Plug-and-Play Posterior Sampling under Mismatched Measurement and Prior Models - Archive ouverte HAL
Communication Dans Un Congrès Année : 2024

Plug-and-Play Posterior Sampling under Mismatched Measurement and Prior Models

Résumé

Posterior sampling has been shown to be a powerful Bayesian approach for solving imaging inverse problems. The recent plug-and-play unadjusted Langevin algorithm (PnP-ULA) has emerged as a promising method for Monte Carlo sampling and minimum mean squared error (MMSE) estimation by combining physical measurement models with deep-learning priors specified using image denoisers. However, the intricate relationship between the sampling distribution of PnP-ULA and the mismatched data-fidelity and denoiser has not been theoretically analyzed. We address this gap by proposing a posterior-L2 pseudometric and using it to quantify an explicit error bound for PnP-ULA under mismatched posterior distribution. We numerically validate our theory on several inverse problems such as sampling from Gaussian mixture models and image deblurring. Our results suggest that the sensitivity of the sampling distribution of PnP-ULA to a mismatch in the measurement model and the denoiser can be precisely characterized.

Dates et versions

hal-04307874 , version 1 (26-11-2023)

Identifiants

Citer

Marien Renaud, Jiaming Liu, Valentin de Bortoli, Andrés Almansa, Ulugbek Kamilov. Plug-and-Play Posterior Sampling under Mismatched Measurement and Prior Models. (ICLR 2024) The Twelfth International Conference on Learning Representations, May 2024, Wien, Austria. ⟨hal-04307874⟩
34 Consultations
0 Téléchargements

Altmetric

Partager

More