Parallel Magnetic Resonance Imaging as Approximation in a Reproducing Kernel Hilbert Space

High-Frequency Space Diffusion Model for Accelerated MRI

Diffusion models with continuous stochastic differential equations (SDEs) have shown superior performances in image generation. It can serve as a deep generative prior to solving the inverse problem in magnetic resonance (MR) reconstruction. However, low-frequency regions of k -space data are typically fully sampled in fast MR imaging, while existing diffusion models are performed throughout the entire image or k -space, inevitably introducing uncertainty in the reconstruction of low-frequency regions. Additionally, existing diffusion models often demand substantial iterations to converge, resulting in time-consuming reconstructions. To address these challenges, we propose a novel SDE tailored specifically for MR reconstruction with the diffusion process in high-frequency space (referred to as HFS-SDE). This approach ensures determinism in the fully sampled low-frequency regions and accelerates the sampling procedure of reverse diffusion. Experiments conducted on the publicly available fastMRI dataset demonstrate that the proposed HFS-SDE method outperforms traditional parallel imaging methods, supervised deep learning, and existing diffusion models in terms of reconstruction accuracy and stability. The fast convergence properties are also confirmed through theoretical and experimental validation. Our code and weights are available at https://github.com/Aboriginer/HFS-SDE.

T-Hex: Tilted hexagonal grids for rapid 3D imaging

PURPOSE

The purpose of this work is to devise and demonstrate an encoding strategy for 3D MRI that reconciles high speed with flexible segmentation, uniform k-space density, and benign T 2 ∗ effects.

METHODS

Fast sampling of a 3D k-space is typically accomplished by 2D readouts per shot using EPI trains or spiral readouts. Tilted hexagonal (T-Hex) sampling is a way of acquiring more k-space volume per excitation while maintaining uniform sampling density and a smooth T 2 ∗ filter. The k-space volume covered per shot is controlled by the tilting angle. Image reconstruction is performed with a 3D extension of the iterative SENSE approach, incorporating actual field dynamics and static off-resonance. T-Hex imaging is compared with established 3D schemes in terms of speed and noise performance.

RESULTS

Tilted hexagonal acquisition is found to achieve greater imaging speed than known alternatives, particularly in combination with spiral trajectories. The interplay of the proposed 3D trajectories, array detection, and off-resonance is successfully addressed by iterative inversion of the full signal model. Enhanced coverage per shot is of greatest utility for high speed in an intermediate resolution regime of 1 to 4 mm. T-Hex EPI combines the benefits of extended coverage per shot with increased robustness against off-resonance effects.

CONCLUSION

Sampling of tilted hexagonal grids is a feasible means of gaining 3D imaging speed with near-optimal SNR efficiency and benign depiction properties. It is a particularly promising technique for time-resolved applications such as fMRI.

Statistically Segregated k-Space Sampling for Accelerating Multiple-Acquisition MRI

A central limitation of multiple-acquisition magnetic resonance imaging (MRI) is the degradation in scan efficiency as the number of distinct datasets grows. Sparse recovery techniques can alleviate this limitation via randomly undersampled acquisitions. A frequent sampling strategy is to prescribe for each acquisition a different random pattern drawn from a common sampling density. However, naive random patterns often contain gaps or clusters across the acquisition dimension that, in turn, can degrade reconstruction quality or reduce scan efficiency. To address this problem, a statistically segregated sampling method is proposed for multiple-acquisition MRI. This method generates multiple patterns sequentially while adaptively modifying the sampling density to minimize k-space overlap across patterns. As a result, it improves incoherence across acquisitions while still maintaining similar sampling density across the radial dimension of k-space. Comprehensive simulations and in vivo results are presented for phase-cycled balanced steady-state free precession and multi-echo [Formula: see text]-weighted imaging. Segregated sampling achieves significantly improved quality in both Fourier and compressed-sensing reconstructions of multiple-acquisition datasets.

Reducing acquisition time for MRI-based forensic age estimation

Radiology-based estimation of a living person’s unknown age has recently attracted increasing attention due to large numbers of undocumented immigrants entering Europe. To avoid the application of X-ray-based imaging techniques, magnetic resonance imaging (MRI) has been suggested as an alternative imaging modality. Unfortunately, MRI requires prolonged acquisition times, which potentially represents an additional stressor for young refugees. To eliminate this shortcoming, we investigated the degree of reduction in acquisition time that still led to reliable age estimates. Two radiologists randomly assessed original images and two sets of retrospectively undersampled data of 15 volunteers (N = 45 data sets) applying an established radiological age estimation method to images of the hand and wrist. Additionally, a neural network-based age estimation method analyzed four sets of further undersampled images from the 15 volunteers (N = 105 data sets). Furthermore, we compared retrospectively undersampled and acquired undersampled data for three volunteers. To assess reliability with increasing degree of undersampling, intra-rater and inter-rater agreement were analyzed computing signed differences and intra-class correlation. While our findings have to be confirmed by a larger prospective study, the results from both radiological and automatic age estimation showed that reliable age estimation was still possible for acquisition times of 15 seconds.

On-the-Fly Adaptive ${k}$ -Space Sampling for Linear MRI Reconstruction Using Moment-Based Spectral Analysis

In high-dimensional magnetic resonance imaging applications, time-consuming, sequential acquisition of data samples in the spatial frequency domain ( -space) can often be accelerated by accounting for dependencies in linear reconstruction, at the cost of noise amplification that depends on the sampling pattern. Common examples are support-constrained, parallel, and dynamic MRI, and -space sampling strategies are primarily driven by image-domain metrics that are expensive to compute for arbitrary sampling patterns. It remains challenging to provide systematic and computationally efficient automatic designs of arbitrary multidimensional Cartesian sampling patterns that mitigate noise amplification, given the subspace to which the object is confined. To address this problem, this paper introduces a theoretical framework that describes local geometric properties of the sampling pattern and relates them to the spread in the eigenvalues of the information matrix described by its first two spectral moments. This new criterion is then used for very efficient optimization of complex multidimensional sampling patterns that does not require reconstructing images or explicitly mapping noise amplification. Experiments with in vivo data show strong agreement between this criterion and traditional, comprehensive image-domain- and -space-based metrics, indicating the potential of the approach for computationally efficient (on-the-fly), automatic, and adaptive design of sampling patterns.

3D Cartesian MRI with compressed sensing and variable view sharing using complementary poisson-disc sampling

PURPOSE

To enable robust, high spatio-temporal-resolution three-dimensional Cartesian MRI using a scheme incorporating a novel variable density random k-space sampling trajectory allowing flexible and retrospective selection of the temporal footprint with compressed sensing (CS).

METHODS

A complementary Poisson-disc k-space sampling trajectory was designed to allow view sharing and varying combinations of reduced view sharing with CS from the same prospective acquisition. These schemes were used for two-point Dixon-based dynamic contrast-enhanced MRI (DCE-MRI) of the breast and abdomen. Results were validated in vivo with a novel approach using variable-flip-angle data, which was retrospectively accelerated using the same methods but offered a ground truth.

RESULTS

In breast DCE-MRI, the temporal footprint could be reduced 2.3-fold retrospectively without introducing noticeable artifacts, improving depiction of rapidly enhancing lesions. Further, experiments with variable-flip-angle data showed that reducing view sharing improved accuracy in reconstruction and T₁ mapping. In abdominal MRI, 2.3-fold and 3.6-fold reductions in temporal footprint allowed reduced motion artifacts.

CONCLUSION

The complementary-Poisson-disc k-space sampling trajectory allowed a retrospective spatiotemporal resolution tradeoff using CS and view sharing, imparting robustness to motion and contrast enhancement. The technique was also validated using a novel approach of fully acquired variable-flip-angle acquisition. Magn Reson Med 77:1774-1785, 2017. © 2016 International Society for Magnetic Resonance in Medicine.