## Fast hyperbolic Radon transform represented as convolutions in log-polar coordinates

Centre for Mathematical Sciences, Lund University, Solvegatan 18, Box 118, SE-22100 Lund, Sweden

arXiv:1604.07651 [math.NA], (22 Apr 2016)

@article{nikitin2016fast,

title={Fast hyperbolic Radon transform represented as convolutions in log-polar coordinates},

author={Nikitin, Viktor V. and Andersson, Fredrik and Carlsson, Marcus and Duchkov, Anton A.},

year={2016},

month={apr},

archivePrefix={"arXiv"},

primaryClass={math.NA}

}

The hyperbolic Radon transform is a commonly used tool in seismic processing, for instance in seismic velocity analysis, data interpolation and for multiple removal. A direct implementation by summation of traces with different moveouts is computationally expensive for large data sets. In this paper we present a new method for fast computation of the hyperbolic Radon transforms. It is based on using a log-polar sampling with which the main computational parts reduce to computing convolutions. This allows for fast implementations by means of FFT. In addition to the FFT operations, interpolation procedures are required for switching between coordinates in the time-offset; Radon; and log-polar domains. Graphical Processor Units (GPUs) are suitable to use as a computational platform for this purpose, due to the hardware supported interpolation routines as well as optimized routines for FFT. Performance tests show large speed-ups of the proposed algorithm. Hence, it is suitable to use in iterative methods, and we provide examples for data interpolation and multiple removal using this approach.

May 3, 2016 by hgpu

Fast hyperbolic Radon transform represented as convolutions in log-polar coordinates,