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

• URL: http://arxiv.org/abs/2508.04051v1
• Date: Wed, 06 Aug 2025 03:24:28 GMT
• Title: Towards Globally Predictable k-Space Interpolation: A White-box Transformer Approach
• Abstract summary: We propose GPI-WT, a white-box Transformer framework based on Globally Predictable Interpolation (GPI) for k-space.<n> Experimental results demonstrate that the proposed method significantly outperforms state-of-the-art approaches in k-space accuracy while providing superior interpretability.
• Score: 9.242448133816037
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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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