[Paper Review] Model-based Convolutional De-Aliasing Network Learning for Parallel MR Imaging

Yanxia Chen, Taohui Xiao+3 more|arXiv (Cornell University)|Aug 6, 2019

Advanced MRI Techniques and Applications13 references4 citations

TL;DR

This paper proposes a model-based convolutional de-aliasing network that leverages deep learning to reconstruct high-quality parallel MRI images from undersampled k-space data without requiring explicit coil sensitivity estimation. By combining a split Bregman algorithm with a learnable filtering operator, the method effectively exploits spatial redundancy and multi-coil correlations, achieving superior image quality and robustness across diverse acceleration factors and sampling patterns, with PSNR gains of up to 5 dB over conventional methods.

ABSTRACT

Parallel imaging has been an essential technique to accelerate MR imaging. Nevertheless, the acceleration rate is still limited due to the ill-condition and challenges associated with the undersampled reconstruction. In this paper, we propose a model-based convolutional de-aliasing network with adaptive parameter learning to achieve accurate reconstruction from multi-coil undersampled k-space data. Three main contributions have been made: a de-aliasing reconstruction model was proposed to accelerate parallel MR imaging with deep learning exploring both spatial redundancy and multi-coil correlations; a split Bregman iteration algorithm was developed to solve the model efficiently; and unlike most existing parallel imaging methods which rely on the accuracy of the estimated multi-coil sensitivity, the proposed method can perform parallel reconstruction from undersampled data without explicit sensitivity calculation. Evaluations were conducted on \emph{in vivo} brain dataset with a variety of undersampling patterns and different acceleration factors. Our results demonstrated that this method could achieve superior performance in both quantitative and qualitative analysis, compared to three state-of-the-art methods.

Motivation & Objective

• To address the limitations of existing parallel MRI reconstruction methods that rely on accurate coil sensitivity estimation, which can introduce artifacts when inaccurate.
• To improve reconstruction accuracy and speed for highly accelerated parallel MRI by exploiting spatial redundancy and multi-coil correlations through deep learning.
• To develop a model-based deep learning framework that avoids explicit sensitivity calculation while maintaining robustness across diverse undersampling patterns.
• To achieve superior quantitative and qualitative reconstruction performance compared to state-of-the-art methods like MoDL, SPIRiT, and SAKE.

Proposed method

• A de-aliasing reconstruction model is formulated as an unconstrained optimization problem combining data consistency and a learned regularization term.
• The split Bregman algorithm is employed to efficiently solve the optimization problem, enabling end-to-end learning and reconstruction.
• A learnable filtering operator Φ is incorporated into the regularization term to capture spatial and multi-coil correlations via convolutional neural networks.
• The method operates directly on undersampled k-space data without requiring coil sensitivity maps, reducing dependency on potentially inaccurate sensitivity estimation.
• The model is trained end-to-end using a deep learning framework that integrates physical constraints with data-driven priors.
• The algorithm is designed to be robust across various undersampling patterns, including 1D uniform, 1D random, 2D Poisson, and 2D radial sampling.

Experimental results

Research questions

• RQ1 Can a deep learning-based method achieve superior parallel MRI reconstruction without explicit coil sensitivity estimation?
• RQ2 How effectively can a model-based convolutional network exploit both spatial redundancy and multi-coil correlations in undersampled k-space data?
• RQ3 Does the proposed split Bregman-based optimization framework enable faster and more stable reconstruction than traditional iterative methods?
• RQ4 How does the method perform across diverse undersampling patterns and high acceleration factors?
• RQ5 Can the proposed method outperform state-of-the-art methods like MoDL, SPIRiT, and SAKE in both quantitative metrics and visual quality?

Key findings

• The proposed method achieved a mean PSNR of 36.99 dB and SSIM of 0.96 under 3x acceleration with a 1D uniform mask, outperforming MoDL (36.53 dB, 0.94) and SAKE (30.66 dB, 0.84).
• Under 4x acceleration with a 1D random mask, the method achieved 33.56 dB PSNR and 0.93 SSIM, significantly outperforming SPIRiT (28.25 dB, 0.74) and SAKE (27.93 dB, 0.80).
• At 6x acceleration with 2D Poisson sampling, the method achieved 32.64 dB PSNR and 0.90 SSIM, surpassing MoDL (32.63 dB, 0.90) and SAKE (27.15 dB, 0.74).
• For 9x radial sampling, the method achieved 32.49 dB PSNR and 0.91 SSIM, demonstrating robustness at high acceleration factors where MoDL showed increased edge noise and instability.
• The method reduced NMSE by nearly 5 dB on average compared to SAKE and SPIRiT across all tested acceleration factors and sampling patterns.
• Error maps revealed that the proposed method produced fewer artifacts and less noise at image edges compared to MoDL, especially under high acceleration.