Implementation of Variational Networks for image reconstruction in tensorflow

Variational Networks for image reconstruction in tensorflow

This is a generic implementation of Variational Network (loop unrolling) for MR image reconstruction, proposed by Hammerick et al.. MRI data used to train the network is introduced and described by Johannes Schmidt and Sebastian Kozerke. The full code is available at github: https://github.com/visva89/VarNetRecon

Running the code

• Download 2D short axis cardiac MRI dataset https://polybox.ethz.ch/index.php/s/E9FgAzi21iVJiF5
• Inspect configuration of the network in recon_model_300_066.py. We used:
  • 10 layers
  • 7x7 filters
  • 30 filters per layer
  • 35 knots to parametrize activations
  • cubic interpolation for activations
• Run example.sh for training, or use saved parameters ckpts/model.ckpt and run recon_model_300_066.py
• Run matlab script report_imgs.m for illustrations of reconstruction and learned parameters

Demo

For training we used fully sampled 128x128 short axis MR images of the heart with artificially generated smooth phase offset. The k-space was retrospectively undersampled to achieve acceleration factor of ~3. Variational Network reconstruction was compared to total variation (TV) regularized reconstruction (with the optimal regularization weight).
Reconstruction for each layer of the network:
Learned filters (real part):
Learned activation functions (integral of activation, i.e. element-wise potentials):

Important Notes

• We are reconstructing smaller images compared to original work. Hence different filter sizes are used.
• Multi coil acquisition as well as coil sensitivity maps are not modeled.
• Batch size is fixed at configuration time.
• Cubic interpolation is used by default instead of RBF, since it is more memory efficient. You can choose linear, cubic, or RBF in the network configuration.
• Maximal estimated filter response is fixed for all layers.