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

TL;DR

Spectral Homogenization (SH), a frequency-domain adaptation mechanism that modulates these structured residuals into statistically compliant pseudo-AWGN inputs, effectively aligns the solver's rigorous optimization trajectory with the denoiser's valid statistical manifold, achieving state-of-the-art fidelity with significantly accelerated convergence.

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.

Figures (10)

• Figure 1: Qualitative comparisons on two CT reconstruction tasks. Visualization windows are set to $[-800, 800]$ HU for LACT and $[-175, 500]$ HU for SVCT, respectively.
• Figure 2: Qualitative comparisons of accelerated MRI (AF = 10) on knee proton density (PD) and proton density fat-suppressed (PD-FS) scans. Red arrows highlight major improvements and remaining aliasing artifacts.
• Figure 3: Mechanism Verification: Why Spectral Homogenization Matters. We analyze the spectral characteristics (Top) and the corresponding denoising outputs (Bottom) at iteration $k=6$. (a) Ideal Reference (Green): The on-manifold input ($x_{gt}+\sigma_t n$). (b) Ours (Orange): Our SH module aligns the spectrum perfectly, yielding clean results. (c) Naive Injection (Red): Adding noise ($x+u+\sigma_t n$) creates an over-energized spectrum, leading to over-smoothing. (d) No Injection (Blue): The raw dual input ($x+u$) causes OOD hallucinations.
• Figure 4: Convergence Efficiency Analysis. We compare the PSNR progression of DC-PnPDP (Red) vs. DiffPIR (Blue) over increasing NFE. Remarkably, DC-PnPDP achieves comparable or superior performance at just 30 steps than DiffPIR at 100 steps, demonstrating a $\sim 3.3\times$ acceleration in inference efficiency.
• Figure 5: Qualitative comparisons on LACT of [0, 90]$^\circ$ reconstruction tasks. Visualization windows are set to $[-800, 800]$ HU.

Theorems & Definitions (8)

• Proposition 3.1: Second-Order Spectral Consistency
• Remark 3.2
• Theorem 3.1: Optimality of Dual-Coupled Fixed Points
• proof
• Theorem 4.2
• proof
• Theorem 4.3
• proof