Xiaoqun Zhang (Shanghai Jiao Tong University, Chine)

Titre : Accelerated Diffusion Posterior Sampling Models for Linear and Nonlinear Inverse Problems

Résumé : Diffusion models have emerged as powerful generative tools for solving inverse problems, particularly due to their ability to produce high-quality reconstructions from noisy and incomplete data. In medical imaging, inverse problems like CT reconstruction and travel-time tomography benefit from diffusion models' capability to conditionally sample based on observed data, promising advancements in both image quality and computational efficiency. This talk introduces accelerated diffusion posterior sampling methods tailored to improve both speed and accuracy in these settings, with specific focus on reducing radiation risks in CT and handling nonlinear complexities in PDE-based tomography.  For CT, we propose a fast-sampling method that incorporates data consistency through an optimization step, initialized with a pretrained diffusion model conditioned on measurement data. This approach includes an iterative adaptation to noisy timesteps and a strategy to start sampling from the filtered back-projection (FBP) image midway, significantly reducing computational steps. For nonlinear PDE-based problems like travel-time tomography, we implement a plug-and-play posterior sampling process using the adjoint-state equation, along with a subspace-based dimension reduction to refine across grids efficiently. Experimental results show significant improvements, with a 20x speedup in CT reconstructions compared to original diffusion posterior sampling method and enhanced imaging quality in travel-time tomography, demonstrating the practical utility of diffusion models in clinical and other high-stakes applications.