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Deep Generative Adversarial Networks for Compressed Sensing Automates MRI
Morteza Mardani, Enhao Gong, Joseph Y. Cheng, Shreyas Vasanawala, Greg Zaharchuk, Marcus Alley, Neil Thakur, Song Han, William Dally, John M. Pauly, Lei Xing
TL;DR
MRI reconstruction is slow and ill-posed after undersampling, while conventional compressed sensing does not directly target diagnostic image quality. GANCS learns a diagnostic-quality, data-consistent image manifold with adversarial and ℓ1 training, then applies the generator directly to new measurements. On the evaluated MRI data, expert radiologists found GANCS images to have superior diagnostic quality, while reconstruction took about 10 msec and was more than 100 times faster than state-of-the-art CS MRI software.
Problem
MRI reconstruction is a slow, severely ill-posed task after undersampling, and existing compressed-sensing analytics are not cognizant of diagnostic image quality.
Method
GANCS learns a low-dimensional manifold of diagnostic-quality MR images using a generator–discriminator network with data consistency and adversarial regularization.
Results
Expert radiologist evaluations confirm superior diagnostic quality, while GANCS reconstructs images in about 10 msec, more than 100 times faster than state-of-the-art CS MRI software.
Takeaways & Limitations
GANCS offers sharp, high-contrast, data-consistent reconstructions suitable for real-time MRI visualization through direct generator inference.
Takeaways & Limitations
Experiments assume that only 20% of Fourier coefficients are collected and use λ = 0.1.
Abstract
from arXiv · showhide
Magnetic resonance image (MRI) reconstruction is a severely ill-posed linear inverse task demanding time and resource intensive computations that can substantially trade off {\it accuracy} for {\it speed} in real-time imaging. In addition, state-of-the-art compressed sensing (CS) analytics are not cognizant of the image {\it diagnostic quality}. To cope with these challenges we put forth a novel CS framework that permeates benefits from generative adversarial networks (GAN) to train a (low-dimensional) manifold of diagnostic-quality MR images from historical patients. Leveraging a mixture of least-squares (LS) GANs and pixel-wise $\ell_1$ cost, a deep residual network with skip connections is trained as the generator that learns to remove the {\it aliasing} artifacts by projecting onto the manifold. LSGAN learns the texture details, while $\ell_1$ controls the high-frequency noise. A multilayer convolutional neural network is then jointly trained based on diagnostic quality images to discriminate the projection quality. The test phase performs feed-forward propagation over the generator network that demands a very low computational overhead. Extensive evaluations are performed on a large contrast-enhanced MR dataset of pediatric patients. In particular, images rated based on expert radiologists corroborate that GANCS retrieves high contrast images with detailed texture relative to conventional CS, and pixel-wise schemes. In addition, it offers reconstruction under a few milliseconds, two orders of magnitude faster than state-of-the-art CS-MRI schemes.
1 Introduction
MRI acquisition is slow and undersampling makes reconstruction ill-posed, while pixel-wise reconstruction methods can lose diagnostic texture. GANCS addresses this gap by learning diagnostic-quality image manifolds for fast, non-iterative aliasing suppression.
- MRI scans can take several minutes, and undersampling creates a seriously ill-posed linear inverse reconstruction problem.
- CNN and denoising autoencoder methods speed reconstruction but can produce blurry and aliasing artifacts because pixel-wise costs overlook high-frequency texture.
- GANCS learns a low-dimensional manifold of diagnostic-quality MR images and uses a residual generator with skip connections to remove aliasing artifacts while maintaining measurement consistency.
- The framework is presented as a data-driven regularizer and a non-iterative GAN technique for aliasing suppression with a trade-off between data consistency and manifold learning.
- Evaluations use a large contrast-enhanced pediatric MRI dataset and expert-radiologist ratings of reconstructed images.
2 Problem Statement
The paper models undersampled MRI as an ill-posed linear system whose images lie on an unknown low-dimensional manifold. Reconstruction learns that manifold from paired training samples, then projects an aliased image onto it.
- The observation model is y = Φx + v with M ≪ N, where x is a complex-valued image assumed to lie on an unknown low-dimensional manifold.
- Training data consist of image samples X and corresponding possibly noisy observations Y, while the reconstruction goal is to recover x from a new observation y.
- For MRI, Φ is the partial 2D Fourier transform producing undersampled k-space data, and the initial aliased image can be obtained with the pseudo-inverse Φ†y.
- The reconstruction procedure first learns the image manifold and then projects the aliased image onto it to discard artifacts.
3 Manifold Learning via Generative Adversarial Networks
GANCS learns a plausible, data-consistent image manifold with adversarial training, residual networks, and explicit consistency penalties. Its generator is trained with LSGAN and ℓ1 objectives, then applied directly to new measurements.
- The method uses a generator–discriminator network in which the generator projects undersampled images onto a manifold of high-quality images and the discriminator scores diagnostic plausibility.
- A feasible-set projection or alternating residual and data-consistency layers constrain generated images toward the intersection of the image manifold and measurement-consistent space.
- LSGAN pulls generated samples toward the discriminator decision boundary, while an ℓ1 criterion suppresses high-frequency noise and preserves fine texture details.
- The soft least-squares fitting term enforces data consistency, while λ and η balance manifold projection, noise suppression, and data consistency.
- The generator is an expected regularized-LS estimator whose training-time learned regularization enables direct application to new samples without iterative reconstruction optimization.
- Under the noise-free infinite-capacity assumption, the optimal adversarial equilibrium is achieved when the generated distribution matches the true data distribution.
- The discriminator and generator are trained by mini-batch stochastic alternating minimization with momentum-based gradient steps and backpropagation.
4 Experiments
Experiments evaluate GANCS for undersampled MRI reconstruction using pediatric contrast-enhanced data, image-quality metrics, radiologist ratings, and analyses of speed, learned features, training costs, and data requirements.
- Experimental setup: Experiments use 20% of Fourier coefficients with variable-density radial sampling and evaluate reconstruction on contrast-enhanced pediatric MRI volumes.The dataset contains 350 patients, with 300 used for training and 50 for testing.
- Image quality: GANCS produces the most detailed, high-contrast images, whereas ℓ2-net is over-smoothed, ℓ1-net is sharper but inferior to GANCS, and conventional CS introduces blurring.GAN alone produces sharp images but retains noise, while GANCS combines texture detail with improved visual quality.
- Speed and quantitative trade-offs: 10 msec reconstruction time enables approximately 100 frames per second, contrasting with conventional CS methods that require a few seconds for iterative reconstruction.CS methods achieve higher SNR and SSIM but miss high-frequency textures.
- Radiologist assessment: Expert radiologists rate GANCS nearly as perceptually pleasing as gold-standard scans and superior in diagnostic quality to the other alternatives.Radiologists assess image quality, residual artifacts, and sharpness using normalized scores.
- Learned manifold: Discriminator feature maps progress from edge detection in early layers to anatomically and texturally meaningful regions in later layers.The observed progression is consistent with how expert radiologists inspect images for diagnostic quality.
5 Conclusions and Future Work
GANCS uses historical abdominal MR data to reconstruct highly undersampled images with diagnostic quality and about 10 msec inference, over 100 times faster than state-of-the-art CS MRI.
- GANCS learns a low-dimensional manifold that produces sharp, high-contrast images consistent with MRI data and the acquisition model.
- 10 msec inference makes GANCS more than 100 times faster than the state-of-the-art CS MRI toolbox.
- The authors identify future work in 3D spatial correlations, abnormal patients, and variations in acquisition models such as sampling strategies.