k-Space Deep Learning for Accelerated MRI (1805.03779v3)

Abstract: The annihilating filter-based low-rank Hankel matrix approach (ALOHA) is one of the state-of-the-art compressed sensing approaches that directly interpolates the missing k-space data using low-rank Hankel matrix completion. The success of ALOHA is due to the concise signal representation in the k-space domain thanks to the duality between structured low-rankness in the k-space domain and the image domain sparsity. Inspired by the recent mathematical discovery that links convolutional neural networks to Hankel matrix decomposition using data-driven framelet basis, here we propose a fully data-driven deep learning algorithm for k-space interpolation. Our network can be also easily applied to non-Cartesian k-space trajectories by simply adding an additional regridding layer. Extensive numerical experiments show that the proposed deep learning method consistently outperforms the existing image-domain deep learning approaches.

• The paper introduces k-Space Deep Learning, a novel deep learning framework that directly interpolates missing k-space data for accelerated MRI reconstruction, building on concepts like low-rank Hankel matrix completion.
• The proposed method uses convolutional neural networks within the k-space domain and includes a regridding layer for non-Cartesian trajectories, demonstrating a theoretical link to data-driven framelet bases and image-domain sparsity.
• Numerical experiments show this approach significantly outperforms existing techniques (like ALOHA and image-domain deep learning) across various sampling patterns with improved PSNR, NMSE, and SSIM metrics, suggesting high efficiency and generalizability.

$k$-Space Deep Learning for Accelerated MRI

The paper investigates a novel approach, termed $k$-Space Deep Learning, for the acceleration of MRI reconstruction through direct interpolation of the missing $k$-space data utilizing deep learning techniques. The method builds upon state-of-the-art compressed sensing strategies, particularly the annihilating filter-based low-rank Hankel matrix method (ALOHA), which efficiently reconstructs MR images by leveraging low-rank matrix completion in the $k$-space domain.

Methodology

The authors present an innovative end-to-end deep learning framework, specifically engineered to interpolate missing data directly within the $k$-space. This approach significantly differs from existing solutions that perform image-domain post-processing or iterative updates between the $k$-space and image domains. The proposed method employs convolutional neural networks (CNNs) and introduces an additional regridding layer to handle non-Cartesian $k$-space trajectories, thereby extending its applicability beyond traditional Cartesian acquisitions.

The paper elucidates the connection between convolutional neural networks and Hankel matrix decomposition through data-driven framelet bases. This theoretical foundation ensures that the proposed deep learning approach capitalizes on the structured low-rankness inherent in $k$-space data, which correlates with image-domain sparsity. By comprehensively exploring this link, the authors posit that $k$-Space Deep Learning can outperform conventional image-domain deep learning methods consistently.

Results

Numerical experiments conducted with various sampling patterns, such as Cartesian, radial, and spiral trajectories, demonstrate the superiority of this approach over existing techniques. Quantitatively, the paper provides empirical evidence, showcasing improved PSNR, NMSE, and SSIM metrics when compared to total variation penalized compressed sensing MRI, ALOHA, and multiple deep learning models, including variational networks and image-domain learning frameworks. The proposed method attains substantial performance improvements while minimizing computational complexity.

Implications and Future Prospects

The implications of this research are multifaceted:

1. Efficiency and Scalability: The integration of CNNs within the $k$-space domain fosters efficient signal representation and interpolation, resulting in marked reductions in computation time and the potential for scalable applications in real-time MRI.
2. Generalizability: By employing ReLU nonlinearities and leveraging the combinatorial nature of network filters, this approach demonstrates remarkable adaptability and generalizability across diverse input datasets—an attribute not feasible with static convolution filters.
3. Innovative Frameworks: This work opens avenues for future advancements in other Fourier imaging modalities, proposing that similar frameworks could be employed to refine signal recovery processes for CT or PET imaging.

The paper culminates in advocating for further exploration into the integration of deep learning within the $k$-space domain, arguing that doing so can provide unprecedented improvements in MRI acceleration technologies. It invites subsequent research to expand upon the defined architectures, examining their efficacy and adaptability in broader clinical contexts.