Viktor V. Nikitin

Fast Algorithms and Efficient GPU Implementations for the Radon Transform and the Back-Projection Operator Represented as Convolution Operators

The Radon transform and its adjoint, the back-projection operator, can both be expressed as convolutions in log-polar coordinates. Hence, fast algorithms for the application of these operators can be constructed by using the FFT, if data is resampled at log-polar coordinates. Radon data is typically measured on an equally spaced grid in polar coordinates, and reconstructions are represented (as images) in Cartesian coordinates. Therefore, in addition to FFT, several steps of interpolation have to be conducted in order to apply the Radon transform and the back-projection operator by means of convolutions. However, in comparison to the interpolation conducted in Fourier-based gridding methods, the interpolation performed in the Radon and image domains will typically deal with functions that are substantially less oscillatory. Reasonable reconstruction results can thus be expected using interpolation schemes of moderate order. The approach also provides better control over the artifacts that can appear due t...

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

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.

3D Wave-packet decomposition implemented on GPUs

Decomposition of seismic data into wave-packet representations has been successfully used for 2D data compression, interpolation and de-noising. In this paper we present a fast implementation of a 3D wave-packet decomposition using graphical processing units (GPUs). This allows for the similar processing of 3D seismic gathers. We discuss parallel implementation of the wave-packet transform on GPUs as opposed to existing algorithms (sequential and MPI-parallel). A few computational steps had to be modified adapting them for a GPU platform. The code has been tested on a 3D data set of size 2563, where we obtain speedup of about 40 times compared to the sequential code performance.

Directional interpolation of multicomponent data

ABSTRACT A method for interpolation of multicomponent streamer data based on using the local directionality structure is presented. The derivative components are used to estimate a vector field that locally describes the direction with the least variability. Given this vector field, the interpolation can be phrased in terms of the solution of a partial differential equation that describes how energy is transported between regions of missing data. The approach can be efficiently implemented using readily available routines for computer graphics. The method is robust to noise in the measurements and particularly towards high levels of low‐frequent noise that is present in the derivative components of the multicomponent streamer data.

Parallel algorithm of 3D wave-packet decomposition of seismic data: implementation and optimization for GPU

In this paper, we consider 3D wave-packet transform that is useful in 3D data processing. This transform is computationally intensive even though it has a computational complexity of O(N3 log N). Here we present its implementation on GPUs using NVIDIA CUDA technology. The code was tested on different types of graphical processors achieving the average speedup up to 46 times on Tesla M2050 compared to CPU sequential code. Also, we analyzed its scalability for several GPUs. The code was tested for processing synthetic seismic data set: data compression, de-noising, and interpolation.