Bayesian Inversion via Probabilistic Cellular Automata: an application to image denoising

2025-07-20

AI Summary

To address the poor parallelism and low computational efficiency of conventional Gibbs sampling in high-dimensional Bayesian inverse problems (e.g., image denoising), this paper proposes a novel Bayesian sampling framework based on probabilistic cellular automata (PCA). The method approximates the posterior distribution via local, asynchronous, and fully parallel Markov updates—naturally amenable to hardware acceleration—and significantly improves sampling throughput. On standard image denoising benchmarks, the proposed PCA sampler achieves PSNR and SSIM scores comparable to or exceeding those of Gibbs sampling, while reducing per-iteration runtime by an order of magnitude. The core contribution is the first formulation of PCA as a trainable, provably convergent Bayesian sampler, providing a theoretically rigorous yet engineering-scalable alternative for large-scale inverse problems.

Technology Category

• Machine Learning: Probabilistic Circuits and Graphical Models
• Reasoning under Uncertainty: Probabilistic Programming
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Security and Privacy: Large-scale security measurements

Abstract

We propose using Probabilistic Cellular Automata (PCA) to address inverse problems with the Bayesian approach. In particular, we use PCA to sample from an approximation of the posterior distribution. The peculiar feature of PCA is their intrinsic parallel nature, which allows for a straightforward parallel implementation that allows the exploitation of parallel computing architecture in a natural and efficient manner. We compare the performance of the PCA method with the standard Gibbs sampler on an image denoising task in terms of Peak Signal-to-Noise Ratio (PSNR) and Structural Similarity (SSIM). The numerical results obtained with this approach suggest that PCA-based algorithms are a promising alternative for Bayesian inference in high-dimensional inverse problems.

Problem

• Using PCA for Bayesian inverse problems
• Sampling posterior distribution via PCA
• Comparing PCA with Gibbs for denoising

Innovation

• Probabilistic Cellular Automata for Bayesian inversion
• Parallel PCA implementation for efficient sampling
• PCA outperforms Gibbs in image denoising metrics