SGAM: Shared Gaussian Geometry with Implicit Amplitude Modeling for Scan-Specific 3D Multi-Contrast MRI Reconstruction

Three-dimensional (3D) multi-contrast magnetic resonance imaging (MCMRI) provides rich anatomical and quantitative information but requires long acquisition times, motivating k-space undersampling. However, reconstruction of large volumetric datasets imposes substantial computational and memory demands. To address this challenge, we propose SGAM, a memory-efficient, scan-specific framework for joint full-volume 3D MCMRI reconstruction. SGAM is based on a shared-geometry Gaussian representation in which amplitudes are modeled by a multi-output implicit neural representation (INR) and contrast-specific phases by explicit variables. This design exploits common anatomical structure across contrasts while preserving contrast-specific signal variations. The representation is jointly optimized using only the acquired multi-coil k-space without external training data. Experiments showed that SGAM consistently outperformed the comparison methods across imaging tasks and acceleration factors, with greater improvements under stronger undersampling. SGAM also achieved a favorable balance between reconstruction quality and computational cost, demonstrating its effectiveness for 3D multi-contrast MRI reconstruction.