K-space Gaussian Representation for Parallel MRI

2026-07-29

AI Summary

Existing parallel MRI reconstruction methods are confined to discrete k-space grids and struggle to explicitly model continuous signals, limiting reconstruction accuracy. This work proposes k-space Gaussian Representation (KGR), the first approach to establish an explicit continuous signal model directly in the native k-space domain. KGR parameterizes the continuous spectrum using Gabor-Gaussian primitives that share spatial geometry, integrating low-rank manifold projection, frequency-adaptive fitting, and multi-coil phase smoothness constraints. By design, the method inherently preserves inter-coil correlations. Extensive experiments across multiple datasets and sampling patterns demonstrate that KGR consistently achieves superior quantitative metrics and visual quality compared to current baselines, validating the efficacy of combining continuous modeling with structured priors.

Abstract

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.

Problem

• k-space
• continuous signal modeling
• parallel MRI
• accelerated MRI
• reconstruction

Innovation

• K-space Gaussian Representation
• continuous signal modeling
• parallel MRI
• low-rank manifold
• Gabor-Gaussian primitives