Consecutive Posterior Fusion for Diffusive Recovery of Unobservable Image Structures

2026-10-02

AI Summary

This study addresses the challenge of recovering unobservable structures in severely ill-posed imaging inverse problems by proposing CPF-DDNM, a novel inference strategy built upon diffusion models and the DDNM framework. Through range-null space decomposition and time-dependent fusion coefficient analysis, the method integrates continuous measurement-aware estimation into the diffusion process. A key innovation lies in its ability to substantially enhance null-space estimation accuracy via geometric interpretation and extrapolation mechanisms, without requiring retraining or auxiliary denoising networks. Experimental results demonstrate that CPF-DDNM significantly outperforms existing baselines across sparse-view CT, low-dose CT, and medical super-resolution tasks, establishing strong competitiveness for solving challenging inverse problems in medical imaging.

Abstract

Solving severely ill-posed imaging inverse problems requires recovering image structures that are unobservable or weakly constrained by the measurements. Diffusion models provide expressive learned priors for inferring such missing information, while posterior sampling incorporates measurement consistency along the reverse process. Standard diffusion posterior samplers, however, rely on instantaneous measurement-aware estimates, without explicitly exploiting information carried by previous posterior corrections. We introduce Consecutive Posterior Fusion Denoising Diffusion Null-Space Models (CPF-DDNM), an inference-time strategy that fuses consecutive measurement-aware estimates to improve the diffusive recovery of unobservable image structures, without requiring retraining or additional denoiser evaluations. We instantiate this principle within DDNM, whose range/null-space decomposition reveals that consecutive fusion preserves the measurement-determined component while acting exclusively on the prior-driven null-space estimate. We thus provide a geometric interpretation of CPF-DDNM and a local error analysis that characterizes the optimal time-dependent fusion coefficient, including the extrapolative regime. Experiments on sparse-view and simulated low-dose computed tomography, as well as medical image super-resolution, show consistent improvements over DDNM and competitive performance against diffusion-based inverse solvers.

Problem

• ill-posed inverse problems
• diffusion models
• posterior sampling
• unobservable image structures
• computed tomography

Innovation

• Consecutive Posterior Fusion
• Diffusion Models
• Inverse Problems
• Null-Space Decomposition
• DDNM