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We establish lower bounds on the complexity of computing the following number-theoretic functions and relations from piecewise linear primitives: (i) the Legendre and Jacobi symbols, (ii) pseudoprimality, and (iii) modular exponentiation. As a corollary to the lower bound obtained for (i), an algorithm of Shallit and Sorenson is optimal (up to a(More)
BACKGROUND The accuracy of phase-contrast cardiovascular magnetic resonance (PC-CMR) can be compromised by background phase errors. It is the objective of the present work to provide an analysis of the temperature dependence of background phase errors in PC-CMR by means of gradient mount temperature sensing and magnetic field monitoring. METHODS(More)
PURPOSE Fast dynamic imaging of hyperpolarized (13) C-labeled pyruvate and its downstream metabolites shows great potential for probing metabolic changes in the heart. Sequences that allow for fast encoding of the spectral and spatial information of the myocardial metabolism and optimal signal excitation are usually limited by gradient performance,(More)
PURPOSE To implement hyperpolarized magnetic resonance (MR) imaging in an animal model of ischemia-reperfusion and to assess in vivo the regional changes in pyruvate metabolism within the 1st hour and at 1 week after a brief episode of coronary occlusion and reperfusion. MATERIALS AND METHODS All animal experiments were performed with adherence to the(More)
Three-dimensional phase-contrast velocity vector field mapping shows great potential for clinical applications; however measurement inaccuracies may limit the utility and robustness of the technique. While parts of the error in the measured velocity fields can be minimized by background phase estimation in static tissue and magnetic field monitoring,(More)
Hyperpolarized (13)C-labeled pyruvate is a promising tool to investigate cardiac metabolism. It has been shown that changes in substrate metabolism occur following the induction of ischemia. To investigate the metabolic changes that are confined to spatial regions, high spatiotemporal resolution is required. The present work exploits both spatial and(More)
PURPOSE To improve velocity vector field reconstruction from undersampled four-dimensional (4D) flow MRI by penalizing divergence of the measured flow field. THEORY AND METHODS Iterative image reconstruction in which magnitude and phase are regularized separately in alternating iterations was implemented. The approach allows incorporating prior knowledge(More)
PURPOSE Gradient imperfections remain a challenge in MRI, especially for sequences relying on long imaging readouts. This work aims to explore image reconstruction based on k-space trajectories predicted by an impulse response model of the gradient system. THEORY AND METHODS Gradient characterization was performed twice with 3 years interval on a(More)
In this work an approach is described to efficiently reduce inaccuracies of flow data acquired with reduced data acquisition methods based on the physical prior knowledge of zero divergence in 3D velocity vector fields. The divergence-free condition is implemented using a synergistic combination of normalized convolution and divergence-free radial basis(More)
Introduction: Despite its value in the research setting, the translation of phase-contrast magnetic resonance imaging (PC-MRI) into the clinical realm is still limited. Background phase offsets have been identified as one of the key issues [1]. While concomitant and non-linear field effects can be well compensated for [2, 3], correction of phase offsets(More)