Fast High-Resolution Hyperbolic Radon Transform

Due to its time-variant nature, the computationally expensive hyperbolic Radon transform (RT) is not easy to be accelerated, e.g., based on the convolution theorem in the frequency domain. However, the hyperbolic RT better matches the trajectories of reflection events in prestack gathers than other time-invariant RTs, e.g., linear or parabolic RTs. Hence, despite its large computational cost, the time-domain hyperbolic RT is still preferred in many seismic processing applications. We propose a fast high-resolution hyperbolic RT (HRHRT) with a fast butterfly algorithm. The forward and adjoint RTs can be greatly accelerated based on a fast butterfly algorithm by reformulating the time-space domain Radon operator as a frequency-domain Fourier integral operator (FIO). The fast butterfly algorithm solves the FIO problem by a blockwise low-rank approximation scheme. The single-step hyperbolic RT can be much faster (e.g., hundreds of times faster for a large problem) than the traditional implementation, resulting in a significant computational boost when the transform is taken in an iterative fashion to estimate the high-resolution Radon coefficients. We demonstrate the similar performance and the much different computational efficiencies between the proposed fast HRHRT and the traditional method over several different problems, i.e., random noise suppression, big-gap seismic reconstruction, and multiples attenuation.