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

arXiv: https://arxiv.org/abs/2508.04051 · HTML: https://mlsanity.com/paper/2508.04051/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 35 references that are in the map.
- First posted on arXiv 6 Aug 2025.

## Builds on (most cited first, 13 of 13)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [MoDL: Model Based Deep Learning Architecture for Inverse Problems](https://mlsanity.com/paper/1712.02862/) (2017)
- [White-Box Transformers via Sparse Rate Reduction](https://mlsanity.com/paper/2306.01129/) (2023)
- [ReconFormer: Accelerated MRI Reconstruction Using Recurrent Transformer](https://mlsanity.com/paper/2201.09376/) (2022)
- [Deep Generalization of Structured Low-Rank Algorithms (Deep-SLR)](https://mlsanity.com/paper/1912.03433/) (2019)
- [LORAKI: Autocalibrated Recurrent Neural Networks for Autoregressive MRI Reconstruction in k-Space](https://mlsanity.com/paper/1904.09390/) (2019)
- [Structured Low-Rank Algorithms: Theory, MR Applications, and Links to Machine Learning](https://mlsanity.com/paper/1910.12162/) (2019)
- [Matrix Completion-Informed Deep Unfolded Equilibrium Models for Self-Supervised k-Space Interpolation in MRI](https://mlsanity.com/paper/2309.13571/) (2023)
- [K-Space Transformer for Undersampled MRI Reconstruction](https://mlsanity.com/paper/2206.06947/) (2022)

## Abstract (arXiv)

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.