A fast butterfly algorithm for generalized Radon transforms |

In this section we provide several numerical examples to illustrate the empirical properties of the fast butterfly algorithm. To check the results *qualitatively*, we compare with the *velocity scan* method (the nearest neighbor interpolation is used to minimize the interpolation cost); to test the results *quantitatively*, however, it makes more sense to compare with the direct evaluation of equation 3, since the fast algorithm is to speed up this summation in the frequency domain, whereas the *velocity scan* computes a slightly different sum in the time domain, which may contain interpolation artifacts.

There is no general rule for selecting parameters , , , ... The larger is, the fewer Chebyshev points are needed, and vice versa. In practice, parameters can be tuned to achieve the best efficiency and accuracy trade-off. For simplicity, in the following examples and , , , are chosen such that the relative error between the fast algorithm and the direct computation of equation 3 is about . These combinations are not necessarily optimal in terms of efficiency.

- Synthetic data -- square sampling
- Synthetic data -- rectangular sampling
- Synthetic data -- irregular sampling
- Field data
- Computing the adjoint operator

A fast butterfly algorithm for generalized Radon transforms |

2013-07-26