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 and the large speedups obtained with this approach suggest that PCA-based algorithms are a promising alternative for Bayesian inference in high-dimensional inverse problems.

翻译：本文提出使用概率元胞自动机（Probabilistic Cellular Automata, PCA）以贝叶斯方法解决反问题。具体而言，我们利用PCA从后验分布的近似分布中采样。PCA的独特之处在于其内在的并行性，这使得自然高效的并行计算架构得以直接实现。我们在图像去噪任务上，以峰值信噪比（PSNR）和结构相似性（SSIM）为指标，比较了PCA方法与标准吉布斯采样器的性能。数值结果及该方法获得的大幅加速表明，基于PCA的算法是高维反问题中贝叶斯推断的一种有前景的替代方案。