{x}N_{y}\log ({N_{x}N_{y}}) + N_{x}N_{y}$|) | |$\mathcal {O}(N_{\rm vis}$|) |
| DDFacet | |$\mathcal {O}(N_{x}N_{y}\log ({N_{x}N_{y}/N_{\rm fac}) + N_{x}N_{y}}$|) | |$\mathcal {O}(N_{\rm vis}N_{\rm fac}/B)$| |
| Method . | FFT cost . | Gridding cost . |
|---|---|---|
| W-Snapshot(snapshot imaging) | |$\mathcal {O}(N_{x}N_{y}\log ({N_{x}N_{y}}))$| | |$\mathcal {O}(N_{\rm vis}$|) |
| W-Stacking | |$\mathcal {O}(W_{\rm range} \times FOV \times N_{x}N_{y}\log ({N_{x}N_{y}})$|) | |$\mathcal {O}(N_{\rm vis})$| |
| WS-Snapshot(snapshot imaging) | |$\mathcal {O}(W_{\rm range\_fit} \times FOV \times N_{x}N_{y}\log ({N_{x}N_{y}}) + N_{x}N_{y}$|) | |$\mathcal {O}(N_{\rm vis}$|) |
| DDFacet | |$\mathcal {O}(N_{x}N_{y}\log ({N_{x}N_{y}/N_{\rm fac}) + N_{x}N_{y}}$|) | |$\mathcal {O}(N_{\rm vis}N_{\rm fac}/B)$| |
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