# Diffusion-Encoding Gaussian Field for Joint k-q dMRI Reconstruction

arXiv: https://arxiv.org/abs/2609.02288 · HTML: https://mlsanity.com/paper/2609.02288/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 32 references that are in the map.
- First posted on arXiv 2 Sep 2026.

## Builds on (most cited first, 15 of 15)

- [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)
- [4D Gaussian Splatting for Real-Time Dynamic Scene Rendering](https://mlsanity.com/paper/2310.08528/) (2023)
- [MoDL: Model Based Deep Learning Architecture for Inverse Problems](https://mlsanity.com/paper/1712.02862/) (2017)
- [NeRP: Implicit Neural Representation Learning with Prior Embedding for Sparsely Sampled Image Reconstruction](https://mlsanity.com/paper/2108.10991/) (2021)
- [R2-Gaussian: Rectifying Radiative Gaussian Splatting for Tomographic Reconstruction](https://mlsanity.com/paper/2405.20693/) (2024)
- [Spatio-Angular Convolutions for Super-resolution in Diffusion MRI](https://mlsanity.com/paper/2306.00854/) (2023)
- [Three-Dimensional MRI Reconstruction with Gaussian Representations: Tackling the Undersampling Problem](https://mlsanity.com/paper/2502.06510/) (2025)
- [Angular Super-Resolution in Diffusion MRI with a 3D Recurrent Convolutional Autoencoder](https://mlsanity.com/paper/2203.15598/) (2022)
- [Neural Spherical Harmonics for structurally coherent continuous representation of diffusion MRI signal](https://mlsanity.com/paper/2308.08210/) (2023)
- [4DRGS: 4D Radiative Gaussian Splatting for Efficient 3D Vessel Reconstruction from Sparse-View Dynamic DSA Images](https://mlsanity.com/paper/2412.12919/) (2024)
- [(k,q)-Compressed Sensing for dMRI with Joint Spatial-Angular Sparsity Prior](https://mlsanity.com/paper/1707.09958/) (2017)
- [Model-Based Deep Learning for Reconstruction of Joint k-q Under-sampled High Resolution Diffusion MRI](https://mlsanity.com/paper/2001.08307/) (2020)
- [Physics-Guided Diffusion Transformer with Spherical Harmonic Posterior Sampling for High-Fidelity Angular Super-Resolution in Diffusion MRI](https://mlsanity.com/paper/2509.07020/) (2025)
- [Self-Supervised Spatial And Zero-Shot Angular Super-Resolution by Spatial-Angular Implicit Representation For Rotating-View SNR-Efficient Diffusion MRI](https://mlsanity.com/paper/2605.02575/) (2026)

## Abstract (arXiv)

Diffusion MRI requires repeated k-space acquisitions over multiple diffusion-encoding directions, making acquisition time dependent on both spatial and angular sampling. Existing joint k-q methods either associate directional parameters with fixed voxels or separate spatial reconstruction from angular completion. However, diffusion-weighted images acquired under different directions share the same anatomical organization, while their local signal intensities vary with diffusion encoding. Existing formulations do not fully exploit the complementarity between shared anatomy and direction-dependent signal variation. Consequently, residual spatial errors may be misinterpreted as genuine angular variation and propagated to unobserved directions. We propose a subject-specific spatial-angular Gaussian field for self-supervised joint k-q dMRI reconstruction. Shared 3D Gaussian primitives provide local spatial support, with each primitive carrying a continuous q-conditioned tensor-residual response. The signal at each location is synthesized from multiple overlapping primitive responses, coupling neighboring spatial regions and diffusion directions. The field is progressively optimized from undersampled k-space measurements of observed directions, without fully sampled targets or held-out-direction supervision. Experiments on three HCP diffusion shells under multiple acceleration settings demonstrated consistent improvements in missing-direction DWI reconstruction, tensor-derived metrics, and principal diffusion orientation estimation.