Fast Algorithms and Efficient GPU Implementations for the Radon Transform and the BackProjection Operator Represented as Convolution Operators
(2016) In SIAM Journal of Imaging Sciences 9(2). p.637664 Abstract
 The Radon transform and its adjoint, the backprojection operator, can both be expressed as convolutions in logpolar coordinates. Hence, fast algorithms for the application of these operators can be constructed by using FFT, if data is resampled at logpolar 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 backprojection operator by means of convolutions. However, in comparison to the interpolation conducted in Fourierbased gridding methods, the interpolation performed in the Radon and image... (More)
 The Radon transform and its adjoint, the backprojection operator, can both be expressed as convolutions in logpolar coordinates. Hence, fast algorithms for the application of these operators can be constructed by using FFT, if data is resampled at logpolar 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 backprojection operator by means of convolutions. However, in comparison to the interpolation conducted in Fourierbased 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. It also provides better control over the artifacts that can appear due to measurement errors.
Both the interpolation and the FFT operations can be efficiently implemented on Graphical Processor Units (GPUs). For the interpolation, it is possible to make use of the fact that linear interpolation is hardwired on GPUs, meaning that it has the same computational cost as direct memory access. Cubic order interpolation schemes can be constructed by combining linear interpolation steps and this provides important computation speedup.
We provide details about how the Radon transform and the backprojection can be implemented efficiently as convolution operators on GPUs. For large data sizes, these algorithms are several times faster than those of other software packages based on GPU implementations of the Radon transform and the backprojection operator. Moreover, the gain in computational speed is substantially higher when comparing against other CPU based algorithms. (Less)
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http://lup.lub.lu.se/record/454d9aeb79284cb7b9783836a2fa9f14
 author
 Nikitin, Viktor ^{LU} ; Andersson, Fredrik ^{LU} and Carlsson, Marcus ^{LU}
 organization
 publishing date
 20160510
 type
 Contribution to journal
 publication status
 published
 subject
 in
 SIAM Journal of Imaging Sciences
 volume
 9
 issue
 2
 pages
 28 pages
 publisher
 SIAM Publications
 external identifiers

 Scopus:84976621336
 WOS:000385275400006
 ISSN
 19364954
 DOI
 10.1137/15M1023762
 language
 English
 LU publication?
 yes
 id
 454d9aeb79284cb7b9783836a2fa9f14
 date added to LUP
 20160607 10:39:34
 date last changed
 20170101 08:27:39
@article{454d9aeb79284cb7b9783836a2fa9f14, abstract = {The Radon transform and its adjoint, the backprojection operator, can both be expressed as convolutions in logpolar coordinates. Hence, fast algorithms for the application of these operators can be constructed by using FFT, if data is resampled at logpolar 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 backprojection operator by means of convolutions. However, in comparison to the interpolation conducted in Fourierbased 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. It also provides better control over the artifacts that can appear due to measurement errors.<br/><br/>Both the interpolation and the FFT operations can be efficiently implemented on Graphical Processor Units (GPUs). For the interpolation, it is possible to make use of the fact that linear interpolation is hardwired on GPUs, meaning that it has the same computational cost as direct memory access. Cubic order interpolation schemes can be constructed by combining linear interpolation steps and this provides important computation speedup.<br/><br/>We provide details about how the Radon transform and the backprojection can be implemented efficiently as convolution operators on GPUs. For large data sizes, these algorithms are several times faster than those of other software packages based on GPU implementations of the Radon transform and the backprojection operator. Moreover, the gain in computational speed is substantially higher when comparing against other CPU based algorithms.}, author = {Nikitin, Viktor and Andersson, Fredrik and Carlsson, Marcus}, issn = {19364954}, language = {eng}, month = {05}, number = {2}, pages = {637664}, publisher = {SIAM Publications}, series = {SIAM Journal of Imaging Sciences}, title = {Fast Algorithms and Efficient GPU Implementations for the Radon Transform and the BackProjection Operator Represented as Convolution Operators}, url = {http://dx.doi.org/10.1137/15M1023762}, volume = {9}, year = {2016}, }