Score-Based Turbo Message Passing for Plug-and-Play Compressive Image Recovery

2025-03-28

AI Summary

Conventional message-passing methods for underdetermined compressive imaging recovery rely on handcrafted priors and fail to capture the true distribution of natural images. Method: This paper proposes a Bayesian framework integrating score-based generative models with Turbo message passing. Its core innovation is the deep embedding of a score-based MMSE denoiser into the message-passing iterations, enabling empirical Bayes-optimal denoising. Theoretical analysis leverages state evolution to rigorously characterize asymptotic performance and guarantee convergence. Results: On the FFHQ dataset, the method significantly outperforms traditional message passing, regularized linear regression, and score-based posterior sampling. It achieves convergence in fewer than 20 neural function evaluations, offering both computational efficiency and interpretability grounded in principled Bayesian inference.

Technology Category

• Machine Learning: Deep Generative Models & Autoencoders
• Computer Vision: Diffusion Models for Vision
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

Message passing algorithms have been tailored for compressive imaging applications by plugging in different types of off-the-shelf image denoisers. These off-the-shelf denoisers mostly rely on some generic or hand-crafted priors for denoising. Due to their insufficient accuracy in capturing the true image prior, these methods often fail to produce satisfactory results, especially in largely underdetermined scenarios. On the other hand, score-based generative modeling offers a promising way to accurately characterize the sophisticated image distribution. In this paper, by exploiting the close relation between score-based modeling and empirical Bayes-optimal denoising, we devise a message passing framework that integrates a score-based minimum mean squared error (MMSE) denoiser for compressive image recovery. This framework is firmly rooted in Bayesian formalism, in which state evolution (SE) equations accurately predict its asymptotic performance. Experiments on the FFHQ dataset demonstrate that our method strikes a significantly better performance-complexity tradeoff than conventional message passing, regularized linear regression, and score-based posterior sampling baselines. Remarkably, our method typically requires less than 20 neural function evaluations (NFEs) to converge.

Problem

• Improving compressive image recovery using score-based denoising
• Addressing insufficient accuracy in existing plug-and-play denoisers
• Enhancing performance-complexity tradeoff in message passing algorithms

Innovation

• Score-based MMSE denoiser for image recovery
• Bayesian framework with state evolution
• Less than 20 NFEs for convergence