Highly Accelerated MRI via Implicit Neural Representation Guided Posterior Sampling of Diffusion Models

TL;DR

This work addresses the ill-posed problem of reconstructing high-fidelity MR images from under-sampled k-space data by marrying a pre-trained diffusion prior with an implicit neural representation (INR) to enforce data consistency during posterior sampling. The authors introduce DiffINR, a two-stage INR-guided posterior sampler that first embeds a diffusion-informed prior via an INR and then refines it using the MRI forward model, employing Tweedie denoising and a DC refinement step. Key contributions include a training-free INR module compatible with any diffusion model, a two-stage learning strategy (Stage 1: Prior Embedding; Stage 2: Data Consistency Refinement), and demonstrated superiority over multiple baselines on fastMRI knee data, including highly accelerated and multi-channel scenarios. The approach yields accurate, stable reconstructions with robustness to sampling patterns and acceleration factors, offering a generalizable framework for inverse problems in medical imaging.

Abstract

Reconstructing high-fidelity magnetic resonance (MR) images from under-sampled k-space is a commonly used strategy to reduce scan time. The posterior sampling of diffusion models based on the real measurement data holds significant promise of improved reconstruction accuracy. However, traditional posterior sampling methods often lack effective data consistency guidance, leading to inaccurate and unstable reconstructions. Implicit neural representation (INR) has emerged as a powerful paradigm for solving inverse problems by modeling a signal's attributes as a continuous function of spatial coordinates. In this study, we present a novel posterior sampler for diffusion models using INR, named DiffINR. The INR-based component incorporates both the diffusion prior distribution and the MRI physical model to ensure high data fidelity. DiffINR demonstrates superior performance on experimental datasets with remarkable accuracy, even under high acceleration factors (up to R=12 in single-channel reconstruction). Notably, our proposed framework can be a generalizable framework to solve inverse problems in other medical imaging tasks.

Figures (3)

• Figure 1: Overview of the proposed DiffINR framework. (a) The reverse sampling process of DiffINR with iterative INR-based modules. The total number of reverse sampling steps is $T$. $t^*$ indicates the INR start timestep and $k$ denotes the INR interval. (b) INR-based posterior sampling for temporal diffusion prior. This process is divided into two stages: In Stage 1, the diffusion prior image is embedded into the INR as an initial weight for following Stage 2. In Stage 2, the INR combines the physical model with the acquired data, guaranteeing data fidelity.
• Figure 2: Comparisons of different methods on the single-channel knee dataset. (a) and (b) are reconstruction results of Random 1D sampling with R=8 (ACS=12) and R=12 (ACS=12), respectively. (c) are the results of 1/2 Partial Fourier under-sampling. (d) Gaussian 2D results at R=15. Red arrows point to the artifacts on the magnitude images reconstructed by Score-MRI and DPS. SSIM and PSNR are reported and the best results are in bold and yellow. The ×5 error maps are displayed.
• Figure 3: Comparsion results of different methods on the multi-channel dataset with different acceleration factors and sampling masks. (a) is the reconstruction result under Gaussian 1D sampling masks with R=8 (ACS=12). (b) is the result of Poisson 2D with R=18. Quantitative evaluation metrics (SSIM and PSNR) are reported and the best results are emphasized in bold and yellow. The ×10 error maps are displayed.