Plug-and-Play Diffusion Meets ADMM: Dual-Variable Coupling for Robust Medical Image Reconstruction

TL;DR

This paper introduces a dual-variable coupling framework for diffusion-based medical image reconstruction, addressing bias and hallucination issues in existing plug-and-play methods, and demonstrates improved accuracy and convergence in CT and MRI tasks.

Contribution

It proposes Dual-Coupled PnP Diffusion with spectral homogenization to guarantee convergence and reduce hallucinations, advancing the robustness of inverse imaging problems.

Findings

Achieves state-of-the-art reconstruction fidelity.

Reduces hallucinations caused by residual artifacts.

Speeds up convergence in medical imaging tasks.

Abstract

Plug-and-Play diffusion prior (PnPDP) frameworks have emerged as a powerful paradigm for solving imaging inverse problems by treating pretrained generative models as modular priors. However, we identify a critical flaw in prevailing PnP solvers (e.g., based on HQS or Proximal Gradient): they function as memoryless operators, updating estimates solely based on instantaneous gradients. This lack of historical tracking inevitably leads to non-vanishing steady-state bias, where the reconstruction fails to strictly satisfy physical measurements under heavy corruption. To resolve this, we propose Dual-Coupled PnP Diffusion, which restores the classical dual variable to provide integral feedback, theoretically guaranteeing asymptotic convergence to the exact data manifold. However, this rigorous geometric coupling introduces a secondary challenge: the accumulated dual residuals exhibit spectrally colored, structured artifacts that violate the Additive White Gaussian Noise (AWGN) assumption of diffusion priors, causing severe hallucinations. To bridge this gap, we introduce Spectral Homogenization (SH), a frequency-domain adaptation mechanism that modulates these structured residuals into statistically compliant pseudo-AWGN inputs. This effectively aligns the solver's rigorous optimization trajectory with the denoiser's valid statistical manifold. Extensive experiments on CT and MRI reconstruction demonstrate that our approach resolves the bias-hallucination trade-off, achieving state-of-the-art fidelity with significantly accelerated convergence.