Synopsis

Conventional non-Cartesian parallel imaging reconstruction in k-space necessitates large amounts of calibration data for successful estimation of region-specific interpolation kernels. In this work, we propose a self-calibration strategy for obtaining region-specific non-Cartesian interpolation kernels from a single calibration dataset. This enables simple and efficient high-quality reconstruction of non-Cartesian parallel imaging.

Introduction

Non-Cartesian undersampled acquisition for parallel imaging is commonly reconstructed using CG-SENSE¹ type methods. k-space interpolation methods can also be used, but it is challenging to acquire sufficient number of identical patches of an undersampled patch for determining interpolation kernels and applying it to recover missing data². Region-specific kernels can be calibrated from repeatedly acquired fully sampled calibration scans, and provide improved reconstruction because of better match with the theoretical model, but with the cost of large number of calibration scans^3,4.

In this work, we propose a scalable non-Cartesian region-specific GRAPPA method called SING (Scalable self-calibrated interpolation of non-Cartesian data with GRAPPA) which uses a single calibration dataset. The proposed method resamples ACS data for calibration of region-specific kernels. Subsequently, an explicit noise-based regularized solution is utilized to estimate region-specific kernels, similar to TT-GRAPPA³. The efficacy of the method is demonstrated in 2D radial cardiac imaging.

Method

Imaging: Cine cardiac MRI was acquired at 3T (Siemens Prisma) using a 30-channel body array with a GRE sequence. Imaging parameters were: TE/TR/α=2.3ms/3.9ms/12°, bandwidth=440Hz/pixel, resolution 2×2 mm², temporal resolution=45ms. Data was fully sampled with 216 views using a linear view order in a single breath hold. For TT-GRAPPA calibration, additional 20 free-breathing fully-sampled acquisitions were obtained shortly after the breath hold. Data was retrospectively undersampled uniformly for each cardiac phase, which was rotationally shifted between successive phases by the angle of a single view (180/216=0.83°).

SING: The proposed self-calibration strategy is depicted in Figure 1. First, the central k-space data is resampled onto a Cartesian grid, then the region-specific kernel is calibrated on this data. Subsequently, the system is regularized in step 4 by adding i.i.d. Gaussian noise to synthetic points on each equation in order to match the SNR of undersampled patch, which is lower on outer k-space. The least-squares solution of the new system

$$\hspace{9.1cm} (b+Δb)=(A+ΔA)x,\hspace{9.1cm} [1]$$

is the calibrated kernel for the undersampled patch. $$$b$$$ and $$$A$$$ are synthetic target and source points. The corresponding rows in $$$Δb$$$ and $$$ΔA$$$ have the same noise level, and different rows have different noise levels. After reconstructing the whole k-space by iterating through step 1-5 for each region-specific kernel, gridding reconstruction is applied to generate an image with root-sum-of-squares coil combination.

TT-GRAPPA: TT-GRAPPA was implemented for comparison, with each region-specific kernel calibrated from local measurements spanning ±1 readouts and ±2 views in separate free-breathing calibration data.

Effect of regularization: The SNR-matched regularization strategy of Eq. [1] was compared with Tikhonov regularization. The Tikhonov regularization parameter was chosen in a readout-dependent manner and modelled by the theoretical SNR decay along the readout (1/r²).

Results

Non-Cartesian GRAPPA reconstructions are shown in Figure 2. At R=6, the reconstruction quality of TT-GRAPPA and SING are visually similar to the reference, outperforming CG-SENSE. At R=16, both TT-GRAPPA and SING suffer from reconstruction artifacts, although their quality is visually comparable. RMSE errors further show that SING performs similar to TT-GRAPPA.

For the effect of regularization, images reconstructed from SING using no regularization, Tikhonov regularization and the SNR-matched regularization in Eq. [1] are shown in Figure 3. The proposed regularization in Eq. [1] reduces noise and blurring artifacts compared to the unregularized and Tikhonov regularized approaches, respectively.

A temporal view through a cross-section of the heart is depicted in Figure 4, showing similar temporal fidelity between SING, TT-GRAPPA and fully sampled acquisitions. This is consistent with the fact that none of these approaches utilize temporal regularization.

Discussion

In 2D non-Cartesian imaging, SING is able to reconstruct images with similar quality to TT-GRAPPA without separate calibration acquisitions. This self-calibration strategy has the potential to scale up to 3D non-Cartesian imaging, since it does not require additional calibration volumes, which is especially prohibitive in 3D acquisitions.

The proposed regularization in Eq. [1] is established upon the inherent noise regularization effect in TT-GRAPPA. The superior reconstruction of TT-GRAPPA over other parallel imaging reconstruction methods may result from the implicit inclusion of noise on the target points.

Previous work has considered a SENSE based composite method⁵ for obtaining region specific kernel and is outperformed by this newer strategy. We also note a related method to SING was proposed⁶, with the main difference being that shifted ACS data is utilized for calibration of kernels without a noise-aware of calibration.

The effect of correlation in the composite data generated from Kaiser-Bessel convolution was not considered, but warrants further investigation.

Acknowledgements

1. BTRC P41 EB015894
2. NIH R00HL111410
3. NSF CCF-1651825

References

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