  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.
