通过概率细胞自动机进行贝叶斯反演：应用于图像去噪的应用
Bayesian Inversion via Probabilistic Cellular Automata: an application to image denoising
AI总结：
本文提出利用概率细胞自动机解决逆问题的贝叶斯方法，通过PSNR和SSIM指标比较了PCA与Gibbs采样在图像去噪中的性能，证明PCA在高维逆问题中具有潜力。
摘要：
我们提出利用概率细胞自动机（PCA）以贝叶斯方法解决逆问题。特别地，我们使用PCA从后验分布的近似值中进行采样。PCA的特殊之处在于其内在的并行性质，允许进行直接的并行实现，从而可以自然高效地利用并行计算架构。我们在图像去噪任务中从PSNR和SSIM指标上比较了PCA方法与标准Gibbs采样器的性能。数值结果和由此获得的大量加速效果表明，基于PCA的算法是高维逆问题中贝叶斯推断的一种有前途的替代方法。
英文摘要：
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.
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