Deconvolution-interpolation gridding (DING): accurate reconstruction for arbitrary k-space trajectories

Rapid compressed sensing reconstruction of 3D non-Cartesian MRI

PURPOSE

Conventional non-Cartesian compressed sensing requires multiple nonuniform Fourier transforms every iteration, which is computationally expensive. Accordingly, time-consuming reconstructions have slowed the adoption of undersampled 3D non-Cartesian acquisitions into clinical protocols. In this work we investigate several approaches to minimize reconstruction times without sacrificing accuracy.

METHODS

The reconstruction problem can be reformatted to exploit the Toeplitz structure of matrices that are evaluated every iteration, but it requires larger oversampling than what is strictly required by nonuniform Fourier transforms. Accordingly, we investigate relative speeds of the two approaches for various nonuniform Fourier transform kernel sizes and oversampling for both GPU and CPU implementations. Second, we introduce a method to minimize matrix sizes by estimating the image support. Finally, density compensation weights have been used as a preconditioning matrix to improve convergence, but this increases noise. We propose a more general approach to preconditioning that allows a trade-off between accuracy and convergence speed.

RESULTS

When using a GPU, the Toeplitz approach was faster for all practical parameters. Second, it was found that properly accounting for image support can prevent aliasing errors with minimal impact on reconstruction time. Third, the proposed preconditioning scheme improved convergence rates by an order of magnitude with negligible impact on noise.

CONCLUSION

With the proposed methods, 3D non-Cartesian compressed sensing with clinically relevant reconstruction times (<2 min) is feasible using practical computer resources. Magn Reson Med 79:2685-2692, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

Non-Cartesian parallel imaging reconstruction

Non-Cartesian parallel imaging has played an important role in reducing data acquisition time in MRI. The use of non-Cartesian trajectories can enable more efficient coverage of k-space, which can be leveraged to reduce scan times. These trajectories can be undersampled to achieve even faster scan times, but the resulting images may contain aliasing artifacts. Just as Cartesian parallel imaging can be used to reconstruct images from undersampled Cartesian data, non-Cartesian parallel imaging methods can mitigate aliasing artifacts by using additional spatial encoding information in the form of the nonhomogeneous sensitivities of multi-coil phased arrays. This review will begin with an overview of non-Cartesian k-space trajectories and their sampling properties, followed by an in-depth discussion of several selected non-Cartesian parallel imaging algorithms. Three representative non-Cartesian parallel imaging methods will be described, including Conjugate Gradient SENSE (CG SENSE), non-Cartesian generalized autocalibrating partially parallel acquisition (GRAPPA), and Iterative Self-Consistent Parallel Imaging Reconstruction (SPIRiT). After a discussion of these three techniques, several potential promising clinical applications of non-Cartesian parallel imaging will be covered.

Optimal compressed sensing reconstructions of fMRI using 2D deterministic and stochastic sampling geometries

BACKGROUND

Compressive sensing can provide a promising framework for accelerating fMRI image acquisition by allowing reconstructions from a limited number of frequency-domain samples. Unfortunately, the majority of compressive sensing studies are based on stochastic sampling geometries that cannot guarantee fast acquisitions that are needed for fMRI. The purpose of this study is to provide a comprehensive optimization framework that can be used to determine the optimal 2D stochastic or deterministic sampling geometry, as well as to provide optimal reconstruction parameter values for guaranteeing image quality in the reconstructed images.

METHODS

We investigate the use of frequency-space (k-space) sampling based on: (i) 2D deterministic geometries of dyadic phase encoding (DPE) and spiral low pass (SLP) geometries, and (ii) 2D stochastic geometries based on random phase encoding (RPE) and random samples on a PDF (RSP). Overall, we consider over 36 frequency-sampling geometries at different sampling rates. For each geometry, we compute optimal reconstructions of single BOLD fMRI ON & OFF images, as well as BOLD fMRI activity maps based on the difference between the ON and OFF images. We also provide an optimization framework for determining the optimal parameters and sampling geometry prior to scanning.

RESULTS

For each geometry, we show that reconstruction parameter optimization converged after just a few iterations. Parameter optimization led to significant image quality improvements. For activity detection, retaining only 20.3% of the samples using SLP gave a mean PSNR value of 57.58 dB. We also validated this result with the use of the Structural Similarity Index Matrix (SSIM) image quality metric. SSIM gave an excellent mean value of 0.9747 (max = 1). This indicates that excellent reconstruction results can be achieved. Median parameter values also gave excellent reconstruction results for the ON/OFF images using the SLP sampling geometry (mean SSIM > =0.93). Here, median parameter values were obtained using mean-SSIM optimization. This approach was also validated using leave-one-out.

CONCLUSIONS

We have found that compressive sensing parameter optimization can dramatically improve fMRI image reconstruction quality. Furthermore, 2D MRI scanning based on the SLP geometries consistently gave the best image reconstruction results. The implication of this result is that less complex sampling geometries will suffice over random sampling. We have also found that we can obtain stable parameter regions that can be used to achieve specific levels of image reconstruction quality when combined with specific k-space sampling geometries. Furthermore, median parameter values can be used to obtain excellent reconstruction results.

Iterative image reconstruction for PROPELLER-MRI using the nonuniform fast fourier transform

PURPOSE

To investigate an iterative image reconstruction algorithm using the nonuniform fast Fourier transform (NUFFT) for PROPELLER (Periodically Rotated Overlapping ParallEL Lines with Enhanced Reconstruction) MRI.

MATERIALS AND METHODS

Numerical simulations, as well as experiments on a phantom and a healthy human subject were used to evaluate the performance of the iterative image reconstruction algorithm for PROPELLER, and compare it with that of conventional gridding. The trade-off between spatial resolution, signal to noise ratio, and image artifacts, was investigated for different values of the regularization parameter. The performance of the iterative image reconstruction algorithm in the presence of motion was also evaluated.

RESULTS

It was demonstrated that, for a certain range of values of the regularization parameter, iterative reconstruction produced images with significantly increased signal to noise ratio, reduced artifacts, for similar spatial resolution, compared with gridding. Furthermore, the ability to reduce the effects of motion in PROPELLER-MRI was maintained when using the iterative reconstruction approach.

CONCLUSION

An iterative image reconstruction technique based on the NUFFT was investigated for PROPELLER MRI. For a certain range of values of the regularization parameter, the new reconstruction technique may provide PROPELLER images with improved image quality compared with conventional gridding.

RT-GROG: parallelized self-calibrating GROG for real-time MRI

A real-time implementation of self-calibrating Generalized Autocalibrating Partially Parallel Acquisitions (GRAPPA) operator gridding for radial acquisitions is presented. Self-calibrating GRAPPA operator gridding is a parallel-imaging-based, parameter-free gridding algorithm, where coil sensitivity profiles are used to calculate gridding weights. Self-calibrating GRAPPA operator gridding's weight-set calculation and image reconstruction steps are decoupled into two distinct processes, implemented in C++ and parallelized. This decoupling allows the weights to be updated adaptively in the background while image reconstruction threads use the most recent gridding weights to grid and reconstruct images. All possible combinations of two-dimensional gridding weights G(x)(m)G(y)(n) are evaluated for m,n = {-0.5, -0.4, ..., 0, 0.1, ..., 0.5} and stored in a look-up table. Consequently, the per-sample two-dimensional weights calculation during gridding is eliminated from the reconstruction process and replaced by a simple look-up table access. In practice, up to 34x faster reconstruction than conventional (parallelized) self-calibrating GRAPPA operator gridding is achieved. On a 32-coil dataset of size 128 x 64, reconstruction performance is 14.5 frames per second (fps), while the data acquisition is 6.6 fps.

Spiral demystified

Spiral acquisition schemes offer unique advantages such as flow compensation, efficient k-space sampling and robustness against motion that make this option a viable choice among other non-Cartesian sampling schemes. For this reason, the main applications of spiral imaging lie in dynamic magnetic resonance imaging such as cardiac imaging and functional brain imaging. However, these advantages are counterbalanced by practical difficulties that render spiral imaging quite challenging. Firstly, the design of gradient waveforms and its hardware requires specific attention. Secondly, the reconstruction of such data is no longer straightforward because k-space samples are no longer aligned on a Cartesian grid. Thirdly, to take advantage of parallel imaging techniques, the common generalized autocalibrating partially parallel acquisitions (GRAPPA) or sensitivity encoding (SENSE) algorithms need to be extended. Finally, and most notably, spiral images are prone to particular artifacts such as blurring due to gradient deviations and off-resonance effects caused by B(0) inhomogeneity and concomitant gradient fields. In this article, various difficulties that spiral imaging brings along, and the solutions, which have been developed and proposed in literature, will be reviewed in detail.

Self-calibrating GRAPPA operator gridding for radial and spiral trajectories

Self-calibrating GRAPPA operator gridding (GROG) is a method by which non-Cartesian MRI data can be gridded using spatial information from a multichannel coil array without the need for an additional calibration dataset. Using self-calibrating GROG, the non-Cartesian datapoints are shifted to nearby k-space locations using parallel imaging weight sets determined from the datapoints themselves. GROG employs the GRAPPA Operator, a special formulation of the general reconstruction method GRAPPA, to perform these shifts. Although GROG can be used to grid undersampled datasets, it is important to note that this method uses parallel imaging only for gridding, and not to reconstruct artifact-free images from undersampled data. The innovation introduced here, namely, self-calibrating GROG, allows the shift operators to be calculated directly out of the non-Cartesian data themselves. This eliminates the need for an additional calibration dataset, which reduces the imaging time and also makes the GROG reconstruction more robust by removing possible inconsistencies between the calibration and non-Cartesian datasets. Simulated and in vivo examples of radial and spiral datasets gridded using self-calibrating GROG are compared to images gridded using the standard method of convolution gridding.