Fast Radon Transforms and Reconstruction Techniques in Seismology
(2016) Abstract
 The measurements conducted in tomography and seismology typically yield large multidimensional data sets. This in combination with the fact that the data may have an irregular structure makes it computationally prohibitive to use simple reconstruction methods directly. Hence, for inverse problems in computed tomography and seismology there is a demand for fast computational methods using highperformance computational facilities to find accurate solutions in a reasonable time.
We exploit the particular structure of operators involved, investigate their properties and then construct algorithms for fast evaluations. Algorithm implementations are done on CPU and GPU with exploiting Intel and Nvidia facilities for parallel computing.... (More)  The measurements conducted in tomography and seismology typically yield large multidimensional data sets. This in combination with the fact that the data may have an irregular structure makes it computationally prohibitive to use simple reconstruction methods directly. Hence, for inverse problems in computed tomography and seismology there is a demand for fast computational methods using highperformance computational facilities to find accurate solutions in a reasonable time.
We exploit the particular structure of operators involved, investigate their properties and then construct algorithms for fast evaluations. Algorithm implementations are done on CPU and GPU with exploiting Intel and Nvidia facilities for parallel computing.
For computed tomography we develop fast algorithms for evaluating the standard Radon transform and the exponential Radon transform, as well as the corresponding adjoint operators and data inversion schemes.
Fast evaluation of the Radon transform is based on using representations in logpolar coordinates, where the operator can be expressed in terms of convolutions and thereby rapidly evaluated by using fast Fourier transforms. Fast evaluation of the exponential Radon transform in turn is based on a generalization of the Fourier slice theorem in the Laplace domain, and here the computations can be made fast by using fast Laplace transforms.
For seismology we construct fast algorithms for data interpolation, compression, denoising, and attenuation of multiple reflections appearing in seismic measurements. Some of these procedures are performed by using sparse representations of seismic data. Sparse representations are for instance obtained with the hyperbolic Radon transform or by decomposing the data with using wave packets. Algorithms for fast evaluation of the hyperbolic Radon transforms are constructed by generalizing the logpolar approach. For the wavepacket decomposition we design fast implementations based on unequally spaced Fourier transforms.
We also provide an approach for interpolation of a new type of retrieving seismic data  multicomponent streamer data. The interpolation is formulated in terms of the solution of a partial differential equation that describes how energy is propagated between different parts of the data. (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/record/0a6f53568cee4d32aff296c236d7e771
 author
 Nikitin, Viktor ^{LU}
 supervisor
 opponent

 Dr. Luis Tenorio, Colorado School of Mines, Illinois, USA.
 organization
 publishing date
 20160517
 type
 Thesis
 publication status
 published
 subject
 keywords
 Fourier transform (FFT), Radon transforms, GPU
 pages
 206 pages
 publisher
 Printed in Sweden by MediaTryck, Lund University
 defense location
 Lecture hall MA:03, Annexet, Sölvegatan 20, Lund University, Faculty of Engineering.
 defense date
 20160819 13:00
 ISBN
 9789176238462
 language
 English
 LU publication?
 yes
 id
 0a6f53568cee4d32aff296c236d7e771
 alternative location
 http://www.maths.lth.se/matematiklth/personal/nikitin/thesis.pdf
 date added to LUP
 20160607 10:32:39
 date last changed
 20160919 08:45:20
@phdthesis{0a6f53568cee4d32aff296c236d7e771, abstract = {The measurements conducted in tomography and seismology typically yield large multidimensional data sets. This in combination with the fact that the data may have an irregular structure makes it computationally prohibitive to use simple reconstruction methods directly. Hence, for inverse problems in computed tomography and seismology there is a demand for fast computational methods using highperformance computational facilities to find accurate solutions in a reasonable time. <br/>We exploit the particular structure of operators involved, investigate their properties and then construct algorithms for fast evaluations. Algorithm implementations are done on CPU and GPU with exploiting Intel and Nvidia facilities for parallel computing. <br/><br/>For computed tomography we develop fast algorithms for evaluating the standard Radon transform and the exponential Radon transform, as well as the corresponding adjoint operators and data inversion schemes. <br/>Fast evaluation of the Radon transform is based on using representations in logpolar coordinates, where the operator can be expressed in terms of convolutions and thereby rapidly evaluated by using fast Fourier transforms. Fast evaluation of the exponential Radon transform in turn is based on a generalization of the Fourier slice theorem in the Laplace domain, and here the computations can be made fast by using fast Laplace transforms.<br/><br/>For seismology we construct fast algorithms for data interpolation, compression, denoising, and attenuation of multiple reflections appearing in seismic measurements. Some of these procedures are performed by using sparse representations of seismic data. Sparse representations are for instance obtained with the hyperbolic Radon transform or by decomposing the data with using wave packets. Algorithms for fast evaluation of the hyperbolic Radon transforms are constructed by generalizing the logpolar approach. For the wavepacket decomposition we design fast implementations based on unequally spaced Fourier transforms.<br/>We also provide an approach for interpolation of a new type of retrieving seismic data  multicomponent streamer data. The interpolation is formulated in terms of the solution of a partial differential equation that describes how energy is propagated between different parts of the data. }, author = {Nikitin, Viktor}, isbn = {9789176238462}, keyword = {Fourier transform (FFT),Radon transforms,GPU}, language = {eng}, month = {05}, pages = {206}, publisher = {Printed in Sweden by MediaTryck, Lund University}, school = {Lund University}, title = {Fast Radon Transforms and Reconstruction Techniques in Seismology}, year = {2016}, }