Radial Trajectories Research Articles

WARF: A Weighted-Sum Approach to Radial MRI Image Reconstruction With a Rotating RF Coil

The recently developed single-element surface rotating radio-frequency coil (RRFC) for magnetic resonance imaging (MRI) is able to acquire signals from around the subject in the manner of a multi-coil array, while exhibiting simplified construction and no coil size restrictions. Herein, we present a novel image reconstruction algorithm for data acquired with the RRFC, which we label WARF (a weighted-sum approach to radial MRI image reconstruction with a rotating RF coil). The algorithm approaches the reconstruction problem by considering each image pixel to be a weighted sum of all acquired k-space data, which is already the case implicitly in several established methods. The problem is thus posed as one of solving for the appropriate weights directly. The theory underlying WARF is presented, and several measures to improve the computational efficiency of a practical implementation are considered. We note that while still computationally expensive, the calculation of the weights themselves would not necessarily need to be repeated each time the algorithm is applied. MR data are simulated for imaging schemes involving the rotating RF coil with both ideal and variable angular velocities, and for the case where the k-space locations of the radial trajectory are deviated from their intended positions. The WARF reconstruction algorithm is applied to each simulated data set, and compared with reconstructions from existing methods, where it is seen to demonstrate a robustness to velocity variation and the suppression of artefacts arising from a deviated trajectory. Finally, WARF is applied to experimental rotating RF coil data, where it is shown to yield good quality images.

Supertranslation hair of Schwarzschild black hole: a Wilson line perspective

We demonstrate within the quantum field theoretical framework that an asymptotic particle falling into the black hole implants soft graviton hair on the horizon, conforming with the classical proposal of Hawking, Perry and Strominger. A key ingredient to this result is the construction of gravitational Wilson line dressings of an infalling scalar field, carrying a definite horizon supertranslation charge. It is shown that a typical Schwarzschild state is degenerate, and can be labeled by different soft supertranslation hairs parametrized for radial trajectories by the mass and energy of the infalling particle and its asymptotic point of contact with the horizon. The supertranslation zero modes are also obtained in terms of zero-frequency graviton operators, and are shown to be the expected canonical partners of the linearized horizon charge that enlarge the horizon Hilbert space.

Unified picture of electromagnetic and gravitational forces in two-spinor language

The well known Geodesic Equation of General Relativity is newly formulated in Weyl two-spinor language in a way susceptible of being generalized via a set of two-spinor equations, equivalent to the Lorentz Force of Electrodynamics, obtained in previous studies. General spinor equations of motion for a test charged spin 1/2 particle in arbitrary electromagnetic and gravitational fields are obtained describing not only spacetime trajectories but also spin precession. For the case of the Schwarzschild metric and radial trajectories, spinor equations unifying gravitational and electric forces are obtained and solved for a weak gravitational field (or long distance from the source).

Rindler horizons in a Schwarzschild spacetime

We investigate the past and future Rindler horizons for radial Rindler trajectories in the Schwarzschild spacetime. We assume the Rindler trajectory to be linearly uniformly accelerated (LUA) throughout its motion, in the sense of the curved spacetime generalisation of the Letaw-Frenet equations. The analytical solution for the radial LUA trajectories along with its past and future intercepts ${\cal C}$ with the past null infinity ${\cal J^-}$ and future null infinity ${\cal J^+}$ are presented. The Rindler horizons, in the presence of the black hole, are found to depend on both the magnitude of acceleration $|a|$ and the asymptotic initial data $h$, unlike in the flat Rindler spacetime case wherein they are only a function of the global translational shift $h$. The horizon features are discussed. The Rindler quadrant structure provides an alternate perspective to interpret the acceleration bounds, $|a| \leq |a|_b$ found earlier in arXiv:1901.04674.

Highly accelerated vessel-selective arterial spin labeling angiography using sparsity and smoothness constraints.

PurposeTo demonstrate that vessel selectivity in dynamic arterial spin labeling angiography can be achieved without any scan‐time penalty or noticeable loss of image quality compared with conventional arterial spin labeling angiography.MethodsSimulations on a numerical phantom were used to assess whether the increased sparsity of vessel‐encoded angiograms compared with non‐vessel‐encoded angiograms alone can improve reconstruction results in a compressed‐sensing framework. Further simulations were performed to study whether the difference in relative sparsity between nonselective and vessel‐selective dynamic angiograms was sufficient to achieve similar image quality at matched scan times in the presence of noise. Finally, data were acquired from 5 healthy volunteers to validate the technique in vivo. All data, both simulated and in vivo, were sampled in 2D using a golden‐angle radial trajectory and reconstructed by enforcing image domain sparsity and temporal smoothness on the angiograms in a parallel imaging and compressed‐sensing framework.ResultsRelative sparsity was established as a primary factor governing the reconstruction fidelity. Using the proposed reconstruction scheme, differences between vessel‐selective and nonselective angiography were negligible compared with the dominant factor of total scan time in both simulations and in vivo experiments at acceleration factors up to R = 34. The reconstruction quality was not heavily dependent on hand‐tuning the parameters of the reconstruction.ConclusionThe increase in relative sparsity of vessel‐selective angiograms compared with nonselective angiograms can be leveraged to achieve higher acceleration without loss of image quality, resulting in the acquisition of vessel‐selective information at no scan‐time cost.

Motion robust respiratory-resolved 3D radial flow MRI and its application in neonatal congenital heart disease.

To test and implement a motion-robust and respiratory-resolved 3D Radial Flow framework that addresses the need for rapid, high resolution imaging in neonatal patients with congenital heart disease. A 4-point velocity encoding and 3D radial trajectory with double-golden angle ordering was combined with bulk motion correction (from projection center of mass) and respiration phase detection (from principal component analysis of heartbeat-averaged data) to create motion-robust 3D velocity cardiac time-averaged data. This framework was tested in a whole-chest digital phantom with simulated bulk and realistic physiological motion. In vivo imaging was performed in 20 congenital heart disease infants under feed-and-sleep with submillimeter isotropic resolution in ~3 min. Flows were validated against clinical 2D PCMRI and whole-heart visualizations of blood flow were performed. The proposed framework resolved all simulated digital phantom motion states (mean ± standard error: rotation - azimuthal = 0.29 ± 0.02°; translation - Ty = 1.29 ± 0.12 mm, Tz = -0.27 ± 0.13 mm; rotation+translation - polar = 0.49 ± 0.16°, Tx = -2.47 ± 0.51 mm, Tz = 5.78 ± 1.33 mm). Measured timing errors of peak expiration across all signal-to-noise ratio values were 22% of the true respiratory period (range = [404-489 ± 298-334] ms). For in vivo imaging, motion correction improved 3D Radial Flow measurements (no correction: R2 = 0.62, root mean square error = 0.80 L/min/m2 , Bland-Altman bias [limits of agreement] = -0.21 [-1.40, 0.94] L/min/m2 ; motion corrected, expiration: R2 = 0.90, root mean square error = 0.46 L/min/m2 , bias [limits of agreement] = 0.06 [-0.49, 0.62] L/min/m2 ). Respiratory-resolved 3D velocity visualizations were achieved in various neonatal pathologies pre- and postsurgical correction. 3D cardiac flow may be visualized and accurately quantified in neonatal subjects using the proposed framework. This technique may enable more comprehensive hemodynamic studies in small infants.

The advantages of radial trajectories for vessel-selective dynamic angiography with arterial spin labeling

ObjectivesTo demonstrate the advantages of radial k-space trajectories over conventional Cartesian approaches for accelerating the acquisition of vessel-selective arterial spin labeling (ASL) dynamic angiograms, which are conventionally time consuming to acquire.Materials and methodsVessel-encoded pseudocontinuous ASL was combined with time-resolved balanced steady-state free precession (bSSFP) and spoiled gradient echo (SPGR) readouts to obtain dynamic vessel-selective angiograms arising from the four main brain-feeding arteries. Dynamic 2D protocols with acquisition times of one minute or less were achieved through radial undersampling or a Cartesian parallel imaging approach. For whole-brain dynamic 3D imaging, magnetic field inhomogeneity and the high acceleration factors required rule out the use of bSSFP and Cartesian trajectories, so the feasibility of acquiring 3D radial SPGR angiograms was tested.ResultsThe improved SNR efficiency of bSSFP over SPGR was confirmed for 2D dynamic imaging. Radial trajectories had considerable advantages over a Cartesian approach, including a factor of two improvements in the measured SNR (p < 0.00001, N = 6), improved distal vessel delineation and the lack of a need for calibration data. The 3D radial approach produced good quality angiograms with negligible artifacts despite the high acceleration factor (R = 13).ConclusionRadial trajectories outperform conventional Cartesian techniques for accelerated vessel-selective ASL dynamic angiography.

Free-running simultaneous myocardial T1/T2 mapping and cine imaging with 3D whole-heart coverage and isotropic spatial resolution

PurposeTo develop a free-running framework for 3D isotropic simultaneous myocardial T1/T2 mapping and cine imaging. MethodsContinuous data acquisition with 3D golden angle radial trajectory is used in conjunction with T2 preparation of varying echo times and inversion recovery (IR) pulses to enable simultaneous myocardial T1/T2 mapping and cine imaging. Data acquisition is retrospectively synchronized with ECG signal, and 1D respiratory self-navigation signal is extracted from the k-space center of all radial spokes. Respiratory binning is performed based on the estimated respiratory signal, enabling estimation and correction of 3D translational respiratory motion. Using high-dimensionality patch-based undersampled reconstruction with dictionary-based low-rank inversion, whole-heart T1/T2 maps and cine images can be generated with 2 mm isotropic spatial resolution. The proposed technique was validated in a standardised phantom and ten healthy subjects in comparison to conventional 2D imaging techniques. ResultsPhantom T1 and T2 measurements demonstrated good agreement with 2D spin echo techniques. Septal T1 estimated with the proposed technique (1185.6 ± 49.8 ms) was longer than with a conventional breath-hold 2D IR-prepared sequence (1044.3 ± 26.7 ms), whereas T2 measurements (47.6 ± 2.5 ms) were lower than a breath-hold 2D gradient spin echo sequence (52.0 ± 1.8 ms). Precision of the proposed 3D mapping was higher than conventional 2D mapping techniques. Ejection fraction measured with the proposed 3D approach (63.8 ± 6.8%) agreed well with conventional breath-held multi-slice 2D cine (62.3 ± 6.4%). ConclusionsThe proposed technique provides co-registered 3D T1/T2 maps and cine images with isotropic spatial resolution from a single free-breathing scan, thereby providing a promising imaging tool for whole-heart myocardial tissue characterization and functional evaluation.

Dynamics of the quark-antiquark interaction and the universality of Regge trajectories

The dynamical picture of a quark-antiquark interaction in light mesons, which provides linearity of radial and orbital Regge trajectories (RT), is studied with the use of the relativistic string Hamiltonian with flattened confining potential and taking into account the self-energy and string corrections. Due to the flattening effect both slopes, $\beta_n$ of the radial and $\beta_l$ of the orbital RT, decrease by $\sim 30\%$ with the value of $\beta_n=1.30(5)$~GeV$^2$ being larger than $ \beta_l=0.95(5)$~GeV. The self-energy correction provides the linearity of RT and remains important up to very high excitations; the string correction decreases the slope of the orbital RT, while the intercept $\beta_0=0.51(1)~ $GeV$^2$ is equal to the squared centroid mass of $\rho(1S)$. If the universal gluon-exchanged potential without fitting parameters and screening function, as in heavy quarkonia, is taken, then the slope of the radial RT decreases, $\beta_n=1.15(8)$~GeV$^2$, and its value coincides with the slope of the orbital RT, $\beta_l=1.08(8)$~GeV$^2$ within theoretical errors, producing the universal RT.

Radial Spectrum of Light Mesons in Planar QCD Sum Rules and the Scalar Sigma-Meson

In the framework of spectral sum rules in the planar limit of quantum chromodynamics, we propose two new methods for calculating the spectra of light mesons based on using linear radial Regge trajectories and the simplest quark-antiquark operators interpolating meson states. Both methods predict a resonance near 500 MeV in the scalar-isoscalar channel, which hypothetically corresponds to the lightest scalar hadron. the σ-meson. This can mean that the quark-antiquark component is strongly dominating in its structure even if the σ-meson is a tetraquark state. In one of the methods, we obtain a reasonable agreement with experimental data using only two input parameters: the phenomenological value of the gluon condensate and the weak decay constant of the pion. In this case, the predicted quark condensate value agrees well with contemporary lattice computation results.

A combined polar and Cartesian piecewise trajectory generation and analysis of a robotic arm

In this paper a combined polar-Cartesian approach to generate a smooth trajectory of a robotic arm along priori defined via-points is presented. Due to the characteristics/- geometry of the robotic arm, cylindrical coordinates are associated with the trajectory of motion. Possible trajectories representing the system dynamics are generated by mix matching higher order polar piecewise polynomials used to devise the radial trajectory and Cartesian piecewise polynomials used to calculate the related height in a normal plane unfolded along the radial trajectory of the motion. To describe the kinematic properties of the end-effector a moving non-inertial orthonormal Frenet frame is considered. Using the Frenet frame, the components of the velocity and acceleration along the frame unit vectors are calculated. Numerical simulations are performed for two different configurations in order to validate the approach.

SANTIS: Sampling-Augmented Neural neTwork with Incoherent Structure for MR image reconstruction.

To develop and evaluate a novel deep learning-based reconstruction framework called SANTIS (Sampling-Augmented Neural neTwork with Incoherent Structure) for efficient MR image reconstruction with improved robustness against sampling pattern discrepancy. With a combination of data cycle-consistent adversarial network, end-to-end convolutional neural network mapping, and data fidelity enforcement for reconstructing undersampled MR data, SANTIS additionally utilizes a sampling-augmented training strategy by extensively varying undersampling patterns during training, so that the network is capable of learning various aliasing structures and thereby removing undersampling artifacts more effectively and robustly. The performance of SANTIS was demonstrated for accelerated knee imaging and liver imaging using a Cartesian trajectory and a golden-angle radial trajectory, respectively. Quantitative metrics were used to assess its performance against different references. The feasibility of SANTIS in reconstructing dynamic contrast-enhanced images was also demonstrated using transfer learning. Compared to conventional reconstruction that exploits image sparsity, SANTIS achieved consistently improved reconstruction performance (lower errors and greater image sharpness). Compared to standard learning-based methods without sampling augmentation (e.g., training with a fixed undersampling pattern), SANTIS provides comparable reconstruction performance, but significantly improved robustness, against sampling pattern discrepancy. SANTIS also achieved encouraging results for reconstructing liver images acquired at different contrast phases. By extensively varying undersampling patterns, the sampling-augmented training strategy in SANTIS can remove undersampling artifacts more robustly. The novel concept behind SANTIS can particularly be useful for improving the robustness of deep learning-based image reconstruction against discrepancy between training and inference, an important, but currently less explored, topic.

Vibration Detection and Experiment of PMSM High Speed Grinding Motorized Spindle Based on Frequency Domain Technology

Abstract The spindle vibrations of the high-speed grinding motorized spindle largely determine the machining quality and precision. In order to accurately predict the spindle vibrations of the PMSM high-speed grinding motorized spindle, the vibration causes are explored and analyzed. The radial vibration, inclined vibration, and axial vibration model are established. The experimental modal analysis method is proposed to analyze the dynamic response of the spindle and to identify the modal parameters of the spindle structure. Thereafter, the frequency response function (FRF) is calculated by self-power spectrum and cross-power spectrum. It is transformed into the vibration spectrum analysis of the spindle. The least-square method is used to fit the radial trajectory of the spindle. This paper aims to propose double standard spheres for 5- DOF spindle vibrations used to detect the spindle vibrations. In the experiment, the method proposed in this paper can effectively and accurately determine the causes of the spindle vibrations. The spectrum analysis and the trajectory are common tools in the spindle vibration detection.

Application of radial GRAPPA techniques to single- and multislice dynamic speech MRI using a 16-channel neurovascular coil.

To investigate: (1) the feasibility of using through-time radial GeneRalized Autocalibrating Partially Parallel Acquisitions (rGRAPPA) and hybrid radial GRAPPA (h-rGRAPPA) in single- and multislice dynamic speech MRI; (2) whether single-slice dynamic speech MRI at a rate of 15 frames per second (fps) or higher and with adequate image quality can be achieved using these radial GRAPPA techniques. Seven healthy adult volunteers were imaged at 3T using a 16-channel neurovascular coil and 2 spoiled gradient echo sequences (radial trajectory, field of view = 192 × 192 mm2 , acquired pixel size = 2.4 × 2.4 mm2 ). One sequence imaged a single slice at 16.8 fps, the other imaged 2 interleaved slices at 7.8 fps per slice. Image sets were reconstructed using rGRAPPA and h-rGRAPPA, and their image quality was compared using the root mean square error, structural similarity index, and visual assessments. Image quality deteriorated when fewer than 170 calibration frames were used in the rGRAPPA reconstruction. rGRAPPA image sets demonstrated: (1) in 97% of cases, a similar image quality to h-rGRAPPA image sets reconstructed using a k-space segment size of 4, (2) in 98% of cases, a better image quality than h-rGRAPPA image sets reconstructed using a k-space segment size of 32. This study confirmed: (1) the feasibility of using rGRAPPA and h-rGRAPPA in single- and multislice dynamic speech MRI, (2) that single-slice speech imaging at a frame rate higher than 15 fps and with adequate image quality can be achieved using these radial GRAPPA techniques.

Bound on Rindler trajectories in a black hole spacetime

We investigate radial Rindler trajectories in a static spherically symmetric black hole spacetime. We assume the trajectory to remain linearly uniformly accelerated throughout its motion, in the sense of the curved spacetime generalisation of the Letaw-Frenet equations. For the Schwarzschild spacetime, we arrive at a bound on the magnitude of the acceleration $|a|$ for radially inward moving trajectories, in terms of the mass $M$ of the black hole given by $|a| \leq 1/(\sqrt{27} M)$ for a particular choice of asymptotic initial data $h$, such that, for acceleration $|a|$ greater than the bound value, the linearly uniformly accelerated trajectory always falls into the black hole. For $|a|$ satisfying the bound, there is a minimum radius or the distance of closest approach for the radial linearly uniformly accelerated trajectory to escape back to infinity. However, this distance of closest approach is found to approach its lowest value of $r_b = 3M $, greater than the Schwarzschild radius of the black hole, when the bound, $|a| = 1/( \sqrt{27}M)$ is saturated. We further show that a finite bound on the value of acceleration, $ |a| \leq B(M,h)$ and a corresponding distance of closest approach $r_{b} > 2M$ always exists, for all finite asymptotic initial data $h$.

Diffusion-weighted MRI of the prostate without susceptibility artifacts: Undersampled multi-shot turbo-STEAM with rotated radial trajectories.

The aim of this study was to develop and evaluate a clinically feasible approach to diffusion-weighted (DW) MRI of the prostate without susceptibility-induced artifacts. The proposed method relies on an undersampled multi-shot DW turbo-STEAM sequence with rotated radial trajectories and a multi-step inverse reconstruction with denoised multi-shot phase maps. The total acquisition time was below 6min for a resolution of 1.4×1.4×3.5mm3 and six directions at b=600smm-2 . Studies of eight healthy subjects and two patients with prostate cancer were performed at 3T employing an 18-channel body-array coil and elements of the spine coil. The method was compared with conventional DW echo-planar imaging (EPI) of the prostate. The results confirm that DW STEAM MRI avoids geometric distortions and false image intensities, which were present for both single-shot EPI (ssEPI) and readout-segmented EPI, particularly near the intestinal wall of the prostate. Quantitative accuracy of the apparent diffusion coefficient (ADC) was validated with use of a numerical phantom providing ground truth. ADC values in the central prostate gland of healthy subjects were consistent with those measured using ssEPI and with literature data. Preliminary results for patients with prostate cancer revealed a correct anatomical localization of lesions with respect to T2 -weighted MRI in both mean DW STEAM images and ADC maps. In summary, DW STEAM MRI of the prostate offers clinically relevant advantages for the diagnosis of prostate cancer compared with state-of-the-art EPI-based approaches. The method warrants extended clinical trials.

Regge-like spectra of excited singly heavy mesons

In this work, we study the Regge-like spectra of excited singly heavy mesons by proposing a general Regge-like mass relation, in which the slope ratio $ \alpha^{\prime}/\beta^{\prime}$ between the radial and angular-momentum Regge trajectories is $ \pi$ /2 and the hadron mass undergoes a shift including the heavy quark mass and an extra binding energy between heavy quark and strange anti-quark. The relation is successfully tested against the observed spin-averaged data of the singly heavy mesons in their radially and angularly excited states. Some new predictions are made for more excited heavy-light mesons and the discussion is given associated with the QCD string (flux tube) picture.

Fast quantitative 3D ultrashort echo time MRI of cortical bone using extended cones sampling.

To investigate the effect of stretching sampling window on quantitative 3D ultrashort TE (UTE) imaging of cortical bone at 3 T. Ten bovine cortical bone and 17 human tibial midshaft samples were imaged with a 3T clinical MRI scanner using an 8-channel knee coil. Quantitative 3D UTE imaging biomarkers, including T1 , , magnetization transfer ratio and magnetization transfer modeling, were performed using radial or spiral Cones sampling trajectories with various durations. Errors in UTE-MRI biomarkers as a function of sampling time were evaluated using radial sampling as a reference standard. For both bovine and human cortical bone samples, no significant differences were observed for all UTE biomarkers (single-component , bicomponent and relative fractions, T1 , magnetization transfer ratio, and magnetization transfer modeling of macromolecular fraction) for spiral sampling windows of 992 µs to 1600 µs compared with a radial sampling window of 688 µs. The total scan time can be reduced by 76% with quantification errors less than 5%. Quantitative UTE-MRI techniques can be greatly accelerated using longer sampling windows without significant quantification errors.

Trajectory analysis for field free line magnetic particle imaging.

Magnetic particle imaging (MPI) is a relatively new method to image the spatial distribution of magnetic nanoparticle (MNP) tracers administered to the body with high spatial and temporal resolution using an inhomogeneous magnetic field. The spatial information of the MNP's is encoded using a field free point (FFP), or a field free line (FFL), in which the magnetic field vanishes at a point, or on a line, respectively. FFL scanning has the advantage of improved sensitivity compared to FFP scanning as a result of higher signal-to-noise ratio. The trajectory traversed by the FFL or FFP is an important parameter of the MPI system and should be selected to achieve the best imaging quality in minimum scan time, while considering hardware constraints and patient safety. In this study, we analyzed the image quality of different FFL trajectories for a large field of view (FOV) using simulations, to provide a baseline information for FFL scanning MPI system design. We simulated a human-sized FFL scanning MPI configuration to image a circular FOV with 160mm diameter, and compared Radial, Spiral, Uniform Spiral, Flower, and Lissajous trajectories with different trajectory densities scanned by the FFL for constant scan time. We analyzed the system matrices of the trajectories in terms of mutual coherence and homogeneity of the spatial sensitivity. We calculated the maximum electric fields induced on a homogeneous conductive body by the selection field (SF) and the focus field (FF) to compare the trajectories based on the nerve stimulation threshold. The images were obtained using the system matrix reconstruction approach with two different image reconstruction methods. In the first one, we used the conventional image reconstruction method, algebraic reconstruction technique (ART), which gives a regularized least-squares solution. In the second one, we used the state-of-the-art alternating direction method of multipliers (ADMM), which minimizes a weighted sum of the l1 -norm and the total variation (TV) of the images. The Radial and Spiral trajectories resulted in a poor imaging performance at low trajectory densities due to relatively high coherency and poor sensitivity of the measurements, respectively. For ART reconstruction, the highest image quality with the lowest trajectory density was achieved with the Uniform Spiral trajectory. Uniform Spiral, Flower, and Lissajous trajectories yielded comparable performance with ADMM reconstruction. The rotating SF induced higher electric field amplitude compared to the FF. Consequently, maximum allowable gradient at the same trajectory density was greater for the Radial trajectory compared to the other trajectories. For a large FOV coverage, the Uniform Spiral trajectory offers a good compromise between image quality and imaging time, taking safety and hardware limitations into account. The Radial trajectory, especially using l1 -norm and TV priors in the reconstruction, may be favorable in case the SF induced electric field is higher than that of the FF at the same frequency (e.g., relatively small FOV coverage). In general, ADMM reconstruction resulted in higher contrast and resolution compared to ART, leading to lighter requirements on the density of the trajectory.

SPARKLING: variable-density k-space filling curves for accelerated T2* -weighted MRI.

To present a new optimition-driven design of optimal k-space trajectories in the context of compressed sensing: Spreading Projection Algorithm for Rapid K-space sampLING (SPARKLING). The SPARKLING algorithm is a versatile method inspired from stippling techniques that automatically generates optimized sampling patterns compatible with MR hardware constraints on maximum gradient amplitude and slew rate. These non-Cartesian sampling curves are designed to comply with key criteria for optimal sampling: a controlled distribution of samples (e.g., variable density) and a locally uniform k-space coverage. Ex vivo and in vivo prospective -weighted acquisitions were performed on a 7-Tesla scanner using the SPARKLING trajectories for various setups and target densities. Our method was compared to radial and variable-density spiral trajectories for high-resolution imaging. Combining sampling efficiency with compressed sensing, the proposed sampling patterns allowed up to 20-fold reductions in MR scan time (compared to fully sampled Cartesian acquisitions) for two-dimensional -weighted imaging without deterioration of image quality, as demonstrated by our experimental results at 7 Tesla on in vivo human brains for a high in-plane resolution of 390μm. In comparison to existing non-Cartesian sampling strategies, the proposed technique also yielded superior image quality. The proposed optimization-driven design of k-space trajectories is a versatile framework that is able to enhance MR sampling performance in the context of compressed sensing.