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

arXiv: https://arxiv.org/abs/2609.24468 · HTML: https://mlsanity.com/paper/2609.24468/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 36 references that are in the map.
- First posted on arXiv 21 Sep 2026.

## Builds on (most cited first, 16 of 16)

- [3D Gaussian Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2308.04079/) (2023)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [MoDL: Model Based Deep Learning Architecture for Inverse Problems](https://mlsanity.com/paper/1712.02862/) (2017)
- [Learning a Variational Network for Reconstruction of Accelerated MRI Data](https://mlsanity.com/paper/1704.00447/) (2017)
- [Deep Learning Methods for Parallel Magnetic Resonance Image Reconstruction](https://mlsanity.com/paper/1904.01112/) (2019)
- [Zero-Shot Self-Supervised Learning for MRI Reconstruction](https://mlsanity.com/paper/2102.07737/) (2021)
- [Low-Rank Tensor Function Representation for Multi-Dimensional Data Recovery](https://mlsanity.com/paper/2212.00262/) (2022)
- [IMJENSE: Scan-specific Implicit Representation for Joint Coil Sensitivity and Image Estimation in Parallel MRI](https://mlsanity.com/paper/2311.12892/) (2023)
- [Joint multi-contrast Variational Network reconstruction (jVN) with application to rapid 2D and 3D imaging](https://mlsanity.com/paper/1910.03273/) (2019)
- [Three-Dimensional MRI Reconstruction with Gaussian Representations: Tackling the Undersampling Problem](https://mlsanity.com/paper/2502.06510/) (2025)
- [Zero-DeepSub: Zero-Shot Deep Subspace Reconstruction for Rapid Multiparametric Quantitative MRI Using 3D-QALAS](https://mlsanity.com/paper/2307.01410/) (2023)
- [A Tutorial on MRI Reconstruction: From Modern Methods to Clinical Implications](https://mlsanity.com/paper/2507.16715/) (2025)
- [Fast and Explicit: Slice-to-Volume Reconstruction via 3D Gaussian Primitives with Analytic Point Spread Function Modeling](https://mlsanity.com/paper/2512.11624/) (2025)
- [mcLARO: Multi-Contrast Learned Acquisition and Reconstruction Optimization for simultaneous quantitative multi-parametric mapping](https://mlsanity.com/paper/2304.03458/) (2023)
- [INR meets Multi-Contrast MRI Reconstruction](https://mlsanity.com/paper/2509.04888/) (2025)
- [Spatiotemporal Gaussian representation-based dynamic reconstruction and motion estimation framework for time-resolved volumetric MR imaging (DREME-GSMR)](https://mlsanity.com/paper/2604.06482/) (2026)

## Abstract (arXiv)

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.