并行磁共振成像的K空间高斯表示
K-space Gaussian Representation for Parallel MRI
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- Nanchang University（南昌大学）
- Chinese Academy of Sciences（中国科学院）
- Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences（中国科学院深圳先进技术研究院）
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中文总结 AI 辅助
针对并行MRI现有K空间重建方法未显式建模连续信号的局限，提出KGR方法，通过Gabor-高斯基元参数化连续信号并结合低秩流形约束，在多数据集上较基线实现重建性能提升。
中文摘要 AI 辅助
加速磁共振成像（MRI）旨在从采集的测量值中恢复K空间信号，准确估计缺失样本是高保真重建的关键。现有K空间重建方法通过离散采样网格上的插值算子或结构先验估计缺失样本，尽管这些方法能有效利用局部插值关系和全局K空间冗余，但仅重建离散频率系数，未显式建模底层连续信号。为克服此局限，我们提出K空间高斯表示（KGR），这是首个直接在原生K空间域构建的显式连续表示。KGR不估计离散网格上的未知样本，而是用具有共享空间几何的Gabor-高斯基元参数化连续信号，生成能自然保留线圈间相关性的紧凑表示。由于无约束连续拟合未必满足多线圈信号的固有结构特性，我们将估计的表示投影到低秩流形上，以施加由平滑变化相位和线圈冗余产生的代数约束。频率自适应拟合策略可适配不同K空间区域的异质性特征。在多个数据集和采样方案上的全面验证显示，与代表性重建基线相比，KGR在定量指标和视觉质量上均实现了一致提升。这些结果表明，原生K空间的显式连续参数化为将连续信号建模与结构化低秩重建相结合提供了原则性框架。
英文摘要
Accelerated magnetic resonance imaging (MRI) aims to recover the k-space signal from acquired measurements, where accurate estimation of missing samples is essential for high-fidelity reconstruction. Existing k-space reconstruction methods estimate missing samples through interpolation operators or structure priors defined on discrete sampling grids. Although these formulations effectively exploit local interpolation relationships and global k-space redundancy, they reconstruct only discrete frequency coefficients and therefore do not explicitly model the underlying continuous signal. To overcome this limitation, we propose K-space Gaussian Representation (KGR), the first explicit continuous representation formulated directly in the native k-space domain. Rather than estimating unknown samples on discrete grids, KGR parameterizes the continuous signal using Gabor-Gaussian primitives with shared spatial geometry, yielding a compact representation that naturally preserves inter-coil correlations. Because unconstrained continuous fitting does not necessarily satisfy the intrinsic structural properties of multi-coil signal, the estimated representation is projected onto a low-rank manifold to enforce the algebraic constraints arising from smoothly varying phase and coil redundancy. A frequency-adaptive fitting strategy accommodates the heterogeneous characteristics of different k-space regions. Comprehensive validation across multiple datasets and sampling schemes shows consistent improvements over representative reconstruction baselines in both quantitative metrics and visual quality. These results suggest that explicit continuous parameterization of native k-space provides a principled framework for integrating continuous signal modeling with structured low-rank reconstruction.
