Learning a Variational Network for Reconstruction of Accelerated MRI Data (1704.00447v1)

Abstract: Purpose: To allow fast and high-quality reconstruction of clinical accelerated multi-coil MR data by learning a variational network that combines the mathematical structure of variational models with deep learning. Theory and Methods: Generalized compressed sensing reconstruction formulated as a variational model is embedded in an unrolled gradient descent scheme. All parameters of this formulation, including the prior model defined by filter kernels and activation functions as well as the data term weights, are learned during an offline training procedure. The learned model can then be applied online to previously unseen data. Results: The variational network approach is evaluated on a clinical knee imaging protocol. The variational network reconstructions outperform standard reconstruction algorithms in terms of image quality and residual artifacts for all tested acceleration factors and sampling patterns. Conclusion: Variational network reconstructions preserve the natural appearance of MR images as well as pathologies that were not included in the training data set. Due to its high computational performance, i.e., reconstruction time of 193 ms on a single graphics card, and the omission of parameter tuning once the network is trained, this new approach to image reconstruction can easily be integrated into clinical workflow.

• The paper presents a variational network that merges deep learning with traditional variational models to achieve fast, artifact-suppressed MRI reconstructions.
• It employs an unrolled gradient descent framework to simultaneously learn filter kernels, activation functions, and data weights during offline training.
• The approach outperforms conventional methods by producing sharper images with reduced reconstruction times, achieving around 193 ms per slice.

Learning a Variational Network for Reconstruction of Accelerated MRI Data

Abstract

The paper "Learning a Variational Network for Reconstruction of Accelerated MRI Data" by Kerstin Hammernik et al. presents a novel approach to reconstructing accelerated MRI data using a Variational Network (VN). The VN integrates the mathematical structure of variational models with the capabilities of deep learning. The VN approach leverages offline training to learn the optimal parameters for MRI image reconstruction, thus enabling fast, high-quality reconstructions without the need for extensive parameter tuning during clinical application.

Introduction

Deep learning has significantly impacted various domains of computer vision, including medical imaging. Traditional MRI reconstruction techniques, such as Parallel Imaging (PI) and Compressed Sensing (CS), have limitations regarding the speed and quality of image reconstruction, mainly when the sampling conditions specified by CS are not fully met. This paper introduces a VN to bridge the gap by combining deep learning techniques with the robust mathematical formulations of variational models, allowing for the efficient and high-quality reconstruction of undersampled MRI data.

Methodology

The VN architecture is formulated as a generalized compressed sensing problem embedded within an unrolled gradient descent scheme. This approach allows the simultaneous learning of all necessary parameters, including filter kernels, activation functions, and data term weights, during a focused offline training phase. Specifically, the VN is structured to perform iterative gradient descent steps, where each step refines the image reconstruction by learning separate filters for the real and imaginary components of the complex-valued MRI data.

Results

The authors evaluated the proposed VN method on a clinical knee imaging dataset, comparing performance against traditional reconstruction methods like CG SENSE and PI-CS TGV. The VN achieved significant improvements in image quality and artifact suppression, as quantitatively validated by metrics such as Mean Squared Error (MSE) and Structural Similarity Index (SSIM).

• Acceleration Factors and Sampling Patterns: For acceleration factors R=3 and R=4 combined with both regular Cartesian and variable-density random sampling, the VN provided sharper and more natural reconstructions than CG SENSE and PI-CS TGV consistently across all scenarios.
• Speed of Reconstruction: The VN demonstrated high computational efficiency, with reconstruction times around 193 ms per slice on a single graphics card, vastly outpacing traditional iterative methods.

Discussion

The VN's ability to outperform traditional methods is attributed to its robust learning framework, which generalizes well across different data contrasts and sampling patterns. The VN's structured learning of filter kernels and activation functions allows for a nuanced understanding and suppression of undersampling artifacts, analogous to, but far more effective than, traditional handcrafted regularizers like TV and TGV.

The integration of variational methods with deep learning offers a transparent insight into the optimization outcomes, distinguishing VN from typical "black-box" machine learning models. Interestingly, the paper observes that moderate acceleration factors might benefit less from randomness in sampling patterns, a finding that invites further investigation into adaptive sampling strategies.

Implications and Future Work

The VN approach holds transformational potential for clinical MRI by providing swift, high-quality reconstructions, thus enhancing workflow efficiency without compromising diagnostic accuracy. Future research directions include expanding VN applications to non-Cartesian sampling, dynamic imaging, and multiparametric MRI data. Exploring alternative loss functions aligned with perceptual similarity metrics rather than conventional MSE and SSIM could further refine reconstruction quality.

Conclusion

This paper presents a comprehensive paper of leveraging a VN for MRI reconstruction, illustrating how integrating deep learning with variational models leads to superior performance over traditional methods. By shifting the computational burden to an offline training phase, the VN permits fast and reliable online reconstructions suitable for clinical settings. The nuanced parameter learning and artifact suppression capabilities of the VN mark a significant stride towards more effective and efficient MRI image reconstruction.

This research underlines the potential of variational networks to not only enhance current practices but also inspire further advancements in medical imaging technologies.