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Compressed Sensing MRI Reconstruction using a Generative Adversarial Network with a Cyclic Loss
Tran Minh Quan, Thanh Nguyen-Duc, Won-Ki Jeong
TL;DR
CS-MRI reconstruction must overcome slow iterative solvers and limited early adoption of deep networks for MRI. The paper introduces RefineGAN, a residual adversarial model with cyclic data consistency and chained refinement. It reports faster reconstruction and better image quality than recent CS-MRI methods, including at very low sampling rates.
Problem
CS-MRI commonly relies on iterative numerical solvers, while deep-learning adaptation for MRI reconstruction remains at an early stage, limiting time-critical applications.
Method
RefineGAN combines fully residual convolutional networks, adversarial training, cyclic data consistency, and chained generator networks for CS-MRI reconstruction.
Results
RefineGAN outperforms state-of-the-art CS-MRI methods in running time and image quality across several open-source MRI databases, including extremely low sampling rates.
Takeaways & Limitations
The reported speed and reconstruction quality indicate potential usefulness for time-critical clinical applications.
Abstract
from arXiv · showhide
Compressed Sensing MRI (CS-MRI) has provided theoretical foundations upon which the time-consuming MRI acquisition process can be accelerated. However, it primarily relies on iterative numerical solvers which still hinders their adaptation in time-critical applications. In addition, recent advances in deep neural networks have shown their potential in computer vision and image processing, but their adaptation to MRI reconstruction is still in an early stage. In this paper, we propose a novel deep learning-based generative adversarial model, RefineGAN, for fast and accurate CS-MRI reconstruction. The proposed model is a variant of fully-residual convolutional autoencoder and generative adversarial networks (GANs), specifically designed for CS-MRI formulation; it employs deeper generator and discriminator networks with cyclic data consistency loss for faithful interpolation in the given under-sampled k-space data. In addition, our solution leverages a chained network to further enhance the reconstruction quality. RefineGAN is fast and accurate -- the reconstruction process is extremely rapid, as low as tens of milliseconds for reconstruction of a 256x256 image, because it is one-way deployment on a feed-forward network, and the image quality is superior even for extremely low sampling rate (as low as 10%) due to the data-driven nature of the method. We demonstrate that RefineGAN outperforms the state-of-the-art CS-MRI methods by a large margin in terms of both running time and image quality via evaluation using several open-source MRI databases.
I. INTRODUCTION
MRI acquisition is lengthy despite acceleration efforts, motivating methods that shift reconstruction cost into training and use fast neural-network inference. The paper proposes a residual GAN architecture with cyclic data consistency and chained refinement for fast, accurate CS-MRI reconstruction.
- Long MRI acquisition causes patient discomfort and hinders time-critical diagnoses such as strokes.
- Conventional CS-MRI methods rely on sparsifying transforms and nonlinear optimization, while dictionary learning improves data-specific feature representation.
- Deep learning can shift computationally intensive processing into training and enable one-pass neural-network deployment for faster prediction.
- RefineGAN combines residual convolutional autoencoders, GANs, and cyclic loss to enforce data consistency during undersampled k-space interpolation.
- The chained generator first maps zero-filling reconstructions to full reconstructions, then improves accuracy through successive refinement networks.
II. RELATED WORK
CS-MRI methods span universal sparsifying transforms, dictionary learning, and deep neural networks. The related work contrasts their reconstruction strategies, computational demands, and efforts to improve speed and image quality.
- Universal transform-based methods: Conventional methods use universal transforms or low-rank techniques but incur computational overhead from expensive nonlinear optimization.
- Dictionary learning-based methods: Dictionary learning addresses the mismatch between general transforms and input data by learning data-specific dictionaries from image patches.
- Deep learning-based methods: Deep learning methods reconstruct high-quality images from undersampled k-space data using multilayer neural networks.
- Deep learning-based methods: Deep ADMM-Net learns optimization parameters through staged networks, while other approaches cascade networks with data-consistency layers.
A. Problem Definition and Notations
The problem is to recover a full MR image from undersampled k-space measurements while respecting the measurement constraint. The formulation replaces regularized numerical minimization with neural-network training.
- Undersampled raw MRI k-space measurements are represented by m and sampling mask R, while zero-filling reconstruction s0 is obtained from them.
- The Fourier operator F and its conjugate transpose F^H connect images and undersampled measurements through the reconstruction and sampling processes.
- The overview compares reconstructions generated from undersampled data with fully sampled reference images processed through the same undersampling procedure.
- CS-MRI reconstruction generates a full image s from undersampled k-space data m under the measurement constraint.
- The regularizer J(s) used in the ill-posed optimization formulation is replaced by neural-network training in the proposed method.
B. Overview of the Proposed Method
RefineGAN uses a chained generator to reconstruct images from zero-filled inputs and adversarial training to make outputs resemble fully sampled MRI. The discriminator distinguishes generated from real reconstructions during training.
- The generator uses two chained networks to produce full MR images directly from zero-filling reconstructions, including up to two channels for complex-valued data.
- Generative Adversarial Loss: The generator transforms zero-filling inputs into fully reconstructed images, while the discriminator distinguishes generated images from reconstructions based on fully sampled k-space data.
- Generative Adversarial Loss: During adversarial training, the generator seeks outputs that fool the discriminator, while the discriminator maximizes correct real-versus-fake classification.
- Generative Adversarial Loss: The adversarial objective is represented by Ladv(G,D), with its expanded expectation-based form given for generator and discriminator training.
- Generative Adversarial Loss: The adversarial process drives generated images toward fully sampled reconstructions, and Wasserstein GAN energy is adopted to improve training stability.
D. Cyclic Data Consistency Loss
The cyclic data consistency loss supplements adversarial training because adversarial loss alone may not correctly map undersampled data to full reconstructions. It combines frequency-domain and image-domain constraints evaluated cyclically.
- Adversarial loss alone is insufficient to correctly map undersampled data to full reconstructions.
- The cyclic loss combines under-sampled frequency loss with fully reconstructed image loss.
- Frequency loss minimizes discrepancies after reconstructed images are re-undersampled to k-space measurements.
- Image loss encourages generated reconstructions to resemble fully reconstructed images derived from undersampled inputs.
- The consistency loss affects only the generator, while its component losses use independently sampled undersampled measurements and fully reconstructed images.
E. Model Architecture
The model architecture combines convolutional autoencoder and deep residual-network components. Its generator reconstructs a residual correction from undersampled data and adds that correction to the zero-filling reconstruction.
- The architecture is a variant of a convolutional autoencoder and deep residual network.
- The generator uses encoder, decoder, and residual-block components as its fundamental building blocks.
- The generator reconstructs the inverse-amplitude residual caused by undersampled k-space reconstruction rather than directly reconstructing the image.
- The final reconstruction is formed by adding the zero-filling reconstruction to the generator output.
- The generator is organized in one-fold and two-fold architectures.
2) Generator architecture:
The generator performs end-to-end reconstruction by learning a residual correction to the zero-filling MRI. Training combines adversarial, frequency-consistency, and image-consistency losses with weighted contributions.
- The generator produces a residual correction rather than directly reconstructing the image, which is added to the zero-filling input.
- The system trains generator and discriminator subnetworks adversarially.
- Total training loss combines adversarial loss, frequency loss, and image loss.The objective is Ltotal = Ladv (G, D) + αLfreq (G) + γLimag (G).
- The experiments set α = 1.0 and γ = 10.0 to balance the loss contributions.
G. Chaining with Refinement Network
The refinement design chains multiple generators so later stages can improve an initial reconstruction. Ground truth is enforced between stages, producing a target-driven, single-input and multi-output model.
- Multiple generators are chained to resolve ambiguities in the initial prediction and refine reconstruction accuracy.
- Ground truth is forced between generators, making the chained solution target-driven.
- The chained model accepts one input and produces multiple outputs, with each checkpoint attempting a better reconstruction.
- The unfolded sub-generators share architecture but not weights, resembling a recurrent network whose state is an entire sub-generator.
A. Results on real-valued MRI data
On real-valued brain and chest MRI data, RefineGAN was evaluated across undersampling rates against state-of-the-art reconstruction methods, with emphasis on speed and image quality. The method achieved fast reconstruction and better quantitative and qualitative results, including at low sampling rates.
- Evaluation setup: 100 brain and 100 chest images were used for training, with another 100 images from each database reserved for testing.Experiments used 256x256 images and sampling rates of 10%, 20%, 30%, and 40%, corresponding to 10×, 5×, 3.3×, and 2.5× acceleration.
- Running time: RefineGAN reconstructs 256x256 images in under 100 ms, while dictionary-based methods require roughly 9 to 600 seconds.Feed-forward deep learning methods are faster because deployment requires single-pass convolutional processing; RefineGAN is slower than single-generator GAN variants because it chains two generators.
- Image quality: RefineGAN and ReconGAN achieve better PSNR, SSIM, and NRMSE than the compared CS-MRI methods on the brain and chest test sets.The evaluation uses PSNR, SSIM, and NRMSE, with results shown in Figures 8–10.
- Image quality: A cyclic loss increases PSNR by around 1 dB, while the refinement network further reduces reconstruction error by a similar degree.The comparison uses identical generator and discriminator sizes for SingleGAN and the proposed method.
- Qualitative comparison: Deep learning methods produce more natural images than dictionary-based methods, preserving edges and reducing noise relative to full reconstructions.RefineGAN is reported to remain superior especially at sampling rates as low as 10%.
B. Results on complex-valued MRI data
For complex-valued knee MRI, RefineGAN reconstructs magnitude and phase images from undersampled data and is evaluated across sampling patterns. It produces lower-error reconstructions and consistently outperforms the compared GAN variants across strategies.
- Dataset and representation: The knee dataset contains 20 fully sampled 3D fast spin echo cases, yielding 100 training and 100 testing images from selected slices.The model accepts two-channel complex-valued zero-filling images and returns two-channel complex-valued reconstructions.
- Image quality: At a 10% sampling rate, RefineGAN reconstructs knee magnitude and phase images with less error than the other evaluated methods.Figure 12 presents reconstruction and zoom-in results with 10× magnified error plots.
- Sampling strategies: At a 20% sampling rate, RefineGAN consistently outperforms SingleGAN and ReconGAN across radial, Cartesian, random, and spiral sampling strategies.Figure 13 reports NRMSE curves for these sampling patterns.
- Sampling strategies: Radial sampling gives the best performance among the evaluated strategies, while RefineGAN makes differences between sampling strategies less severe.The comparison is based on knee-dataset NRMSE curves at a 20% sampling rate.
V. CONCLUSION
The paper concludes that RefineGAN is a deep learning GAN architecture for CS-MRI reconstruction using deeper networks and cyclic data consistency. It outperforms state-of-the-art methods in speed and image quality, while future work targets deeper chains, dynamic MRI, and distributed deployment.
- V. CONCLUSION: RefineGAN combines a deeper generator, adversarial discriminator training, and cyclic data consistency for end-to-end reconstruction from undersampled k-space data.The architecture is inspired by U-net, residual CNNs, and GANs.
- V. CONCLUSION: RefineGAN outperforms state-of-the-art CS-MRI methods in both running time and image quality, indicating usefulness for time-critical clinical applications.This conclusion summarizes the paper’s reported evaluation outcome.
- V. CONCLUSION: Future work includes analyzing the architecture, constructing deeper multi-fold chains, extending the method to dynamic MRI, and developing distributed training and deployment.These directions are proposed rather than evaluated in the paper.