Quasi-Random Single-Point Imaging Using Low-Discrepancy $k$ -Space Sampling

Reducing clustering of readouts in non-Cartesian cine magnetic resonance imaging

BACKGROUND

Non-Cartesian magnetic resonance imaging trajectories at golden angle increments have the advantage of allowing motion correction and gating using intermediate real-time reconstructions. However, when the acquired data are cardiac binned for cine imaging, trajectories can cluster together at certain heart rates (HR) causing image artifacts. Here, we demonstrate an approach to reduce clustering by inserting additional angular increments within the trajectory, and optimizing them while still allowing for intermediate reconstructions.

METHODS

Three acquisition models were simulated under constant and variable HR: golden angle (Mtrd), random additional angles (Mrnd), and optimized additional angles (Mopt). The standard deviations of trajectory angular differences (STAD) were compared through their interquartile ranges (IQR) and the Kolmogorov-Smirnov test (significance level: p = 0.05). Agreement between an image reconstructed with uniform sampling and images from Mtrd, Mrnd, and Mopt was analyzed using the structural similarity index measure (SSIM). Mtrd and Mopt were compared in three adults at high, low, and no HR variability.

RESULTS

STADs from Mtrd were significantly different (p < 0.05) from Mopt and Mrnd. STAD (IQR × 10-2 rad) showed that Mopt (0.5) and Mrnd (0.5) reduced clustering relative to Mtrd (1.9) at constant HR. For variable HR, Mopt (0.5) and Mrnd (0.5) outperformed Mtrd (0.9). The SSIM (IQR) showed that Mopt (0.011) produced the best image quality, followed by Mrnd (0.014), and Mtrd (0.030). Mopt outperformed Mtrd at reduced HR variability in in-vivo studies. At high HR variability, both models performed well.

CONCLUSION

This approach reduces clustering in k-space and improves image quality.

Three-dimensional sector-wise golden angle-improved k-space uniformity after electrocardiogram binning

PURPOSE

To develop and evaluate a 3D sector-wise golden-angle (3D-SWIG) profile ordering scheme for cardiovascular MR cine imaging that maintains high k-space uniformity after electrocardiogram (ECG) binning.

METHOD

Cardiovascular MR (CMR) was performed at 1.5 T. A balanced SSFP pulse sequence was implemented with a novel 3D-SWIG radial ordering, where k-space was divided into wedges, and each wedge was acquired in a separate heartbeat. The high uniformity of k-space coverage after physiological binning can be used to perform functional imaging using a very short acquisition. The 3D-SWIG was compared with two commonly used 3D radial trajectories for CMR (i.e., double golden angle and spiral phyllotaxis) in numerical simulations. Free-breathing 3D-SWIG and conventional breath-held 2D cine were compared in patients (n = 17) referred clinically for CMR. Quantitative comparison was performed based on left ventricular segmentation.

RESULTS

Numerical simulations showed that 3D-SWIG both required smaller steps between successive readouts and achieved better k-space sampling uniformity after binning than either the double golden angle or spiral phyllotaxis trajectories. In vivo evaluation showed that measurements of left ventricular ejection fraction calculated from a 48 heart-beat free-breathing 3D-SWIG acquisition were highly reproducible and agreed with breath-held 2D-Cartesian cine (mean ± SD difference of -3.1 ± 3.5% points).

CONCLUSIONS

The 3D-SWIG acquisition offers a simple solution for highly improved k-space uniformity after physiological binning. The feasibility of the 3D-SWIG method is demonstrated in this study through whole-heart cine imaging during free breathing with an acquisition time of less than 1 min.

Single point imaging with radial acquisition and compressed sensing

PURPOSE

To accelerate the Pointwise Encoding Time Reduction with Radial Acquisition (PETRA) sequence using compressed sensing while preserving the image quality for high-resolution MRI of tissue with ultra-short T 2 ∗ values.

METHODS

Compressed sensing was introduced in the PETRA sequence (csPETRA) to accelerate the time-consuming single point acquisition of the k-space center data. Random undersampling was applied to achieve acceleration factors up to Acc = 32. Phantom and in vivo images of the knee joint of six volunteers were measured at 3T using csPETRA sequence with Acc = 4, 8, 12, 16, 24, and 32. Images were compared against fully sampled PETRA data (Acc = 1) for structural similarity and normalized-mean-square-error. Qualitative and semi-quantitative analyses were performed to assess the effect of the acceleration on image artifacts, image quality, and delineation of anatomical structures at the knee.

RESULTS

Even at high acceleration factors of Acc = 16 no aliasing artifacts were observed, and the anatomical details were preserved compared with the fully sampled data. The normalized-mean-square-error was less than 1% for Acc = 16, in which single point imaging acquisition time was reduced from 165 to 10 s, reducing the total scan time from 7.8 to 5.2 min. Semi-quantitative analyses suggest that Acc = 16 yields comparable diagnostic quality as the fully sampled data for knee imaging at a scan time of 5.2 min.

CONCLUSION

csPETRA allows for ultra-short T 2 ∗ imaging of the knee joint in clinically acceptable scan times while maintaining the image quality of original non-accelerated PETRA sequence.

Efficient 3D Low-Discrepancy k -Space Sampling Using Highly Adaptable Seiffert Spirals

The overall duration of acquiring a Nyquist sampled 3D dataset can be significantly shortened by enhancing the efficiency of k -space sampling. This can be achieved by increasing the coverage of k -space for every trajectory interleave. Furthermore, acceleration is possible by making use of advantageous undersampling properties. In this paper, a versatile 3D center-out k -space trajectory based on Jacobian elliptic functions (Seiffert's spiral) is presented. The trajectory leads to a low-discrepancy coverage of k -space using a considerably reduced number of readouts compared with other approaches. Such a coverage is achieved for any number of interleaves, and, therefore, even single-shot trajectories can be constructed to be combined with, for example, hyperpolarized media. Furthermore, acceleration is achievable due to non-coherent undersampling properties of the trajectory in combination with non-linear reconstruction techniques like compressed sensing (CS). Simulations of point-spread functions and discrepancy evaluations compare Seiffert's spiral to the established 3D cones approach. Imaging capabilities are evaluated by comparison of in vivo knee images using Nyquist and undersampled datasets in combination with CS reconstructions.

A fast scanning ion conductance microscopy imaging method using compressive sensing and low-discrepancy sequences

A scanning ion conductance microscope (SICM) is a multifunctional, high-resolution imaging technique whose non-contact nature makes it very suitable for imaging of biological samples such as living cells in a physiological environment. However, a drawback of hopping/backstep mode of SICM is its relatively slow imaging speed, which seriously restricts the study on the dynamic process of biological samples. This paper presents a new undersampled scanning method based on Compressed Sensing (CS-based scanning mode) theory to solve extended acquisition time issues in the hopping/backstep mode. Compressive sensing can break through the limit of the Nyquist sampling theorem and sample the original sparse/compressible signal at a rate lower than the Nyquist frequency. In the CS-based scanning mode, three sampling patterns, including the random sampling pattern and two kinds of sampling patterns produced by low-discrepancy sequences, were employed as the measurement locations to obtain the undersampled data with different undersampling ratios. Also TVAL3 (Total Variation Augmented Lagrangian ALternating-direction ALgorithm) was then utilized as a reconstruction algorithm to reconstruct the undersampled data. Compared with the nonuniform sampling points of random patterns at a low undersampling ratio, low-discrepancy sequences can produce a more uniform distribution point. Three types of samples with different complexity of topography were scanned by SICM using the conventional hopping/backstep mode and CS-based undersampled scanning mode. The comparisons of the imaging speed and quality with two scanning modes illustrate that the CS-based scanning mode can effectively speed up SICM imaging speed while not sacrificing the image quality. Also low-discrepancy sampling patterns can achieve a better reconstruction performance than that of the random sampling pattern under the same undersampling ratio.