In signal processing, the data collected from sensing devices is often a noisy linear superposition of multiple components, and the estimation of components of interest constitutes a crucial pre-processing step. In this work, we develop a Bayesian framework for signal component decomposition, which combines Gibbs sampling with plug-and-play (PnP) diffusion priors to draw component samples from the posterior distribution. Unlike many existing methods, our framework supports incorporating model-driven and data-driven prior knowledge into the diffusion prior in a unified manner. Moreover, the proposed posterior sampler allows component priors to be learned separately and flexibly combined without retraining. Under suitable assumptions, the proposed DiG sampler provably produces samples from the posterior distribution. We also show that DiG can be interpreted as an extension of a class of recently proposed diffusion-based samplers, and that, for suitable classes of sensing operators, DiG better exploits the structure of the measurement model. Numerical experiments demonstrate the superior performance of our method over existing approaches.

翻译：在信号处理中，从传感设备采集的数据通常是多个分量的含噪线性叠加，而感兴趣分量的估计构成了关键的预处理步骤。本文提出了一种用于信号分量分解的贝叶斯框架，该框架将吉布斯采样与即插即用（PnP）扩散先验相结合，以从后验分布中抽取分量样本。与许多现有方法不同，本框架支持以统一的方式将模型驱动和数据驱动的先验知识融入扩散先验中。此外，所提出的后验采样器允许分量先验被单独学习，并灵活组合而无需重新训练。在适当的假设下，所提出的DiG采样器可证明能够从后验分布中生成样本。我们还表明，DiG可被解释为一类近期提出的基于扩散的采样器的扩展，并且对于特定类型的传感算子，DiG能更好地利用测量模型的结构。数值实验证明了本方法相较于现有方法的优越性能。