Introduction

Parallel imaging (PI) methods are widely used to reduce MRI scan time in clinical routine. The basic PI approaches are based on uniform k-space undersampling and simultaneous signal reception with multiple receiver coils. The GRAPPA¹ (GeneRalized Autocalibrating Partially Parallel Acquisitions) method interpolates missing k-space signals by linear combination of adjacent, acquired signals across all channels and can be described by a linear convolution in k-space. In GRAPPA, the convolution kernel is estimated by linear least-squares regression using fully sampled autocalibration signals (ACS). Recently, a more generalized deep-learning based method called RAKI² was introduced. RAKI estimates missing signals non-linearly via Convolutional Neural Networks (CNNs) and has the potential to overcome limitations associated with the linearity of GRAPPA. In this work, we study the influence of the ACS used to calibrate the scan-specific CNN parameters on the image quality of 2D imaging sequences more precisely. In particular, the focus will be on the ACS amount as well as on the contrast information provided for the CNN training.

Methods

RAKI implementation: The CNN architecture is depicted in Figure 1. The input layer S₁ takes in the undersampled, zerofilled k-space data across all coils, mapped to real field (resulting in 2 x N_c total input channels with N_c being the number of coils). The hidden layers are then calculated through linear convolution, and a point-wise activation with the Leaky ReLU function max(0.5x, x): S₂ = LReLU( S₁ ∗ w^C₁ ) and S₃ = LReLU( S₂ ∗ w^C₂ ), with w^C₁ of size 3 x 2 and w^C₂ of size 1 x 1 in read- and phase-encoding direction, respectively. First hidden layer S₂ is assigned 256 channels, while second hidden layer is assigned 128 channels. In contrast to original RAKI, the output layer predicts all missing points across all coils, thus having 2 x (R - 1) x N_c channels where R denotes the undersampling rate. The outer layer is activated with the identity function: S₄ = S₃ ∗ w^C₃ with w^C₃ of size 5 x 1.

In Vivo imaging: 2D anatomical brain imaging with 16 coils was performed on a healthy volunteer at 3 T using TSE sequence with FOV=220 mm x 193 mm, TR/TE=500/10ms (T1-weighted) and 4500/102ms (T2-weighted). Brain imaging was also performed with 32 coils using FLASH sequence with FOV=220 mm x 193 mm, TR/TE=350/2.5ms. All datasets were fully sampled and retrospectively undersampled for reconstruction. Accelerated dynamic cardiac imaging was performed using 12 coils at FOV=360 mm x 270 mm and resolution=1.88 mm x 1.88 mm. The data were acquired under free-breathing conditions using an interleaved acquisition scheme^3-5 with undersampling rate R=4. Full resolution ACS were obtained from the temporal average.

Evaluation: Image reconstruction quality of RAKI was evaluated by varying the number of total ACS lines in the range 20-40 with stepsize 5. To take the inherent stochasticity of RAKI into account, the reconstruction procedure is repeated 100 times. The root-mean-squared error (RMSE) of the fully sampled reference image to the undersampled data (R=4) was calculuated. GRAPPA reconstructions were performed for comparison. Additionally, ACS with different contrast information were used for RAKI training (e.g. T1-weighted ACS were used for RAKI training to reconstruct T2-weighted data). The ACS were not reinserted in the final images.

Results

Figure 2 depicts reconstructions of the brain dataset with 32 coils and 30 ACS (reinserted). We observe that RAKI significantly outperforms GRAPPA in terms of signal-to-noise ratio at R=4 and R=5, but introduces blurring and loss of fine details particularly at R=6. The RMSE for RAKI decreases with increasing amount of ACS (R=4, see Figure 3). In all cases, the RMSE was lower than that of GRAPPA. Consequently, when a large amount of ACS is available for calibrating a large CNN kernel, as in dynamic imaging with interleaved sampling, RAKI provides high quality reconstructions with reduced blurring artifacts (Figure 4). However, RAKI shows poor performance when the contrast in the ACS significantly differs that of the accelerated scan (Figure 5). In contrast, GRAPPA shows only few additional artifacts for the reconstruction of the T2-weighted image when the ACS is from T1-weighted signals.

Discussion

RAKI shows improved image reconstruction quality in comparison with GRAPPA for 2D MRI scans at moderate accelerations (R=4 and R=5 with N_c < 32), but exhibits blurring in areas where GRAPPA suffers from severe noise amplification. However, blurring can potentially be reduced by a larger CNN kernel as indicated by the cardiac imaging experiment. However, there is always a trade-off between kernel size and effective amount of training examples. Thus, data augmentation techniques such as noise superimposition, may need further investigations in future studies. The experiments with significantly varying contrast between ACS and undersampled data indicates, that CNNs process scan-specific tissue contrast information in addition to coil sensitivity information, in a more profound way than GRAPPA.

Conclusion

RAKI has the potential for providing significantly improved SNR in 2D imaging compared to GRAPPA, but may yield blurring and loss of details at high accelerations. Larger CNN kernels in combination with more ACS are useful to alleviate this problem. Furthermore, the contrast between ACS and undersampled data should be similar to prevent reconstruction artifacts.

Acknowledgements

The authors thank Peter Kellman for providing cardiac imaging data and the German Federal Ministry of Education and Research (BMBF) for funding projectline VIP+ (03VP04951).