Kerstin Hammernik^{1}, Erich Kobler^{1}, Teresa Klatzer^{1}, and Michael P Recht^{2}

In this work, we propose variational networks for fast and high-quality reconstruction of accelerated multi-coil MR data. A wide range of experiments and a dedicated user study on clinical patient data show that the proposed variational network reconstructions outperform traditional reconstruction approaches in terms of image quality and residual artifacts. Additionally, variational networks offer high reconstruction speed, which is substantial for the incorporation into clinical workflow.

**Introduction**

**Discussion and Conclusion**

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Figure 1:
(a) Raw k-space data, coil-sensitivity maps are fed along with the zero filling
solution to the variational network (VN). During training, the reconstruction
is compared to a reference using some similarity measure. The reconstruction
error is then used to update the parameters during training. The VN itself
consists of T gradient descent steps. (b) depicts a single gradient descent
step, where the gradient corresponds to the gradient of the generalized
compressed sensing model. Filter kernels for real and imaginary part are learned
together with their corresponding activation function and the data term
weights.

Figure
2: Reconstruction results of a coronal fat-saturated proton-density-weighted
scan with acceleration R=4, for both regular and random sampling. The scans of
the 57-year-old female patient show broad-based, full-thickness chondral loss
and a subchondral cystic change, indicated by the green bracket, and an
extruded and torn medial meniscus, indicated by the green arrow. The VN
reconstruction has less residual artifacts and appears sharper than the other
reconstruction methods. The results for regular sampling are blurrier than for
random sampling. The observations are supported by the quantitative values.

Figure
3: Prospectively undersampled data of a 27-year-old female volunteer. We
observe good reconstruction quality for proton-density scans. The TGV
reconstructions of fat-saturated scans show a blocky, artificial appearance,
while we observe a noise pattern for dictionary learning results. VN
reconstructions have the least amount of remaining artifacts and most improved
SNR.

Table
1: Quantitative evaluation (MSE, NRMSE, SSIM) for regular and random sampling
and acceleration factor R=4. These results support the qualitative
observations. The learning-based VN reconstructions outperform the reference
methods in all cases. Random sampling performs better than regular sampling for
this acceleration factor.

Table
2: Evaluation of the reader study, comparing TGV and VN reconstructions (R=4).
We report mean and standard deviation, averaged over the two readers along with
the p-value resulting from the one-sided Wilcoxon signed-rank test. For a
significance level α=0.05, the null hypothesis that TGV reconstruction are
better or equal VN reconstructions is rejected for most of the quality measures
and sequences.