Multi-modal Magnetic Resonance Imaging (MRI) offers complementary diagnostic information, but some modalities are limited by the long scanning time. To accelerate the whole acquisition process, MRI reconstruction of one modality from highly undersampled k-space data with another fully-sampled reference modality is an efficient solution. However, the misalignment between modalities, which is common in clinic practice, can negatively affect reconstruction quality. Existing deep learning-based methods that account for inter-modality misalignment perform better, but still share two main common limitations: (1) The spatial alignment task is not adaptively integrated with the reconstruction process, resulting in insufficient complementarity between the two tasks; (2) the entire framework has weak interpretability. In this paper, we construct a novel Deep Unfolding Network with Spatial Alignment, termed DUN-SA, to appropriately embed the spatial alignment task into the reconstruction process. Concretely, we derive a novel joint alignment-reconstruction model with a specially designed cross-modal spatial alignment term. By relaxing the model into cross-modal spatial alignment and multi-modal reconstruction tasks, we propose an effective algorithm to solve this model alternatively. Then, we unfold the iterative steps of the proposed algorithm and design corresponding network modules to build DUN-SA with interpretability. Through end-to-end training, we effectively compensate for spatial misalignment using only reconstruction loss, and utilize the progressively aligned reference modality to provide inter-modality prior to improve the reconstruction of the target modality. Comprehensive experiments on three real datasets demonstrate that our method exhibits superior reconstruction performance compared to state-of-the-art methods.

翻译：多模态磁共振成像（MRI）可提供互补的诊断信息，但部分模态受限于较长的扫描时间。为加速整体采集过程，利用另一完全采样的参考模态从高度欠采样的k空间数据中重建目标模态是一种高效方案。然而，临床实践中常见的模态间错位问题会显著影响重建质量。现有考虑跨模态错位因素的深度学习方法虽性能更优，但仍存在两个主要缺陷：（1）空间对齐任务未与重建过程自适应整合，导致两任务间的互补性不足；（2）整个框架可解释性较弱。本文构建了一种新颖的面向空间对齐的深度展开网络（DUN-SA），将空间对齐任务合理嵌入重建过程。具体而言，我们推导出一个带专门设计的跨模态空间对齐项的新型联合对齐-重建模型。通过将该模型松弛为跨模态空间对齐与多模态重建两个子任务，我们提出了一种交替求解该模型的高效算法。随后将算法迭代步骤展开，设计对应网络模块，构建具有可解释性的DUN-SA。通过端到端训练，我们仅利用重建损失即可有效补偿空间错位，并利用渐进对齐的参考模态提供跨模态先验以改善目标模态的重建质量。在三个真实数据集上的综合实验表明，本方法相较于现有最优方法展现出更卓越的重建性能。