A fast butterfly algorithm for generalized Radon transforms |
Going back to the five steps of the butterfly algorithm, it is clear that the input data is only involved at the very first step. Besides, for every the operation connecting and amounts to a matrix-vector multiplication (see equation 23), which does not at all require the input data to be uniformly distributed (the same argument applies to the output data ). Therefore, our algorithm can be easily extended to handle the following problem:
(28) |
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Figure 12. 3D synthetic CMP gather. , . s, km. |
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Figure 13. , . Output of the fast butterfly algorithm applied to the synthetic data in Figure 12. , . CPU time: 1.67 s. Purple curve overlaid is the true slowness. |
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dimod-4
Figure 14. , . Output of the velocity scan applied to the synthetic data in Figure 12. CPU time: 125.54 s. Purple curve overlaid is the true slowness. |
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A fast butterfly algorithm for generalized Radon transforms |