Fast implementation for compressive recovery of highly accelerated cardiac cine MRI using the balanced sparse model.

PURPOSE: Sparsity-promoting regularizers can enable stable recovery of highly undersampled magnetic resonance imaging (MRI), promising to improve the clinical utility of challenging applications. However, lengthy computation time limits the clinical use of these methods, especially for dynamic MRI with its large corpus of spatiotemporal data. Here, we present a holistic framework that utilizes the balanced sparse model for compressive sensing and parallel computing to reduce the computation time of cardiac MRI recovery methods. THEORY AND METHODS: We propose a fast, iterative soft-thresholding method to solve the resulting ℓ1-regularized least squares problem. In addition, our approach utilizes a parallel computing environment that is fully integrated with the MRI acquisition software. The methodology is applied to two formulations of the multichannel MRI problem: image-based recovery and k-space-based recovery. RESULTS: Using measured MRI data, we show that, for a 224 × 144 image series with 48 frames, the proposed k-space-based approach achieves a mean reconstruction time of 2.35 min, a 24-fold improvement compared a reconstruction time of 55.5 min for the nonlinear conjugate gradient method, and the proposed image-based approach achieves a mean reconstruction time of 13.8 s. CONCLUSION: Our approach can be utilized to achieve fast reconstruction of large MRI datasets, thereby increasing the clinical utility of reconstruction techniques based on compressed sensing. Magn Reson Med 77:1505-1515, 2017. © 2016 International Society for Magnetic Resonance in Medicine.

Paradoxical effect of the signal-to-noise ratio of GRAPPA calibration lines: A quantitative study.

PURPOSE: Intuitively, GRAPPA auto-calibration signal (ACS) lines with higher signal-to-noise ratio (SNR) may be expected to boost the accuracy of kernel estimation and increase the SNR of GRAPPA reconstructed images. Paradoxically, Sodickson and his colleagues pointed out that using ACS lines with high SNR may actually lead to lower SNR in the GRAPPA reconstructed images. A quantitative study of how the noise in the ACS lines affects the SNR of the GRAPPA reconstructed images is presented. METHODS: In a phantom, the singular values of the GRAPPA encoding matrix and the root-mean-square error of GRAPPA reconstruction were evaluated using multiple sets of ACS lines with variant SNR. In volunteers, ACS lines with high and low SNR were estimated, and the SNR of corresponding TGRAPPA reconstructed images was evaluated. RESULTS: We show that the condition number of the GRAPPA kernel estimation equations is proportional to the SNR of the ACS lines. In dynamic image series reconstructed with TGRAPPA, high SNR ACS lines result in reduced SNR if appropriate regularization is not applied. CONCLUSION: Noise has a similar effect to Tikhonov regularization. Without appropriate regularization, a GRAPPA kernel estimated from ACS lines with higher SNR amplifies random noise in the GRAPPA reconstruction. Magn Reson Med 74:231-239, 2015. © 2014 Wiley Periodicals, Inc.

SC-GRAPPA: Self-constraint noniterative GRAPPA reconstruction with closed-form solution.

PURPOSE: Parallel MRI (pMRI) reconstruction techniques are commonly used to reduce scan time by undersampling the k-space data. GRAPPA, a k-space based pMRI technique, is widely used clinically because of its robustness. In GRAPPA, the missing k-space data are estimated by solving a set of linear equations; however, this set of equations does not take advantage of the correlations within the missing k-space data. All k-space data in a neighborhood acquired from a phased-array coil are correlated. The correlation can be estimated easily as a self-constraint condition, and formulated as an extra set of linear equations to improve the performance of GRAPPA. The authors propose a modified k-space based pMRI technique called self-constraint GRAPPA (SC-GRAPPA) which combines the linear equations of GRAPPA with these extra equations to solve for the missing k-space data. Since SC-GRAPPA utilizes a least-squares solution of the linear equations, it has a closed-form solution that does not require an iterative solver. METHODS: The SC-GRAPPA equation was derived by incorporating GRAPPA as a prior estimate. SC-GRAPPA was tested in a uniform phantom and two normal volunteers. MR real-time cardiac cine images with acceleration rate 5 and 6 were reconstructed using GRAPPA and SC-GRAPPA. RESULTS: SC-GRAPPA showed a significantly lower artifact level, and a greater than 10% overall signal-to-noise ratio (SNR) gain over GRAPPA, with more significant SNR gain observed in low-SNR regions of the images. CONCLUSIONS: SC-GRAPPA offers improved pMRI reconstruction, and is expected to benefit clinical imaging applications in the future.