AI 中文总结
针对并行磁共振成像重建的数据泄露问题，本文提出HSSRecon框架，通过物理组拆分与多重性归一化分离Hankel域结构学习与物理域数据一致性，在fastMRI脑部数据上取得了竞争力的重建性能。
AI 中文摘要
并行磁共振成像重建是欠采样条件下的不适定逆问题。多线圈采集与Hankel提升技术可揭示互补的重复信息：不同线圈对同一解剖结构的观测结果，以及重叠窗口中重复的局部k空间邻域，这些依赖关系可指导缺失k空间数据的恢复。然而，将提升后的Hankel条目拆分用于自监督时，会使原始样本同时出现在输入和目标中，造成数据泄露。本文提出Hankel子空间自监督重建（HSSRecon），这是一种针对并行磁共振成像的扫描特异性重建框架。HSSRecon在Hankel提升前按物理采集单元划分数据，并对重叠窗口中的重复Hankel副本应用多重性归一化。该网络不学习直接预测缺失数据的映射，而是学习一个紧凑的复值Hankel子空间算子，通过带硬数据一致性的共轭梯度求解器对原始k空间变量执行重建。该设计将Hankel域的结构学习与物理域的数据一致性分离：前者利用多线圈和局部Hankel相关性，后者针对未获取的自由度求解。本文对物理组拆分和多重性归一化进行了理论分析，证明了系统的正定性、唯一性、硬数据一致性以及有限步共轭梯度误差界。在含三种对比度和三种采样掩码的fastMRI脑部数据上，HSSRecon在六个聚合条件下均取得了具有竞争力的峰值信噪比、结构相似性和归一化均方误差。
英文摘要
Parallel magnetic resonance imaging reconstruction is an ill-posed inverse problem under undersampling. Multi-coil acquisition and Hankel lifting expose complementary repeated information: observations of the same anatomy across coils and repeated local k-space neighborhoods in overlapping windows. These dependencies guide recovery of missing k-space data. However, splitting lifted Hankel entries for self-supervision can place the original sample in both input and target, causing data leakage. We propose Hankel Subspace Self-Supervised Reconstruction (HSSRecon), a scan-specific reconstruction framework for parallel magnetic resonance imaging. HSSRecon partitions data by physical acquisition units before Hankel lifting and applies multiplicity normalization to repeated Hankel copies in overlapping windows. Rather than learning a mapping that directly predicts missing data, the network learns a compact complex-valued Hankel subspace operator. Reconstruction is performed over the original k-space variables using a conjugategradient solver with hard data consistency. This design separates structural learning in the Hankel domain from data consistency in the physical domain: the former exploits multi-coil and local Hankel correlations, while the latter solves over unacquired degrees of freedom. We provide theoretical analyses of physicalgroup splitting and multiplicity normalization, and establish positive definiteness, uniqueness, hard data consistency, and a finite-step conjugate-gradient error bound for the system. On fastMRI brain data with three contrasts and three sampling masks, HSSRecon achieves competitive peak signal-to-noise ratio, structural similarity, and normalized mean squared error across six aggregated conditions.
