Andreas Kofler^{1}, Marc Dewey^{1}, Tobias Schaeffter^{2,3}, Christian Wald^{1}, and Christoph Kolbitsch^{2,3}

A well-known bottleneck of neural networks is the requirement of large datasets for successful training. We present a method for reduction of 2D radial cine MRI images which allows to properly train a neural network on limited datasets. The network is trained on spatio-temporal slices of healthy volunteers which are previously extracted from the image sequences and is tested on patients data with known heart dysfunction. The image sequences are reassembled from the processed spatio-temporal slices. Our method is shown to have several advantages compared to other Deep Learning-based methods and achieves comparable results to a state-of-the-art Compressed Sensing-based method.

Data acquisition and image reconstruction: 2D Golden Radial data was acquired continuously during a 10 s breathhold in 15 healthy volunteers and 4 patients with known heart dysfunction (TE/TR 3/1.5ms, FA 60°) ^{2}. For each subject, N_{z} = 12 slices of shape N_{x }x N_{y} = 320 x 320 were acquired in long-axis orientations. The inplane resolution was 2 mm, the slice thickness 8 mm. Based on a recorded ECG-signal, the first N_{θ} = 1130 radial lines (i.e. 3.3s of data acquisition) were retrospectively separated into N_{t} = 30 cardiac phases using a sliding window approach. Each cardiac phase was reconstructed with a standard gridding approach (NUFFT)^{ 3}.

Artefact reduction using neural networks: We reduced undersampling artefacts arising from the NUFFT reconstruction of the undersampled k-space data by training a neural network on the data considered in the spatio-temporal domain. For this purpose, we constructed our training set by extracting two-dimensional spatio-temporal slices from the image sequences, see Figure 1. We used a slightly modified version of the U-net^{ 4} which performs max-pooling only along the spatial dimension. The network is trained to map the spatio-temporal slices of the NUFFT reconstructions to the corresponding ground truth slices obtained with a kt-SENSE^{5} reconstruction using N_{θ} = 3400 lines.

Evaluation: The training and validation set consist of image sequences of 13 and 2 healthy volunteers, respectively, while the test set consists of 4 patients. In order to investigate the applicability of the method for a small number of subjects, we fixed the number of healthy volunteers we extracted the spatio-temporal slices from and did not make use of any data-augmentation technique. We compared our proposed approach to several Deep Learning-based approaches for reducing undersampling artefacts in cine MRI as well as to a state-of-the-art Compressed Sensing-based method.

1. Jin Kyong Hwan, McCann Michael T, Froustey Emmanuel, Unser Michael. Deep convolutional neural network for inverse problems in imaging. IEEE Transactions on Image Processing. 2017;26:4509–4522.

2. Kolbitsch Christoph, Prieto Claudia, Schaeffter Tobias. Cardiac functional assessment without electrocardiogram using physiological self-navigation. Magnetic resonance in medicine. 2014;71:942–954.

3. Jackson John I, Meyer Craig H, Nishimura Dwight G, Macovski Albert. Selection of a convolution function for Fourier inversion using gridding (computerised tomography application). IEEE transactions on Medical Imaging. 1991;10:473–478.

4. Ronneberger Olaf, Fischer Philipp, Brox Thomas. U-net: Convolutional networks for biomedical image segmentation in International Conference on Medical image computing and computer-assisted intervention:234–241Springer 2015.

5. Tsao Jeffrey, Boesiger Peter, Pruessmann Klaas P. k-t BLAST and k-t SENSE: dynamic MRI with high frame rate exploiting spatiotemporal correlations. Magnetic Resonance in Medicine: An Official Journal of the International Society for Magnetic Resonance in Medicine. 2003;50:1031–1042.

6. Sandino Christopher M, Dixit Neerav, Cheng Joseph Y, Vasanawala Shreyas S. Deep convolutional neural networks for accelerated dynamic magnetic resonance imaging. In Proceedings of Medical Imaging meets Neural Information Processing Systems Conference, Long Beach, CA, 2017. p. 19.

7. Jung Hong, Sung Kyunghyun, Nayak Krishna S, Kim Eung Yeop, Ye Jong Chul. k-t FOCUSS: a general compressed sensing framework for high resolution dynamic MRI Magnetic resonance in medicine. 2009;61:103–116.

Figure 1. Proposed approach. The U-net is trained on two-dimensional spatio-temporal slices which are previously extracted from the image sequences. The image sequences can then be reassembled from the spatio-temporal slices.

Figure 2. Results on the test set where the available training data was limited by restricting the number of healthy volunteers from which we extracted the spatio-temporal slices. Proposed approach U-net_{xt,yt} for n = 2 (a), n = 13 (b),U-net_{xy}^{1} with n = 13 (c), kt-SENSE reconstructions with N_{θ} = 3400 radial lines (d).

Figure 3. Comparison with different Deep Learning-based methods. NUFFT reconstruction with N_{θ} = 1130 radial lines, sequence-wise trained residual U-net_{xyt}^{res} (b), sequence-wise trained non-residual single-convolutional-layer network C1 (c), sequence-wise trained non-residual U-net_{xyt}^{n.res} (c), proposed approach (e), ground truth kt-SENSE reconstruction (f).

Figure 4. Comparison with kt-FOCUSS for a patient with hypokinetic anterior and inferior wall and strongly reduced ejection fraction (23%). NUFFT reconstruction with N_{θ} = 1130 radial lines (a), proposed approach U-net_{xt,yt} with N_{θ} = 1130 (b) , kt-FOCUSS with N_{θ} = 1130 (c), kt-SENSE with N_{θ} = 3400 (d).