Interpolating missing data in \( k \) -space is essential for accelerating imaging. However, existing methods, including convolutional neural network-based deep learning, primarily exploit local predictability while overlooking the inherent global dependencies in \( k \) -space. Recently, Transformers have demonstrated remarkable success in natural language processing and image analysis due to their ability to capture long-range dependencies. This inspires the use of Transformers for \( k \) -space interpolation to better exploit its global structure. However, their lack of interpretability raises concerns regarding the reliability of interpolated data. To address this limitation, we propose GPI-WT, a white-box Transformer framework based on Globally Predictable Interpolation (GPI) for \( k \) -space. Specifically, we formulate GPI from the perspective of annihilation as a novel \( k \) -space structured low-rank (SLR) model. The global annihilation filters in the SLR model are treated as learnable parameters, and the subgradients of the SLR model naturally induce a learnable attention mechanism. By unfolding the subgradient-based optimization algorithm of SLR into a cascaded network, we construct the first white-box Transformer specifically designed for accelerated MRI. Experimental results demonstrate that the proposed method significantly outperforms state-of-the-art approaches in \( k \) -space interpolation accuracy while providing superior interpretability.

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Towards Globally Predictable k-Space Interpolation: A White-Box Transformer Approach

  • Chen Luo,
  • Qiyu Jin,
  • Taofeng Xie,
  • Xuemei Wang,
  • Huayu Wang,
  • Congcong Liu,
  • Liming Tang,
  • Guoqing Chen,
  • Zhuo-Xu Cui,
  • Dong Liang

摘要

Interpolating missing data in \( k \) -space is essential for accelerating imaging. However, existing methods, including convolutional neural network-based deep learning, primarily exploit local predictability while overlooking the inherent global dependencies in \( k \) -space. Recently, Transformers have demonstrated remarkable success in natural language processing and image analysis due to their ability to capture long-range dependencies. This inspires the use of Transformers for \( k \) -space interpolation to better exploit its global structure. However, their lack of interpretability raises concerns regarding the reliability of interpolated data. To address this limitation, we propose GPI-WT, a white-box Transformer framework based on Globally Predictable Interpolation (GPI) for \( k \) -space. Specifically, we formulate GPI from the perspective of annihilation as a novel \( k \) -space structured low-rank (SLR) model. The global annihilation filters in the SLR model are treated as learnable parameters, and the subgradients of the SLR model naturally induce a learnable attention mechanism. By unfolding the subgradient-based optimization algorithm of SLR into a cascaded network, we construct the first white-box Transformer specifically designed for accelerated MRI. Experimental results demonstrate that the proposed method significantly outperforms state-of-the-art approaches in \( k \) -space interpolation accuracy while providing superior interpretability.