We propose a Conditional Wasserstein Generative Adversarial Network (cWGAN), trained with a novel Adaptive Loss Balancing (ALB) technique that stabilizes the training and minimizes the presence of artifacts, while maintaining a high-quality reconstruction with more natural appearance (compared to non-GAN techniques). Multi-channel 2D brain data with fourfold undersampling were used as inputs, and the corresponding fully-sampled reconstructed images as references for training. The algorithm produced higher-quality images than state-of-the-art deep learning-based models in terms of perceptual quality and realistic appearance.
Following the success of conditional GANs (cGAN)5 and WGANs6, we apply a cWGAN technique for an MRI sparse reconstruction (MRI-SR) model. Our model combines a generator network and a discriminator network that are being trained against each other. The generator is trained to reconstruct a fully-sampled image from a given under-sampled k-space dataset, that will minimize the approximated Earth Moving Distance (EMD) estimated by the critic (discriminator) and a pixel-wise loss. The critic receives either 1) pairs of zero-filled and generated images or 2) pairs of zero-filled and fully-sampled images and learns to estimate the EMD between the former (fake pairs) and the later (real pairs).
During traditional GAN training, the GAN loss may generate gradients with variable norm. To stabilize the GAN training and to avoid drifting away from the ground-truth spatial information, we use ALB that balances the GAN loss with the pixel-wise loss. ALB insures that the standard deviation (SD) of the GAN loss gradients will be upper-bounded by a ratio with the SD of the pixel-wise loss gradients. Our cWGAN-ALB model uses a cGAN architecture (Fig. 1) trained with ALB and WGAN objective (Fig. 2), where the generator architecture is a DCI-Net7 with 20 iterations and our critic architecture is based on the discriminator from DCGAN8.
Fréchet Inception Distance (FID)9 is a similarity measure between two datasets that correlates well with human judgement of visual quality, and is most often used to evaluate the quality of images generated by GANs10. We utilize FID as a quality metric to evaluate the similarity between the set of our generated images and the corresponding fully-sampled images. FID relies on the Fréchet distance calculated from two Gaussians each fitted on feature vectors taken from a pre-trained Inception network11, one for the generated images and one for the fully-sampled images. To our knowledge, we are the first to utilize FID for measuring image quality of MRI-SR models.
While it is possible to use a non-conditional GAN architecture, it is likely that for a given under-sampled k-space dataset, the generator will reconstruct a fairly realistic image, but since a non-conditional critic sees only the reconstructed image, it is not guaranteed that the generator will learn to reconstruct a realistic image that perceptually matches the given zero-filled image. In other words, a non-conditional critic is only able to learn general properties of the appearance of the entire distribution, however it’s not likely to perfectly match a specific sample.
Our proposed cWGAN-ALB model has three advantages over a conventional GAN: 1) A critic that receives both the input image and the reconstructed image is able to enforce higher data fidelity compared to a non-conditional GAN architecture; 2) Its training leads to perceptually better appearance of the reconstructed images; and 3) It stabilizes the training and leads to better convergence.
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