A Principled Diffusion Posterior Sampling for Inverse Problem with Mixed Poisson-Gaussian Noise

The diffusion posterior sampling has shown promising restoration performance for inverse problem. The existing works focus on the restoration with Gaussian noise. However, the Gaussian noise model is far away from the realistic pixel-dependent noise model. To diminish the discrepancy between the well-studied Gaussian noise and the practical noise model, we investigate the diffusion posterior sampling method for inverse problem with mixed Poisson-Gaussian (MPG) noise. Within the general diffusion posterior sampling iteration, the key component is to update the measurement-informed predicted image. To avoid the complicated expectation computation, the maximum-a-posteriori (MAP) approach to the image prediction is leveraged and additional manifold projection is considered to ensure manifold preserving. To the best of our knowledge, it is the first work to extend the diffusion posterior sampling to inverse problem with mixed Poisson-Gaussian noise. The proposed method outperforms the noise model-agnostic method significantly, producing more consistent restoration.