Kerstin Hammernik^{1}, Matthias Schloegl^{2}, Erich Kobler^{1}, Rudolf Stollberger^{2,3}, and Thomas Pock^{1}

In this work, we present a variational network for reconstructing dynamic multi-coil data. Incorporation of parallel imaging increases the acceleration potential due to additional spatial information, but was not considered so far in other learning-based reconstruction approaches for dynamic MRI. We show that variational network reconstructions with learned spatio-temporal regularization lead to further improvements in image quality compared to state-of-the-art Compressed Sensing approaches for different CINE cardiac datasets and acceleration factors with 10-times faster reconstruction time.

[1] K. Hammernik, T. Klatzer, E. Kobler, M. P. Recht, D. K. Sodickson, T. Pock and F. Knoll. “Learning a Variational Network for Reconstruction of Accelerated MRI Data”. Magnetic Resonance in Medicine, vol. 79, no. 6, pp. 3055-3071, 2018.

[2] J. Schlemper, J. Caballero, J. Hajnal, A. Price, and D. Rueckert. “A Deep Cascade of Convolutional Neural Networks for Dynamic MR Image Reconstruction”. IEEE Transactions on Medical Imaging, vol. 37, no. 2, pp. 491-503, 2018.

[3] C. Qin, J. Schlemper, J. Caballero, A. Price, J. V. Hajnal, and D. Rueckert. “Convolutional Recurrent Neural Networks for Dynamic MR Image Reconstruction”. IEEE Transactions on Medical Imaging, 2018 (in press).

[4] A. Hauptmann, S. Arridge, F. Lucka, V. Muthurangu, and J. A. Steeden. “Real-time cardiovascular MR with spatio-temporal artifact suppression using deep learning-proof of concept in congenital heart disease”. Magnetic Resonance in Medicine, 2018 (in press).

[5] E. Kobler, T. Klatzer, K. Hammernik, and T. Pock. “Variational Networks: Connecting Variational Methods and Deep Learning”. In German Conference on Pattern Recognition (GCPR) 2017, Lecture Notes in Computer Science, vol. 10496, pp. 281-293, 2017.

[6] Y. Chen, W. Yu, T. Pock. “On Learning Optimized Reaction Diffusion Processes for Effective Image Restoration”. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp. 5261-5269, 2015.

[7] M. Schloegl, M. Holler, K. Bredies, and R. Stollberger. “A Variational Approach for Coil-Sensitivity Estimation for Undersampled Phase-Sensitive Dynamic MRI Reconstruction”. In Proceedings of the International Society of Magnetic Resonance in Medicine (ISMRM), vol. 23, p. 3692, Toronto, Canada, 2015.

[8] M. Schloegl, M. Holler, A. Schwarzl, K. Bredies, and R. Stollberger. “Infimal convolution of total generalized variation functionals for dynamic MRI”. Magnetic Resonance in Medicine, vol. 78, no. 1, pp. 142-155, 2018.

Variational network^{1} for 2D+t multi-coil image reconstruction, defined as a sequence of GD steps. Prior information such as 2D+t filter kernels $$$k$$$, non-linear activation functions $$$\phi$$$ and dataterm weights $$$\lambda$$$ are learned from pairs of undersampled multi-coil rawdata $$$f$$$ and fully sampled reference images in an end-to-end manner. $$$u^0$$$ is defined by the initial zero-filled solution $$$u^0=A^*f$$$.

Comparison of zero filling, ICTGV, VN and fully-sampled reference reconstructions for selected CINE cardiac test datasets in two-chamber (first and fourth row), four-chamber (second and fifth row) and short-axis (third and sixth row) view with FLASH and bSSFP contrast and acceleration factor of $$$R=12$$$.

Comparison of zero filling, ICTGV, VN and fully-sampled reference reconstructions for selected short-axis CINE cardiac test datasets with FLASH and bSSFP contrast and different acceleration factors $$$R\in\{8,12,16\}$$$.

Detailed comparison between ICTGV and VN reconstructions against fully-sampled reference for a selected time-frame of one FLASH and bSSFB test dataset and acceleration factor $$$R=12$$$.

Quantitative comparison in terms of RMSE and SSIM for different acceleration factors and CINE test datasets. While the pixel-wise RMSE measure performs similarly for PI-CS ICTGV and VN, the patch-based SSIM values are improved for the VN results in all cases.