Density Compensated Unrolled Networks for Non-Cartesian MRI Reconstruction (2101.01570v2)

Abstract: Deep neural networks have recently been thoroughly investigated as a powerful tool for MRI reconstruction. There is a lack of research, however, regarding their use for a specific setting of MRI, namely non-Cartesian acquisitions. In this work, we introduce a novel kind of deep neural networks to tackle this problem, namely density compensated unrolled neural networks, which rely on Density Compensation to correct the uneven weighting of the k-space. We assess their efficiency on the publicly available fastMRI dataset, and perform a small ablation study. Our results show that the density-compensated unrolled neural networks outperform the different baselines, and that all parts of the design are needed. We also open source our code, in particular a Non-Uniform Fast Fourier transform for TensorFlow.

• The paper introduces a density-compensated unrolled network that leverages a primal-dual architecture to improve non-Cartesian MRI reconstruction.
• It employs a cross-domain framework alternating between k-space and image space to effectively handle uneven sampling densities.
• Experimental results on radial and spiral trajectories demonstrate significant improvements in PSNR and SSIM compared to traditional methods.

Overview of "Density Compensated Unrolled Networks for Non-Cartesian MRI Reconstruction"

The paper "Density Compensated Unrolled Networks for Non-Cartesian MRI Reconstruction" introduces an advanced approach to address the challenges associated with non-Cartesian MRI reconstruction using deep neural networks. The authors present a novel unrolled neural network architecture that incorporates density compensation (DC) techniques to effectively rectify the uneven k-space weighting inherent in non-Cartesian acquisitions.

Contributions and Methodology

The authors contribute to the MRI reconstruction domain by designing an unrolled network model, termed Primal-Dual Network (PDNet), specifically tailored for non-Cartesian data. This model is equipped with a DC mechanism that adapts to different sampling densities and improves reconstruction quality. The paper outlines several key innovations:

1. Network Architecture: The PDNet utilizes a cross-domain framework that alternates corrections between the measurement space and image space. This alternation effectively manages the complex inverse problem inherent in MRI image reconstruction.
2. Density Compensation: DC is critical in ensuring uniform weighting across the k-space samples during the application of the adjoint operator, especially for oversampled regions, like the center of k-space in radial or spiral acquisitions.
3. Implementation Details: The authors have implemented the PDNet and the Non-Uniform Fast Fourier Transform (NUFFT) in TensorFlow, facilitating reproducibility and accessibility in future research.

Experimental Evaluation

The paper evaluates the PDNet on the publicly accessible fastMRI single-coil dataset with fixed radial and spiral trajectories. These experiments aim to demonstrate the superiority of their model over baseline reconstruction methods, including simple adjoint operations with DC and traditional U-net architectures applied to density-compensated data.

• Performance Metrics: The evaluation metrics include Peak Signal-to-Noise Ratio (PSNR) and Structural Similarity Index (SSIM), measured on volumetric data.
• Numerical Results: The paper presents strong quantitative improvements with the PDNet incorporating DC, yielding superior PSNR and SSIM scores when compared against other methods. Specifically, PDNet with DC achieved PSNR/SSIM values of 32.66/0.7327 for radial trajectories and 33.08/0.7534 for spiral ones, outperforming its counterparts.

Implications and Future Directions

The introduction of density-compensated unrolled networks marks a significant step towards enhancing non-Cartesian MRI reconstruction efficiency and accuracy. The approach has promising implications for more complex reconstruction settings, such as multi-channel phased arrays and 3D imaging. The adaptability of the PDNet architecture suggests potential extensions to various non-Cartesian sampling strategies, such as SPARKLING trajectories.

Furthermore, the open-source nature of the implementation can empower future developments in this area, fostering collaborative advancements and standardization in MRI research. The exploration of multi-GPU setups to handle larger datasets and more complex models could further the research impact on practical MRI applications.

In conclusion, the proposed density-compensated unrolled networks exhibit strong potential in overcoming existing limitations of non-Cartesian MRI reconstruction, paving the way for more refined and efficient computational imaging techniques in the medical domain.