arXiv:2608.00075cs.CV2026-08

提出k空间高斯表示,实现连续信号建模与多线圈相关性保留的并行MRI重建。

K-space Gaussian Representation for Parallel MRI

论文配图:K-space Gaussian Representation for Parallel MRI
图 1 · 摘自论文原文
  • 用共享空间几何的Gabor-Gaussian基函数显式建模连续k空间信号。
  • 在多数据集上相比基线方法提升重建质量,峰值信噪比平均提高1.2~2.3dB。
  • 适合需要高保真重建的医学影像研究者,尤其关注连续信号建模的新范式。

加速磁共振成像(MRI)旨在从采样测量中恢复k空间信号,准确估计缺失样本对高质量重建至关重要。现有k空间重建方法通过插值算子或离散采样网格上的结构先验来估计缺失样本,虽能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,无法显式建模潜在连续信号。为此,我们提出首个直接在原生k空间域构建的显式连续表示——K空间高斯表示(KGR)。KGR不基于离散网格估计未知样本,而是使用共享空间几何的Gabor-Gaussian基函数参数化连续信号,得到紧凑表示并自然保留多线圈相关性。由于无约束的连续拟合未必满足多线圈信号的内在结构性质,所估计表示被投影到低秩流形以强制满足平滑相位变化和线圈冗余的代数约束。采用频率自适应拟合策略,适应不同k空间区域的异质特性。在多个数据集和采样方案上的综合验证表明,该方法在定量指标和视觉质量上均一致优于代表性基线。结果表明,原生k空间的显式连续参数化为融合连续信号建模与结构化低秩重建提供了原则性框架。

原文摘要 · Abstract (English)

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.

MRI重建连续表示低秩模型k空间

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