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 the operators can be constructed by using 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. 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 hard-wired 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 which provides important computation speedup. We provide details about how the Radon transform and the back-projection can be implemented efficiently as convolution operators on GPUs. For large data sizes, speedups of about 10 times are obtained in relation to the computational times of other software packages based on GPU implementations of the Radon transform and the back-projection operator. Moreover, speedups of more than a 1000 times are obtained against the CPU-implementations provided in the MATLAB image processing toolbox

Four-dimensional tomographic reconstruction by time domain decomposition

Since the beginnings of tomography, the requirement that the sample does not change during the acquisition of one tomographic rotation is unchanged. We derived and successfully implemented a tomographic reconstruction method which relaxes this decades-old requirement of static samples. In the presented method, dynamic tomographic data sets are decomposed in the temporal domain using basis functions and deploying an L1 regularization technique where the penalty factor is taken for spatial and temporal derivatives. We implemented the iterative algorithm for solving the regularization problem on modern GPU systems to demonstrate its practical use

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.Comment: 21 pages, 10 figures, 2 table

Main results of the Ouabain and Adducin for Specific Intervention on Sodium in Hypertension Trial (OASIS-HT): a randomized placebo-controlled phase-2 dose-finding study of rostafuroxin

Background. The Ouabain and Adducin for Specific Intervention on Sodium in Hypertension (OASIS-HT) Trial was a phase 2 dose-finding study of rostafuroxin, a digitoxygenin deivative, which selectively antagonizes the effects of endogenous ouabain (EO) on Na+,K+-ATPase and mutated adducin. Rostafuroxin lowered blood pressure (BP) in some animal models and in humans. Methods. OASIS-HT consisted of 5 concurrently running double-blind cross-over studies. After 4 weeks without treatment, 435 patients with uncomplicated systolic hypertension (140-169 mm Hg) were randomized to rostafuroxin (0.05, 0.15, 0.5, 1.5 or 5.0 mg/d) or matching placebo, each treatment period lasting 5 weeks. The primary endpoint was the reduction in systolic office BP. Among the secondary endpoints were diastolic office BP, 24 h ambulatory BP, plasma EO concentration and renin activity, 24-h urinary sodium and aldosterone excretion, and safety. ANOVA considered treatment sequence (fixed effect), subjects nested within sequence (random), period (fixed), and treatment (fixed). Results. Among 410 analyzable patients (40.5% women; mean age, 48.4 years), the differences in the primary endpoint (rostafuroxin minus placebo) ranged from -0.18 mm Hg (P=0.90) on 0.15 mg/d rostafuroxin to 2.72 mm Hg (P=0.04) on 0.05 mg/d. In the 5 dosage arms combined, the treatment effects averaged 1.30 mm Hg (P=0.03) for systolic office BP; 0.70 mm Hg (P=0.08) for diastolic office BP; 0.36 mm Hg (P=0.49) for 24-h systolic BP; and 0.05 mm Hg (P=0.88) for 24-h diastolic BP. In the 2 treatment groups combined, systolic (-1.36 mm Hg) and diastolic (-0.97 mm Hg) office BPs decreased from week 5 to 10 (P for period effect ≤=0.028), but carry-over effects were not significant (P≥=0.11). All other endpoints were not different on rostafuroxin and placebo. Minor side-effects occurred with similarly low frequency on rostafuroxin and placebo. Conclusions. In 5 concurrently running double-blind cross-over studies rostafuroxin did not reduce BP at any dose. Trial Registration: NCT00415038 http://www.clinicaltrials.gov)

Measurement of forward W→eνW\to e\nu production in pppp collisions at s=8 \sqrt{s}=8\,TeV

A measurement of the cross-section for $W \to e\nu$ production in $pp$ collisions is presented using data corresponding to an integrated luminosity of $2\,$fb$^{-1}$ collected by the LHCb experiment at a centre-of-mass energy of $\sqrt{s}=8\,$TeV. The electrons are required to have more than $20\,$GeV of transverse momentum and to lie between 2.00 and 4.25 in pseudorapidity. The inclusive $W$ production cross-sections, where the $W$ decays to $e\nu$, are measured to be \begin{align*} \begin{split} \sigma_{W^{+} \to e^{+}\nu_{e}}&=1124.4\pm 2.1\pm 21.5\pm 11.2\pm 13.0\,\mathrm{pb},\\ \sigma_{W^{-} \to e^{-}\bar{\nu}_{e}}&=\,\,\,809.0\pm 1.9\pm 18.1\pm\,\,\,7.0\pm \phantom{0}9.4\,\mathrm{pb}, \end{split} \end{align*} where the first uncertainties are statistical, the second are systematic, the third are due to the knowledge of the LHC beam energy and the fourth are due to the luminosity determination. Differential cross-sections as a function of the electron pseudorapidity are measured. The $W^{+}/W^{-}$ cross-section ratio and production charge asymmetry are also reported. Results are compared with theoretical predictions at next-to-next-to-leading order in perturbative quantum chromodynamics. Finally, in a precise test of lepton universality, the ratio of $W$ boson branching fractions is determined to be \begin{align*} \begin{split} \mathcal{B}(W \to e\nu)/\mathcal{B}(W \to \mu\nu)=1.020\pm 0.002\pm 0.019, \end{split} \end{align*} where the first uncertainty is statistical and the second is systematic.A measurement of the cross-section for $W \to e\nu$ production in $pp$ collisions is presented using data corresponding to an integrated luminosity of $2\,$fb$^{-1}$ collected by the LHCb experiment at a centre-of-mass energy of $\sqrt{s}=8\,$TeV. The electrons are required to have more than $20\,$GeV of transverse momentum and to lie between 2.00 and 4.25 in pseudorapidity. The inclusive $W$ production cross-sections, where the $W$ decays to $e\nu$, are measured to be \begin{equation*} \sigma_{W^{+} \to e^{+}\nu_{e}}=1124.4\pm 2.1\pm 21.5\pm 11.2\pm 13.0\,\mathrm{pb}, \end{equation*} \begin{equation*} \sigma_{W^{-} \to e^{-}\bar{\nu}_{e}}=\,\,\,809.0\pm 1.9\pm 18.1\pm\,\,\,7.0\pm \phantom{0}9.4\,\mathrm{pb}, \end{equation*} where the first uncertainties are statistical, the second are systematic, the third are due to the knowledge of the LHC beam energy and the fourth are due to the luminosity determination. Differential cross-sections as a function of the electron pseudorapidity are measured. The $W^{+}/W^{-}$ cross-section ratio and production charge asymmetry are also reported. Results are compared with theoretical predictions at next-to-next-to-leading order in perturbative quantum chromodynamics. Finally, in a precise test of lepton universality, the ratio of $W$ boson branching fractions is determined to be \begin{equation*} \mathcal{B}(W \to e\nu)/\mathcal{B}(W \to \mu\nu)=1.020\pm 0.002\pm 0.019, \end{equation*} where the first uncertainty is statistical and the second is systematic.A measurement of the cross-section for W → eν production in pp collisions is presented using data corresponding to an integrated luminosity of 2 fb$^{−1}$ collected by the LHCb experiment at a centre-of-mass energy of $\sqrt{s}=8$ TeV. The electrons are required to have more than 20 GeV of transverse momentum and to lie between 2.00 and 4.25 in pseudorapidity. The inclusive W production cross-sections, where the W decays to eν, are measured to be ${\sigma}_{W^{+}\to {e}^{+}{\nu}_e}=1124.4\pm 2.1\pm 21.5\pm 11.2\pm 13.0\kern0.5em \mathrm{p}\mathrm{b},$ ${\sigma}_{W^{-}\to {e}^{-}{\overline{\nu}}_e}=809.0\pm 1.9\pm 18.1\pm \kern0.5em 7.0\pm \kern0.5em 9.4\,\mathrm{p}\mathrm{b},$ where the first uncertainties are statistical, the second are systematic, the third are due to the knowledge of the LHC beam energy and the fourth are due to the luminosity determination